https://maths-angel.com/lessons/distributive-property https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/distributive-property/distributive-property-math-angel.webp Distributive law illustrated with coloured balls showing 3 times (4 + 2) equals 3 times 4 + 3 times 2 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/distributive-property/distributive-property-welcome-visual.webp Distributive Property - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/distributive-property/1)%20The%20Distributive%20Law.webp The Distributive Law for addition and subtraction, illustrated with an example showing 3×(4+2) as 3×4 + 3×2, using green and yellow balls. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/distributive-property/2)%20Applying%20the%20Distributive%20Law.webp Applying the distributive law to expand and factorise brackets, with examples for 15 x (100 + 2) and 50 x (24 - 14) equations. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/distributive-property/3)%20Distributive%20Law%20for%20Multiple%20Numbers.webp The distributive law for multiplying numbers, such as 5*221, by factorising to 5*(200+20+1) and expanding to 5*200+5*20+5*1. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/distributive-property/4)%20Remarks%20on%20the%20Distributive%20Law.webp Explanation that the distributive law generally does not simplify division, showing the example (19+2)/3. https://maths-angel.com/lessons/perpendicular-and-parallel-lines https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-and-parallel-lines/perpendicular-and-parallel-lines-math-angel.webp Lesson preview showing perpendicular and parallel lines. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-and-parallel-lines/perpendicular-and-parallel-lines-welcome-visual.webp Perpendicular and Parallel Lines - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-and-parallel-lines/1)%20Segments%2C%20Rays%2C%20Lines.webp Definition, notation, and visualisation of line segments, rays, and lines. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-and-parallel-lines/2)%20Perpendicular%20vs%20Parallel%20Lines.webp Characteristics, notation, and visualisation of perpendicular and parallel lines. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-and-parallel-lines/3)%20Measuring%20Distances.webp Measuring distances between points and lines, showing examples of point to point, point to line, and between parallel lines. https://maths-angel.com/lessons/number-line-inequality-symbols https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/number-line-inequality-symbols/number-line-and-comparing-numbers-math-angel.webp Number line from −5 to 5 showing negative numbers, the origin, and positive numbers at equal intervals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/number-line-inequality-symbols/number-line-and-comparing-numbers-welcome-visual.webp Number Line and Comparing Numbers - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/number-line-inequality-symbols/1)%20Number%20Line.webp Number line showing positive and negative numbers, with labels for origin, equal intervals, and tips on comparing numbers using the number line. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/number-line-inequality-symbols/2)%20Inequality%20Symbol.webp Inequality symbols explained with examples using the greater than, less than, greater than or equal to, and less than or equal to signs. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/number-line-inequality-symbols/3)%20Comparing%20Numbers.webp Two rules for comparing numbers: First, more digits mean greater value. Second, if the number of digits is equal, compare from left to right. https://maths-angel.com/lessons/tally-marks-bar-chart https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/tally-marks-bar-chart/tally-mark-charts-bar-charts-tables-math-angel.webp Tally marks, bar charts, and tables lesson thumbnail with colourful data display examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/tally-marks-bar-chart/tally-mark-welcome-visual.webp Tally Marks, Bar Charts, Tables - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/tally-marks-bar-chart/1)%20Tally%20Mark%20Chart.webp Tally mark chart comparing counts for white, blue, and yellow categories with totals displayed at the bottom. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/tally-marks-bar-chart/2)%20Bar%20Charts.webp Bar chart comparing the number of white, blue, and yellow cars respectively, illustrating the height of each bar representing the number of cars. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/tally-marks-bar-chart/3)%20Tables.webp Table summarising the number of cars by colour: 12 white, 19 blue, and 8 yellow. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/tally-marks-bar-chart/4)%20Tally%20Marks%2C%20tables%2C%20and%20Bar%20Charts.webp Comparison of tally mark chart, bar chart, and table for counting and presenting data on car colours (white, blue, yellow) with respective counts. https://maths-angel.com/lessons/ratios https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/ratios/introduction-to-ratios-math-angel.webp Introduction to ratios lesson thumbnail with examples of ratio notation https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/ratios/introduction-to-ratios-welcome-visual.webp Introduction to Ratios - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/ratios/1)%20Ratios%20Definition%20and%20Examples.webp Illustration for ratios with 2 apples and 3 bananas as an example. The ratio of apples to bananas is 2:3, and the ratio of bananas to apples is 3:2. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/ratios/2)%20Calculating%20with%20Ratios%20(Finding%20Parts).webp Ratio calculation showing flour to sugar ratio of 5:2 with a worked example of 300 g of flour, determining that 120 g of sugar is needed. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/ratios/3)%20Calculating%20with%20Ratios%20(Dividing%20a%20Whole).webp An example of sharing £200 in the ratio 7:3, total parts calculated as 10, each part worth £20. One person receives £140, the other receives £60. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/ratios/4)%20Simplifying%20and%20Expanding%20Ratios.webp Simplifying the ratio 24:40 by dividing both terms to get 3:5 and expanding the ratio 3:7 by multiplying both terms to get 15:35. https://maths-angel.com/lessons/expressions-with-one-variable https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expressions-with-one-variable/deriving-and-evaluating-expressions-with-one-variable-math-angel.webp Worked examples of deriving and evaluating the one-variable expression 20 + 5x for different x values https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expressions-with-one-variable/deriving-and-evaluating-expressions-with-one-variable-welcome-visual.webp Deriving and Evaluating Expressions with One Variable - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expressions-with-one-variable/1)%20Expression%20with%20One%20Variable.webp Savings (£)=20+5x with x months; examples for x=1,2,3: 20+(5×1), 20+(5×2), 20+(5×3) https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expressions-with-one-variable/2)%20Evaluate%20Expression%20with%20One%20Variable.webp Savings (£)=20+5x evaluated for x=8,12,20: £60=20+(5×8), £80=20+(5×12), £120=20+(5×20) https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expressions-with-one-variable/3)%20How%20to%20Form%20An%20Expression.webp Balance (£)=50−3y for y packs; examples y=1,2,3: £47=50−(3×1), £44=50−(3×2), £41=50−(3×3) https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expressions-with-one-variable/4)%20How%20to%20Evaluate%20An%20Expression.webp Deriving and evaluating one-variable expression Balance(£)=50−3y, with y=10 giving £20 and y=15 giving £5 for £3 per pack. https://maths-angel.com/lessons/measurement-and-types-of-angles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/measurement-and-types-of-angles-math-angel.webp Types of angles lesson preview showing acute, right, obtuse, straight, reflex, and full angles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/measurement-and-types-of-angles-welcome-visual.webp Measurement and Types of Angles - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/1)%20What%20is%20an%20angle.webp Definition of an angle: an angle is formed when two lines meet at a point (the vertex), opens anticlockwise, and is measured in degrees. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/2)%20Categorising%20Angles.webp Illustration of acute, right, obtuse, straight, reflex, and full angles, with corresponding angle measures. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/3)%20Measuring%20Angles.webp Steps for measuring angles using a protractor, with instructions and an illustration of a protractor aligned to measure an angle of 130 degrees. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/4)%20Measuring%20Angles%20over%20180%20degrees.webp Protractor measuring a reflex angle with calculation showing 360 degrees minus 140 degrees equals 220 degrees. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/5)%20Drawing%20Angles.webp Steps for drawing a 40-degree angle using a protractor. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/6)%20Drawing%20Angles%20over%20180%20degrees.webp Drawing a 210-degree reflex angle using a protractor with a pencil, and a diagram showing the sum of 210 and 150 degrees equals 360 degrees. https://maths-angel.com/lessons/place-value-chart-rounding https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/place-value-and-rounding-numbers-math-angel.webp Place value chart and rounding rules for whole numbers with worked examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/place-value-and-rounding-numbers-welcome-visual.webp Place Value and Rounding Numbers - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/1)%20Place%20Value%20Chart.webp Place value chart demonstrating the number 54321 with a breakdown of digits in ten thousands, thousands, hundreds, tens, and ones columns. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/2)%20Base-10%20Number%20System.webp Place value chart for the Base 10 number system, also called decimal system, with columns for trillions, billions, millions, thousands, H, T, and O. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/3)%20Rounding%20Rules%20and%20Steps.webp Place value chart showing how to round 5,024,579 to the nearest thousand using digit rules 0-4 down and 5-9 up. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/4)%20Rounding%20down.webp Place value chart showing how to round down the number 50,245,798 to 50 million by replacing all digits after the thousand place with zeros. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/5)%20Rounding%20up.webp Place value chart showing how to round up the number 50,245,798 to 50,246,000. https://maths-angel.com/lessons/absolute-relative-frequency https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/absolute-relative-frequency/absolute-and-relative-frequency-math-angel.webp Absolute and relative frequency lesson thumbnail with a data table and percentage values https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/absolute-relative-frequency/absolute-and-relative-frequency-welcome-visual.webp Absolute Frequency and Relative Frequency - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/absolute-relative-frequency/1)%20Absolute%20Frequency.webp Table showing absolute frequencies of how Class A students get to school: 5 walk, 12 take the bus, 3 go by car, 5 cycle. Total count is 25. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/absolute-relative-frequency/2)%20Relative%20Frequency.webp Table comparing absolute frequency, relative frequency, and relative frequency percentages for modes of transport. Total sum equals 1 or 100%. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/absolute-relative-frequency/3)%20Absolute%20and%20Relative%20Frequency%20Relationship.webp Table showing how 40 students in Class B get to school, with absolute and relative frequencies for four modes. https://maths-angel.com/lessons/how-to-combine-ratios https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/how-to-combine-ratios/how-to-combine-ratios-math-angel.webp How to combine ratios lesson thumbnail showing two-part ratios merging into a three-part ratio https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/how-to-combine-ratios/how-to-combine-ratios-welcome-visual.webp How to Combine Ratios - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/how-to-combine-ratios/1)%20How%20to%20Combine%20Ratios%20With%20Same%20Common%20Factor.webp Ratio combination showing a to b = 2 to 5 and b to c = 5 to 3, with final combined ratio a to b to c = 2 to 5 to 3. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/how-to-combine-ratios/2)%20How%20to%20Combine%20Ratios%20Using%20LCM%20of%20Common%20Factor.webp How to combine ratios when the middle term is different, a : b = 3 : 5 and b : c = 2 : 7, with final combined ratio a : b : c = 6 : 10 : 35 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/how-to-combine-ratios/3)%20Combining%20Ratios%20Applications%20Question%201.webp Combined ratios calculation of water to cement (4:3) and cement to sand (2:5) to get final ratio 8:6:15. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/how-to-combine-ratios/4)%20Combining%20Ratios%20Applications%20Question%202.webp Example of combined ratios to find sand needed when water to cement is 4:3 and cement to sand is 2:5, with 24 buckets of water. https://maths-angel.com/lessons/simplifying-expressions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions/simplifying-expressions-math-angel.webp Simplifying expressions lesson showing how to expand brackets and collect like terms step by step https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions/simplifying-expressions-welcome-visual.webp Simplifying Expressions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions/1)%20How%20to%20Simplify%20Expressions.webp Steps to simplify an expression by expanding brackets and collecting like terms, showing -5x + 2(3 + x) simplified to -3x + 6. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions/2)%20Simplify%20Expressions%20Example.webp Simplifying expressions by expanding brackets using distributive law, and combining like terms to simplify 3(2x - 1) + 4(-x + 5) into 2x + 17. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions/3)%20Simplify%20Expressions%20Practice.webp Simplifying expressions by expanding brackets using distributive law, and combining like terms to simplify 3(2x - 1) + 4(-x + 5) into 2x + 17. https://maths-angel.com/lessons/angle-relationships https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-relationships/angle-relationships-in-intersecting-and-parallel-lines-math-angel.webp Angle relationships in parallel lines showing corresponding, alternate, and co-interior angles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-relationships/angle-relationships-in-intersecting-and-parallel-lines-welcome-visual.webp Angle Relationships in Intersecting and Parallel Lines - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-relationships/1)%20Vertically%20Opposite%20and%20Adjacent%20Angles.webp Illustrating that vertically opposite angles are equal, and adjacent angles sum to 180° for two intersecting lines. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-relationships/2)%20Corresponding%2C%20Alternate%2C%20Co-Interior%20Angles.webp Diagram showing corresponding angles, alternate angles, and co-interior angles formed by two parallel lines and a transversal. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-relationships/3)%20Finding%20the%20Missing%20Angles.webp Calculations of vertically opposite, supplementary, alternate, and corresponding angles with given values of 40° and 140°. https://maths-angel.com/lessons/natural-numbers-whole-numbers-integers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/natural-numbers-whole-numbers-and-integers-math-angel.webp Defintion of Natural numbers, whole numbers, and integers. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/natural-numbers-whole-numbers-and-integers-welcome-visual.webp Natural Numbers, Whole Numbers, and Integers - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/1)%20Types%20of%20Numbers.webp Integers, whole numbers, and natural numbers with examples, notes that natural numbers are whole numbers and whole numbers are integers. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/2)%20Definition%20of%20Natural%20Numbers.webp Natural numbers 1-5 shown by counting bees, with note that natural numbers exclude zero, negatives, fractions, and decimals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/3)%20Natural%20Numbers%20Practice.webp Practice questions showing zero, −5, 1/3, and 2.5 are not natural numbers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/4)%20Definition%20of%20Whole%20Numbers.webp Whole numbers include natural numbers and zero, shown as 0, 1, 2, 3, 4, … with note that a whole-number answer can be 0 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/5)%20Whole%20Numbers%20Practice.webp Identifying whole numbers: 0, 17, and 31 are whole numbers but −3, −8, −1.5, 0.3, and ⅖ are not https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/6)%20Definition%20of%20Integers.webp Integers shown on a keypad as 2, 1, 0, −1, −2, −3, highlighting that integers include whole numbers, their negatives, and zero https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/7)%20Integers%20Practice.webp Classifying 5, 0, and −7 as natural numbers, whole numbers, or integers: 5 is all three, 0 is whole and integer, −7 is integer only https://maths-angel.com/lessons/pie-chart https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/pie-chart/pie-chart-math-angel.webp Pie chart lesson thumbnail showing a colourful circle divided into percentage slices https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/pie-chart/pie-chart-welcome-visual.webp Pie Chart - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/pie-chart/1)%20Pie%20Chart.webp A pie chart divided into four sections, labelled 40%, 25%, 20%, and 15%, representing different category contributions. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/pie-chart/2)%20How%20to%20Draw%20a%20Pie%20Chart.webp Pie chart of favourite sports of 100 students, football (40%), basketball (25%), swimming (20%), and tennis (15%). Central angle formula is displayed. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/pie-chart/3)%20How%20to%20Read%20a%20Pie%20Chart.webp A visual guide on how to read a pie chart, with a formula for calculating category counts. https://maths-angel.com/lessons/fractions-and-percentages https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/fractions-and-percentages/fractions-and-percentages-math-angel.webp Fractions and percentages: 70% written as 70/100 and simplified to 7/10, showing percent means out of 100 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/fractions-and-percentages/fractions-and-percentages-welcome-visual.webp Fractions and Percentages - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/fractions-and-percentages/1)%20Percentages.webp Introduction to percentages with steps for converting percentages to fractions and real-life examples of percentage use. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/fractions-and-percentages/2)%20Converting%20Fractions%20to%20Percentages.webp Converting fractions to percentages using expanding and simplifying fractions methods. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/fractions-and-percentages/3)%20Percentages%20Example.webp Calculating percentages using footballs and basketballs as examples, showing 40% of 20 balls are footballs and 60% are basketballs. https://maths-angel.com/lessons/simplifying-expressions-multiple-variables https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions-multiple-variables/simplifying-expressions-with-multiple-variables-math-angel.webp Simplifying algebraic expressions with multiple variables using exponents and collecting like terms https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions-multiple-variables/simplifying-expressions-with-multiple-variables-welcome-visual.webp Simplifying Expressions with Multiple Variables - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions-multiple-variables/1)%20Expression%20with%20Multiple%20Variables.webp Expressions with multiple variables include more than one variable, shown by the expression a + 2b + 3c squared. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions-multiple-variables/2)%20Exponents%20to%20Simplify%20Expressions.webp Simplification techniques for exponents showing multiplication rules with variables x and y, and explanation of the commutative law. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions-multiple-variables/3)%20Collecting%20Like%20Terms%20to%20Simplify%20Expressions.webp Simplification techniques showing how to collect like terms by adding coefficients and identifying like terms with the same variables and exponents. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions-multiple-variables/4)%20Simplifying%20Expressions%20with%20Multiple%20Variables%20Example.webp Simplifying algebraic expression involving multiple variables using distributive law, exponents, and collecting like terms. https://maths-angel.com/lessons/polygons-quadrilaterals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/polygons-quadrilaterals/polygons-and-types-of-quadrilaterals-math-angel.webp Polygons and quadrilaterals lesson preview showing different shapes with their names and properties https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/polygons-quadrilaterals/polygons-and-types-of-quadrilaterals-welcome-visual.webp Polygons and Types of Quadrilaterals - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/polygons-quadrilaterals/1)%20Polygons%20vs%20non-polygons.webp Illustrating polygons as 2D closed shapes with straight line segments, showing a triangle and star, and non-polygons like curved shape and 3D cube. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/polygons-quadrilaterals/2)%20Regular%20Polygons.webp Table showing polygons with their corresponding number of sides. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/polygons-quadrilaterals/3)%20Interior%20Angles%20of%20Polygons.webp Table showing polygons, their number of sides, and sum of interior angles. Triangle (180°), quadrilateral (360°), pentagon (540°), and hexagon (720°). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/polygons-quadrilaterals/4)%20Special%20Quadrilaterals.webp Illustrating special types of quadrilaterals, highlighting their unique properties such as parallel sides and equal angles. https://maths-angel.com/lessons/rational-numbers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/rational-numbers-and-their-location-on-a-number-line-math-angel.webp Rational numbers lesson showing fractions, terminating decimals, and recurring decimals. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/rational-numbers-and-their-location-on-a-number-line-welcome-visual.webp Rational Numbers and Their Location on a Number Line - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/1)%20What%20Are%20Rational%20Numbers.webp Rational numbers explained with examples showing that fractions, integers, terminating decimals, and recurring decimals are rational numbers. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/2)%20What%20Are%20Irrational%20Numbers.webp Explaining that irrational numbers are non-terminating decimals without repeating patterns, with examples like π and √2. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/3)%20Locating%20Fractions%20on%20a%20Number%20Line.webp Locating the rational number and fraction 11/3 on a number line by dividing it into 3 and 2/3, demonstrating on number line. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/4)%20Rational%20Decimals%20on%20a%20Number%20Line.webp Locating the rational number and decimal -2.7 on a number line, shown as -2 minus 0.7. https://maths-angel.com/lessons/line-graphs-curve-graphs https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/line-graphs-curve-graphs/line-graphs-and-curve-graphs-math-angel.webp Line graphs and curve graphs lesson thumbnail comparing straight-line and smooth-curve data plots https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/line-graphs-curve-graphs/line-graphs-and-curve-graphs-welcome-visual.webp Line Graphs and Curve Graphs - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/line-graphs-curve-graphs/1)%20Line%20Graph%20from%20a%20Data%20table.webp Line graph showing temperature changes from -3°C to 3°C throughout the day, with instructions on reading and creating line graphs. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/line-graphs-curve-graphs/2)%20Interpreting%20a%20Line%20Graph.webp Line graph illustrating daily sales for a week with a peak on Friday, highlighting sales of 20 on Tuesday and 80 over the weekend. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/line-graphs-curve-graphs/3)%20When%20Curve%20Graphs%20are%20More%20Appropriate.webp A curve graph illustrating the growth of a plant over five weeks and running speed over age. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/line-graphs-curve-graphs/4)%20Line%20vs%20Curve%20Graphs.webp Comparison of line graphs and curve graphs, highlighting differences in representation and complexity of data relationships. https://maths-angel.com/lessons/percentage-of-a-number https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-of-a-number/how-to-find-percentage-of-a-number-math-angel.webp How to find percentage of a number lesson thumbnail with formula and worked percentage examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-of-a-number/how-to-find-percentage-of-a-number-welcome-visual.webp How to Find Percentage of a Number - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-of-a-number/1)%20Percentage%20of%20a%20Number%20Formula.webp Example of finding 30% of 200 using the formula base value × percentage rate = percentage value, result is 60. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-of-a-number/2)%20Percentage%20of%20a%20Number%20Examples.webp Finding 60% of 150 kg equals 90 kg and 25% of 120 cm equals 30 cm using the formula base value × percentage rate = percentage value. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-of-a-number/3)%20Percentage%20of%20a%20Number%20Application.webp Calculating a 20% tip on a $180 bill, resulting in a $36 tip and a total payment of $216. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-of-a-number/4)%20Percentage%20of%20a%20Number%20Trick.webp Quick trick for finding percentage of a number and using it to calculate a 12% discount on a $1500 laptop. https://maths-angel.com/lessons/expanding-double-brackets https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expanding-double-brackets/expanding-double-brackets-math-angel.webp Expanding double brackets formula (a+b)(c+d) = ac+ad+bc+bd shown with coloured rectangles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expanding-double-brackets/expanding-double-brackets-welcome-visual.webp Expanding Double Brackets - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expanding-double-brackets/1)%20The%20Distributive%20Law.webp Visual explanation of the distributive law showing b(c + d) equals bc + bd using coloured rectangles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expanding-double-brackets/2)%20Expanding%20Double%20Brackets%20(Formula).webp Expanding double brackets showing the binomial product formula (a+b)(c+d)=ac+ad+bc+bd step-by-step. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expanding-double-brackets/3)%20Expanding%20Double%20Brackets%20(Example%201).webp Example (2x - 1)(3x + 2) for expanding double brackets, fully simplified to 6x² + x - 2. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expanding-double-brackets/4)%20Expanding%20Double%20Brackets%20(Example%202).webp Example (-3x + 2)(5 - y) for expanding double brackets, fully simplified to -15x + 3xy + 10 - 2y. https://maths-angel.com/lessons/properties-of-circles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/properties-of-circles/properties-of-circles-math-angel.webp Properties of circles lesson preview showing labelled radius, diameter, chord, sector, arc, and tangent https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/properties-of-circles/properties-of-circles-welcome-visual.webp Properties of Circles - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/properties-of-circles/1)%20Circles%20and%20Key%20Terms.webp Diagram of a circle showing key terms: tangent, chord, diameter, radius, sector, segment, and arc, with definitions around the circle. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/properties-of-circles/2)%20Finding%20Points%20with%20Circles.webp Diagram illustrating how to find points that are 5 cm from point A and 3 cm from point B, with circles drawn for each point to show intersections. https://maths-angel.com/lessons/absolute-value https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/absolute-value/absolute-value-math-angel.webp Absolute value is always non-negative: |x| ≥ 0, with examples |5| = 5, |0| = 0, and |−3| = 3 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/absolute-value/absolute-value-welcome-visual.webp Absolute Value - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/absolute-value/1)%20What%20Is%20Absolute%20Value.webp The definition of absolute value, examples include |5| = 5, |0| = 0, and |-3| = 3. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/absolute-value/2)%20Simplifying%20Absolute%20Values.webp Two examples simplifying absolute values, showing final results of 9 and 15 after applying absolute value rules. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/absolute-value/3)%20Calculating%20Negative%20Numbers%20Case%201.webp Absolute value calculation when both numbers are negative, e.g., -30 - 120 = -150, by adding absolute values and keeping the negative sign. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/absolute-value/4)%20Calculating%20Negative%20Numbers%20Case%202.webp Absolute value calculation with different signs by subtracting absolute values and keeping the sign of the larger; e.g., -65 + 15 = -50. https://maths-angel.com/lessons/mean-median-mode-range https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/mean-median-mode-range/how-to-calculate-the-mean-median-mode-and-range-math-angel.webp Mean, median, mode and range lesson thumbnail with formulas and example calculations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/mean-median-mode-range/how-to-calculate-the-mean-median-mode-and-range-welcome-visual.webp How to Calculate the Mean, Median, Mode and Range - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/mean-median-mode-range/1)%20Mean.webp Calculating the mean by adding all values and dividing by the count, with a worked example using five numbers. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/mean-median-mode-range/2)%20Median.webp Finding the median by ordering values from smallest to largest and identifying the middle value in the data set. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/mean-median-mode-range/3)%20Mode.webp Identifying the mode as the most frequently occurring value in a data set, shown with example numbers. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/mean-median-mode-range/4)%20Range.webp Calculating the range by subtracting the smallest value from the largest value in a data set. https://maths-angel.com/lessons/interest-rate-calculation https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/interest-rate-calculation/interest-and-interest-rate-calculation-math-angel.webp Interest and interest rate calculation lesson thumbnail with formula and worked examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/interest-rate-calculation/interest-and-interest-rate-calculation-welcome-visual.webp Interest and Interest Rate Calculation - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/interest-rate-calculation/1)%20Interest%20and%20Interest%20Rate%20Calculation.webp Understanding interest calculation with principal amount, interest rate, and total amount examples. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/interest-rate-calculation/2)%20Calculating%20Interest.webp Example for Interest calculation, showing the formula for calculating interest on £200 at 3% over 60 days, resulting in a total amount of £201. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/interest-rate-calculation/3)%20Calculating%20Interest%20Rate.webp Example for calculating the interest rate, demonstrating the formula for interest with £200 principal and 4% interest rate. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/interest-rate-calculation/4)%20Calculating%20Principal.webp Illustration of calculating the principal using a 5% interest rate, earning £30 after 1 year, with the formula and steps to solve for the principal. https://maths-angel.com/lessons/square-of-a-binomial https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/square-of-a-binomial-math-angel.webp Three binomial formulas: (a+b) squared, (a-b) squared, and (a+b)(a-b) = a squared minus b squared https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/square-of-a-binomial-welcome-visual.webp Square of a Binomial - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/1)%20Square%20of%20a%20Binomial%20Derivation.webp Expansion and simplification of (a + b)² to a² + 2ab + b² using distributive method. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/2)%20Square%20of%20a%20Binomial%20Visualisation.webp Square of a binomial formula, showing (a + b)² = a² + b² + 2ab with coloured squares and rectangles representing each term. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/3)%20Square%20of%20a%20Binomial%203%20Formulas.webp Three binomial square formulas, including (a + b)² = a² + b² + 2ab, (a - b)² = a² + b² - 2ab, and (a + b)(a - b) = a² - b². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/4)%20Square%20of%20a%20Binomial%20Formula%201%20Example.webp Binomial expansion showing the formula (a + b)² = a² + b² + 2ab, and an example (-2x + 3)² = 4x² + 9 - 12x. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/5)%20Square%20of%20a%20Binomial%20Formula%202%20Example.webp Expanding the binomial (5x - 2y)² using the formula (a - b)² = a² + b² - 2ab, resulting in 25x² + 4y² - 20xy. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/6)%20Square%20of%20a%20Binomial%20Formula%203%20Example.webp Identifying variables a and b with signs and coefficients in the formula (a + b)(a - b) = a² - b², using (3x + 4)(3x - 4) = 9x² - 16 as an example. https://maths-angel.com/lessons/thales-theorem https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/thales-theorem/thales-theorem-math-angel.webp Thales' Theorem lesson preview showing a right-angled triangle inscribed in a semicircle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/thales-theorem/thales-theorem-welcome-visual.webp Thales' Theorem - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/thales-theorem/1)%20What%20is%20Thales%27%20Theorem.webp Explanation of Thales's Theorem with a diagram showing a right-angled triangle formed by a diameter and any point on a semicircle. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/thales-theorem/2)%20How%20to%20Apply%20Thales%27%20Theorem.webp Diagram for Thales' theorem with triangle inscribed in a semicircle, showing a right angle at point C and interior angles A = 35° and B = 55°. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/thales-theorem/3)%20Thales%27%20Theorem%20Exercise.webp Semicircle with diameter AB, triangle ACB showing angle ACB as 90° using Thales's theorem, with marked angles 40°, 50°, and 90°. https://maths-angel.com/lessons/basic-arithmetic-inverse-operations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/basic-arithmetic-and-inverse-operations-math-angel.webp Basic arithmetic operations and inverse operations diagram with examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/basic-arithmetic-and-inverse-operations-welcome-visual.webp Basic Arithmetic and Inverse Operations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/1)%20Addition.webp Visual explanation of addition 6 + 6 + 6 = 18, highlighting summands and the sum. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/2)%20Multiplication.webp Explanation of multiplication 3 x 6 = 18, showing multiplier, multiplicand, and product. ​ https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/3)%20Subtraction.webp Subtraction explained with an example showing 18 minus 6 equals 12, including terms minuend, subtrahend, and difference. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/4)%20Division.webp Division of 12 by 4 is explained, including the terms dividend, divisor, and quotient, and an explanation of why division by zero is impossible. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/5)%20Inverse%20Operations.webp Diagram illustrating inverse operations in maths, showing examples of addition, subtraction, multiplication, and division on number lines. https://maths-angel.com/lessons/median-mean-mode-frequency-table https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/median-mean-mode-frequency-table/median-mean-mode-range-from-a-frequency-table-math-angel.webp Mean, median, mode and range from a frequency table lesson thumbnail with worked calculations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/median-mean-mode-frequency-table/median-mean-mode-range-from-a-frequency-table-welcome-visual.webp Median, Mean, Mode and Range from a Frequency Table - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/median-mean-mode-frequency-table/1)%20Mean%20from%20a%20frequency%20table.webp Calculating mean from a frequency table showing number of pets owned, including values and frequency, resulting in a mean of 1.6. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/median-mean-mode-frequency-table/2)%20Median%20from%20a%20frequency%20table.webp Frequency table showing pets owned and their frequency, with the median calculated as 1 using the formula (n+1)/2. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/median-mean-mode-frequency-table/3)%20Mode%20and%20Range%20from%20a%20frequency%20table.webp Frequency table showing pets owned with mode of 1 and range of 9. Pets owned range from 0 to 9, with frequencies of 4, 6, 3, 1, and 1 respectively. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/median-mean-mode-frequency-table/4)%20Overview%20Mean%2C%20Median%2C%20Mode%2C%20Range%20from%20Frequency%20Table.webp Calculations for mean, median, mode, and range of pets owned, based on a frequency table showing values 0 to 9. https://maths-angel.com/lessons/simple-interest-and-compound-interest https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/simple-interest-and-compound-interest/simple-interest-and-compound-interest-math-angel.webp Simple and compound interest lesson thumbnail comparing both formulas and how they grow over time https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/simple-interest-and-compound-interest/simple-interest-and-compound-interest-welcome-visual.webp Simple Interest and Compound Interest - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/simple-interest-and-compound-interest/1)%20Simple%20Interest.webp Simple interest calculation example, showing the principal amount, interest rate, and time in years, resulting in £15 interest over 3 years. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/simple-interest-and-compound-interest/2)%20Compound%20Interest.webp Compound interest calculation over three years showing the formula and total amount of £115.8 from an initial £100. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/simple-interest-and-compound-interest/3)%20Simple%20vs%20Compound%20Interest.webp Comparison of simple interest and compound interest formulas, showing calculations for total amount and interest earned over years. https://maths-angel.com/lessons/introduction-to-mapping https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-mapping/introduction-to-mapping-math-angel.webp Mapping of time to speed shown with a table and graph, illustrating how one quantity relates to another https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-mapping/introduction-to-mapping-welcome-visual.webp Introduction to Mapping - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-mapping/1)%20Mapping%20Definition%20and%20Example.webp Mapping time to speed with a table showing time in hours and corresponding speed in km/h, illustrating the relationship between the two quantities. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-mapping/2)%20Mapping%20Through%20Table%20and%20Graph.webp Mapping of time and speed shown through a table and graph, with time in hours and speed in km/h. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-mapping/3)%20Mapping%20Example%20Types%20of%20Balls%20and%20Their%20Weight.webp Table and graph comparing the weights of different types of balls. https://maths-angel.com/lessons/units-of-area https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/units-of-area/units-of-area-math-angel.webp Units of area table comparing mm², cm², m², and km² with edge lengths and scale examples: pencil, calculator, window, city https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/units-of-area/units-of-area-welcome-visual.webp Units of Area - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/units-of-area/1)%20What%20is%20Area.webp Explaining the concept of area using 25 unit squares, each 1 square metre, to calculate a total area of 25 square metres with a room diagram. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/units-of-area/2)%20Common%20Units%20of%20Area.webp Table comparing units of area: square millimetre, square centimetre, square metre, and square kilometre with examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/units-of-area/3)%20Converting%20Units%20of%20Area%20(Chart).webp Conversion for units of area showing the relationships between square millimetres, centimetres, metres, and kilometres, with examples and steps. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/units-of-area/4)%20Converting%20Area%20Units%20(Examples).webp Explaining area unit conversions, including mm², cm², m², and km², with examples for converting 5000 mm² to 50 cm² and 3 m² to 30,000 cm². https://maths-angel.com/lessons/bidmas-order-of-operations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/bidmas-order-of-operations/bidmas-order-of-operations-math-angel.webp BIDMAS order of operations lesson covering brackets, indices, division, multiplication, addition, subtraction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/bidmas-order-of-operations/BIDMAS-welcome-visual.webp BIDMAS - Order of Operations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/bidmas-order-of-operations/1)%20Mathematical%20Expression.webp Total cost of a £300 phone and £20 each for a charger, headphones, and mouse, paid in 12 installments, as an expression using terms and operators. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/bidmas-order-of-operations/2)%20BIDMAS.webp Expression (300 + 3 × 20) ÷ 12 with terms and operators labelled, applying BIDMAS to a real-world shopping problem. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/bidmas-order-of-operations/3)%20Applying%20BIDMAS.webp Practising BIDMAS with examples such as of division and multiplication, and addition and subtraction. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/bidmas-order-of-operations/4)%20Dealing%20with%20Multiple%20Brackets.webp Step by step example of solving an expression with multiple brackets, 50-(2*(2+4*5)-3), using BIDMAS/BODMAS. https://maths-angel.com/lessons/box-plot https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/box-plot/how-to-draw-and-read-a-box-plot-math-angel.webp Box plot lesson thumbnail showing minimum, quartiles, median, and maximum on a number line https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/box-plot/how-to-draw-and-read-a-box-plot-welcome-visual.webp How to Draw and Read a Box Plot - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/box-plot/1)%20Box%20Plots.webp Box plot definition showing whiskers, quartiles, and median line used to display the distribution of a data set https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/box-plot/2)%20Creating%20Box%20Plot.webp Box plot showing minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value, with example values for hours of exercise. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/box-plot/3)%20Interpreting%20Box%20Plot.webp Box plot showing minimum, maximum, Q1, median, Q3, interquartile range (IQR), and range. https://maths-angel.com/lessons/percentage-increase-and-decrease https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-increase-and-decrease/percentage-increase-and-decrease-math-angel.webp Percentage increase and decrease lesson thumbnail showing the formula and worked examples of price changes https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-increase-and-decrease/percentage-increase-and-decrease-welcome-visual.webp Percentage Increase and Decrease - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-increase-and-decrease/1)%20Percentage%20Increase%20and%20Decrease%20-%20Formula.webp Formula for percentage increase and decrease with examples showing 100 increasing by 20% and decreasing by 10%. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-increase-and-decrease/2)%20Percentage%20Increase%20and%20Decrease%20-%20Examples.webp Percentage increase and decrease examples showing a score increase from 60 to 72 and a jacket price reduced from $90 to $63. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-increase-and-decrease/3)%20Reverse%20Percentage%20-%20Finding%20the%20Original%20Value.webp Reverse percentage example showing how a $36 ticket with 40% discount gives an original price of $60. https://maths-angel.com/lessons/introduction-to-formulas https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-formulas/introduction-to-formulas-math-angel.webp Definition of a formula with y = 2x + 3 and substitution examples for x = 1, 2, and 3 giving y = 5, 7, and 9 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-formulas/introduction-to-formulas-welcome-visual.webp Introduction to Formulas - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-formulas/1)%20What%20is%20a%20Formula.webp Introduction to formulas showing a mathematical equation y = 2x + 3, with examples for x values of 1, 2, and 3, and the definition of a formula. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-formulas/2)%20Visualising%20Formulas.webp Visualising formulas using a table and a graph for the equation y = 2x + 3. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-formulas/3)%20Applying%20Formulas.webp Chart explaining how to use the formula y = 20 + 12x to calculate savings, with an example showing it takes 5 weeks to save £80. https://maths-angel.com/lessons/area-of-a-triangle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-triangle/area-of-a-triangle-math-angel.webp Area of a triangle lesson preview showing the formula ½ × base × height with a labelled triangle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-triangle/area-of-a-triangle-welcome-visual.webp Area of a Triangle - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-triangle/1)%20Area%20of%20Triangles%20Formula.webp Diagram explaining the area of triangles formula 1/2 x b x h, examples of perpendicular height, and notes emphasising any side as base. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-triangle/2)%20Regular%20triangles%20Example.webp Illustration of finding the area of a triangle with a base of 6 cm and height of 5 cm using the formula 1/2 x base x height, resulting in 15 cm². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-triangle/3)%20Right-angled%20triangles%20Example.webp The area question of a right-angled triangle with a base of 5 cm and height of 12 cm. Calculations demonstrate the area formula, yielding 30 cm². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-triangle/4)%20Finding%20the%20height%20from%20the%20area.webp How to calculate the height of a triangle using its area, with given dimensions and a worked-out formula solution. https://maths-angel.com/lessons/commutative-property-associative-property https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/commutative-property-and-associative-property-math-angel.webp Commutative and associative property lesson showing how to swap and regroup numbers in maths https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/commutative-property-and-associative-property-welcome-visual.webp Commutative and Associative Properties - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/1)%20The%20Commutative%20Law.webp Commutative property showing number swapping in addition and multiplication, not applicable to subtraction or division https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/2)%20Commutative%20Law%20Example.webp Commutative law examples in addition (77 + 246 + 23) and multiplication (25 × 19 × 4) with step-by-step solutions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/3)%20The%20Associative%20Law.webp The Associative Law allows grouping numbers when adding or multiplying, but does not apply to subtraction or division. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/4)%20Associative%20Law%20Example.webp Associative law examples in addition (127 + 48) + 52 and multiplication 5 × (2 × 228) with worked solutions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/5)%20Combining%20Commutative%20and%20Associative%20Law.webp Combining commutative and associative laws in addition 32 + (115 + 68) and multiplication 20 × (48 × 5) https://maths-angel.com/lessons/grouped-frequency-table https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/grouped-frequency-table/averages-from-grouped-frequency-table-math-angel.webp Grouped frequency table with class intervals 10 < x ≤ 20 to 40 < x ≤ 50 showing delivery time frequencies https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/grouped-frequency-table/averages-from-grouped-frequency-table-welcome-visual.webp Averages from a Grouped Frequency Table - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/grouped-frequency-table/1)%20Grouped%20Frequency%20Table.webp Grouped frequency table showing delivery time intervals in minutes and their corresponding frequencies. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/grouped-frequency-table/2)%20Modal%20Class.webp Frequency table of delivery times showing modal class 40 < x ≤ 50 with highest frequency of 10. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/grouped-frequency-table/3)%20Median%20from%20a%20Grouped%20Frequency%20Table.webp Grouped frequency table for delivery times, showing frequencies and positions to identify the class containing the median. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/grouped-frequency-table/4)%20Mean%20from%20a%20Grouped%20Frequency%20Table.webp Grouped frequency table showing delivery time intervals and frequencies, with explanations of the modal class, class with the median, estimated mean. https://maths-angel.com/lessons/percentage-change https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-change/how-to-calculate-percentage-change-math-angel.webp Percentage change lesson thumbnail showing the formula with worked increase and decrease examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-change/how-to-calculate-percentage-change-welcome-visual.webp How to Calculate Percentage Change - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-change/1)%20How%20to%20Calculate%20Percentage%20Change.webp Formula for calculating percentage change using change divided by original value times 100, with notes on increase and decrease. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-change/2)%20Percentage%20Change%20Examples.webp Percentage change examples showing a 30% price increase for a board game and a 25% price decrease for a clock. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-change/3)%20Percentage%20Change%20Practice.webp Percentage decrease calculation where a table bought for $1200 and sold for $960 shows a 20% drop over 3 years. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-change/4)%20Percentage%20Change%20Application.webp Percentage change example showing a 5% decrease in cinema visitors from Week 2 (1500) to Week 4 (1425) using the change formula. https://maths-angel.com/lessons/introduction-to-functions-and-graphs https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-functions-and-graphs/introduction-to-functions-and-graphs-math-angel.webp Function f(x) = 2x + 1 with a table of values and plotted graph showing input-output pairs https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-functions-and-graphs/introduction-to-functions-and-graphs-welcome-visual.webp Introduction to Functions and Graphs - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-functions-and-graphs/1)%20Function%20Notation.webp Visual representation of function notation showing the function f(x) = 2x + 1 and its calculated outputs for f(1), f(2), and f(3). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-functions-and-graphs/2)%20Plot%20a%20Graph.webp Steps to graph a function showing a table of values for f(x)=2x+1 and its corresponding plotted graph with points. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-functions-and-graphs/3)%20Graphs%20that%20do%20not%20represent%20a%20function.webp 2 graphs showing non-functions: one with a circle and another with a vertical line, explaining that one x-value must not have multiple y-values. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-functions-and-graphs/4)%20Reading%20Function%20Values%20from%20Graphs.webp Graph showing function values with examples: f(-2) = -3 and f(x) = 0 at x = -4, 0, 5, with a function definition. https://maths-angel.com/lessons/perimeter-of-a-polygon https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perimeter-of-a-polygon/perimeter-of-a-polygon-math-angel.webp Perimeter of a polygon formulas for rectangles, squares, isosceles and equilateral triangles with labelled diagrams https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perimeter-of-a-polygon/perimeter-of-a-polygon-welcome-visual.webp Perimeter of a Polygon - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perimeter-of-a-polygon/1)%20Perimeter%20of%20Polygons%2C%20Quadrilaterals%2C%20Squares.webp Perimeter of a rectangle and square with formulas. Rectangle: length 5 cm, width 3 cm, perimeter 16 cm. Square: side 2 m, perimeter 8 m. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perimeter-of-a-polygon/2)%20Perimeter%20of%20Triangles.webp Comparing the perimeter of an isosceles triangle and an equilateral triangle, showing the formulas and values for calculating their perimeters. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perimeter-of-a-polygon/3)%20Perimeter%20of%20Complex%20Shapes.webp Perimeter of an L-shaped polygon shown with two calculation methods. Method 1 adds all side lengths. Method 2 treats it as a rectangle. https://maths-angel.com/lessons/column-addition-and-subtraction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/column-addition-and-subtraction/column-addition-and-column-subtraction-math-angel.webp Column addition and subtraction worked examples showing carrying and borrowing with multi-digit numbers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/column-addition-and-subtraction/column-addition-and-column-subtraction-welcome-visual.webp Column Addition and Column Subtraction - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/column-addition-and-subtraction/1)%20Column%20Addition%20and%20Carrying%20Over.webp Column addition for 3425 + 782, showing how to align the numbers vertically. Start addition from the right, and carry over for sums over ten. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/column-addition-and-subtraction/2)%20Column%20Subtraction%20and%20Borrowing.webp Column subtraction example showing how to subtract 876 from 2826, with steps including borrowing and aligning numbers, resulting in 1950. https://maths-angel.com/lessons/calculating-probability https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/calculating-probability/calculating-probability-math-angel.webp Calculating probability lesson thumbnail with a probability scale from impossible to certain https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/calculating-probability/calculating-probability-welcome-visual.webp Calculating Probability - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/calculating-probability/1)%20Characteristic%20of%20a%20Probability.webp Explanation of probability, including the likelihood of events happening and a scale ranging from impossible (0%) to certain (100%). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/calculating-probability/2)%20Calculating%20Probabilities.webp Explaining probability of drawing a red ball from a bag of 10 balls (3 red, 7 blue) with a probability formula and example calculation. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/calculating-probability/3)%20Estimating%20Probabilities.webp Drawing 100 times and getting 37 red and 63 blue. Explanation of experimental probability as estimated from outcomes compared to true probability. https://maths-angel.com/lessons/directly-proportional-inversely-proportional https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/directly-proportional-inversely-proportional/directly-proportional-and-inversely-proportional-math-angel.webp Directly and inversely proportional lesson thumbnail comparing both relationship types with examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/directly-proportional-inversely-proportional/directly-proportional-and-inversely-proportional-welcome-visual.webp Directly Proportional and Inversely Proportional - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/directly-proportional-inversely-proportional/1)%20Direct%20Proportion.webp Direct proportionality between the number of watermelons and their total cost, with calculations. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/directly-proportional-inversely-proportional/2)%20Inverse%20Proportion.webp Inverse proportion chart showing number of workers and hours needed, demonstrating that more workers reduce the time required to complete a task. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/directly-proportional-inversely-proportional/3)%20Direct%20Proportion%20vs%20Inverse%20Proportion.webp Direct and inverse proportionality concepts with real-life examples showing the relationship between quantities and costs or time. https://maths-angel.com/lessons/solving-equations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-equations/solving-equations-math-angel.webp Step-by-step solving of a linear equation showing simplification, rearrangement, and finding x https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-equations/solving-equations-welcome-visual.webp Solving Equations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-equations/1)%20What%20Does%20Solving%20Equations%20Mean.webp Solving an equation means finding the value of the unknown that makes the equation true, shown with the example x + 3 = 8, where x = 5. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-equations/2)%20Solving%20Equations%20Techniques.webp Solving a linear equation using distributive law and simplification, steps: simplify both sides, rearrange the equation, and solve for the unknown. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-equations/3)%20Solving%20Equations%20Example.webp Steps for solving an equation using simplification, rearrangement, and solving for the unknown variable, with an example showing the solution x = 3. https://maths-angel.com/lessons/area-of-a-trapezium https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-trapezium/area-of-a-trapezium-math-angel.webp Area of a trapezium formula (a + b) ÷ 2 × h with labelled diagram and worked example showing 60 cm² https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-trapezium/area-of-a-trapezium-welcome-visual.webp Area of a Trapezium - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-trapezium/1)%20What%20is%20a%20Trapezium.webp Trapezium definition diagram showing bases, height, and difference from a parallelogram. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-trapezium/2)%20Area%20of%20a%20Trapezium.webp Diagram showing the trapezium area formula: (a + b) ÷ 2) x h, and example calculation using bases 8 cm and 12 cm, height 6 cm. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-trapezium/3)%20Area%20of%20a%20Right-Angled%20Trapezium.webp Area of a right-angled trapezium formula, with example of a right-angled trapezium with bases 6 cm and 9 cm, height 4 cm, showing result as 30 cm². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-trapezium/4)%20Area%20of%20an%20Isosceles%20Trapezium.webp Area calculation of an isosceles trapezium with bases 5 m and 9 m, total area 21 m², showing height calculated as 3 m. https://maths-angel.com/lessons/long-multiplication https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-multiplication/long-multiplication-math-angel.webp Long multiplication method showing step-by-step partial products for multiplying multi-digit numbers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-multiplication/long-multiplication-welcome-visual.webp Long Multiplication - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-multiplication/1)%20Long%20Multiplication%20Example%201.webp Long multiplication of 352 by 24 showing step-by-step partial products and final answer 8448. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-multiplication/2)%20Long%20Multiplication%20Example%202.webp Long multiplication of 67 by 52 broken into steps, showing partial products and final answer 3484. https://maths-angel.com/lessons/addition-rule-of-probability-expected-frequency https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/addition-rule-of-probability-expected-frequency/addition-rule-of-probability-and-expected-frequency-math-angel.webp Addition rule of probability lesson thumbnail showing P(A or B) = P(A) + P(B) formula https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/addition-rule-of-probability-expected-frequency/addition-rule-of-probability-and-expected-frequency-welcome-visual.webp Addition Rule of Probability and Expected Frequency - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/addition-rule-of-probability-expected-frequency/1)%20Equiprobable%20Events.webp Explanation of equiprobable events by using a die and showing that each face has an equal probability of 1/6. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/addition-rule-of-probability-expected-frequency/2)%20Calculating%20Probability.webp Drawing coloured balls from a bag with 50 balls, showing 50% for blue and 30% for red. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/addition-rule-of-probability-expected-frequency/3)%20Calculating%20Probability%20Example.webp Probability of drawing a red or blue ball from 50 balls, with 25 blue, 15 red, and 10 yellow, equals 80%. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/addition-rule-of-probability-expected-frequency/4)%20Addition%20Rule%20for%20Probabilities.webp Explanation of the probability of drawing blue or red balls from a bag with 50 balls using the addition rule for mutually exclusive events. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/addition-rule-of-probability-expected-frequency/5)%20Expected%20Absolute%20Frequency.webp Calculating the expected absolute frequency using a die, illustrating that the expected absolute frequency of rolling a '3' over 60 trials is 10. https://maths-angel.com/lessons/direct-proportion https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/direct-proportion/direct-proportion-formula-and-examples-math-angel.webp Direct proportion definition, notation y ∝ x, and formula y = kx where k is a constant https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/direct-proportion/direct-proportion-formula-and-examples-welcome-visual.webp Direct Proportion Formula and Examples - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/direct-proportion/1)%20What%20Is%20Direct%20Proportion.webp The definition of direct proportion with notation y∝x and formula y=kx (k is a constant). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/direct-proportion/2)%20Direct%20Proportion%20Formula%20Example%201.webp Direct proportion example: y = kx with x=4, y=20 giving k=5, so y=5x and when x=10, y=50. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/direct-proportion/3)%20Direct%20Proportion%20Formula%20Example%202.webp Direct proportion to x² example: x=3, y=18 gives k=2, so y=2x² and when x=6, y=72 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/direct-proportion/4)%20Direct%20Proportion%20Formula%20Example%203.webp Direct proportion to √x example: x=49, y=14 gives k=2, so y=2√x and when x=100, y=20. https://maths-angel.com/lessons/solving-rational-equations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-rational-equations/solving-rational-equations-math-angel.webp Steps to solve a rational equation with x in the denominator, clearing fractions and checking the answer https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-rational-equations/solving-rational-equations-welcome-visual.webp Solving Rational Equations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-rational-equations/1)%20How%20to%20Solve%20Rational%20Equations%20Step%20by%20Step.webp Steps to solve an equation with x in the denominator, including isolating x, clearing the denominator, and checking the solution. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-rational-equations/2)%20Solving%20Equations%20with%20X%20in%20Denominator%20(Example).webp Solving equations with rational expressions where x is in the denominator, step-by-step process with a worked example and solution x = 1. https://maths-angel.com/lessons/area-parallelograms-triangles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-parallelograms-triangles/area-of-parallelograms-and-triangles-math-angel.webp Area of a parallelogram formula A = b × h with two diagrams showing perpendicular height h inside and outside the shape https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-parallelograms-triangles/area-of-parallelograms-and-triangles-welcome-visual.webp Area of Parallelograms and Triangles - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-parallelograms-triangles/1)%20Height%20of%20a%20Parallelogram.webp Height of a parallelogram illustrated with a perpendicular height h from base b to the opposite side. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-parallelograms-triangles/2)%20Area%20of%20a%20Parallelogram.webp Diagram showing the formula for the area of a parallelogram, A = b⋅h, with labelled base (b) and height (h) on two parallelograms. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-parallelograms-triangles/3)%20Height%20of%20a%20Triangle.webp Height of a triangle, with height h perpendicular to base b and extending from b to the opposite vertex, illustrated with two triangle diagrams. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-parallelograms-triangles/4)%20Area%20of%20a%20Triangle.webp Formula for the area of a triangle with base and height labelled, showing two triangles with base (b) and height (h). https://maths-angel.com/lessons/long-division https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-division/long-division-math-angel.webp Long division worked example showing dividend, divisor, quotient and remainder step by step https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-division/long-division-welcome-visual.webp Long Division - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-division/1)%20Long%20Division%20Example%201.webp Long division example solving 364 divided by 30, showing steps with quotient 12 and remainder 4, including a check with reverse calculation. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-division/2)%20Long%20Division%20Example%202.webp Long division example of 1615 divided by 7, showing step-by-step process with a final result of 230 remainder 5. https://maths-angel.com/lessons/probability-tree-diagrams https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/probability-tree-diagrams/probability-tree-diagrams-math-angel.webp Probability tree diagrams lesson thumbnail with branching outcomes for two-stage events https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/probability-tree-diagrams/probability-tree-diagrams-welcome-visual.webp Probability Tree Diagrams - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/probability-tree-diagrams/1)%20What%20is%20a%20Probability%20Trees%20Diagrams.webp Red and blue balls with numbers 3 and 7 beside a bag of 10 balls, illustrating possible outcomes in a probability experiment. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/probability-tree-diagrams/2)%20How%20to%20Draw%20Probability%20Trees%20Diagrams.webp Probability tree diagram showing two-ball draws without replacement from a bag with 3 red and 6 blue balls. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/probability-tree-diagrams/3)%20Probability%20Tree%20Diagram%20Outcomes.webp Probability tree diagram illustrating the drawing of 9 balls, 3 red and 6 blue, with dependent probabilities and combined event outcomes. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/probability-tree-diagrams/4)%20Finding%20Probabilities%20with%20Probability%20Tree%20Diagram.webp Probability tree diagram for the calculation of drawing two balls of the same colour using equiprobable events and addition rule for probabilities. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/probability-tree-diagrams/5)%20Calculating%20Probabilities%20using%20Probability%20Tree%20Diagrams.webp Probability tree diagram showing the calculation of drawing 2 balls of the same colour with red and blue ball probabilities, expected values. https://maths-angel.com/lessons/inverse-proportion https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/inverse-proportion/inverse-proportion-formula-and-examples-math-angel.webp Inverse proportion definition, notation y ∝ 1/x, and formula y = k/x where xy = k and k is a constant https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/inverse-proportion/inverse-proportion-formula-and-examples-welcome-visual.webp Inverse Proportion Formula and Examples - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/inverse-proportion/1)%20What%20is%20Inverse%20Proportion.webp Inverse proportion with a definition, notation showing y is proportional to 1 divided by x, and the formula y = k divided by x. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/inverse-proportion/2)%20Inverse%20Proportion%20Formula%20Example%201.webp Inverse proportion example y ∝ 1/x: x=6 gives y=8, so k=48 and y=12 when x=4. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/inverse-proportion/3)%20Inverse%20Proportion%20Formula%20Example%202.webp Worked example of inverse proportion y ∝ 1/x²: x=3 gives y=8, so k=72 and y=2 when x=6. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/inverse-proportion/4)%20Inverse%20Proportion%20Formula%20Example%203.webp Inverse proportion example n ∝ 1/√r: n=12 when r=9, so k=36 and n=9 when r=16. https://maths-angel.com/lessons/m-and-c-in-linear-equations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/m-and-c-in-linear-equations/gradient-and-y-intercept-in-linear-equations-math-angel.webp Linear equation y = mx + c on a graph showing gradient m and y-intercept c where the line crosses the y-axis https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/m-and-c-in-linear-equations/gradient-and-y-intercept-in-linear-equations-welcome-visual.webp Gradient and Y-Intercept in Linear Equations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/m-and-c-in-linear-equations/1)%20m%20and%20c%20in%20Linear%20Equations.webp Linear equation y = mx + c showing the gradient (m) and y-intercept (c), with a graph of a straight line. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/m-and-c-in-linear-equations/2)%20Intercept%20Linear%20Equations.webp Linear equation y=mx+c with highlighted y-intercept c where line crosses y-axis. Diagram shows lines with different y-intercepts, one passing origin. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/m-and-c-in-linear-equations/3)%20Slope%20of%20Linear%20Equations.webp Graph illustrating y = mx + c with explanations of gradient (m) and y-intercept (c), and examples of positive and negative gradients. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/m-and-c-in-linear-equations/4)%20Draw%20a%20Linear%20Equation%20y%20%3D%202x%20%2B%201.webp How to draw a linear equation with gradient (m) and y-intercept (c) shown on a graph, step-by-step guide with illustrations. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/m-and-c-in-linear-equations/5)%20Draw%20a%20Linear%20Equation%20y%3D-3x%2B4.webp Steps to draw a linear equation y = -3x + 4, find y-intercept at 4, move 1 step right and 3 steps down, and connect points with the line. https://maths-angel.com/lessons/area-of-compound-shapes https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-compound-shapes/area-of-compound-shapes-math-angel.webp Area of compound shapes lesson preview showing an L-shape split into rectangles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-compound-shapes/area-of-compound-shapes-welcome-visual.webp Area of Compound Shapes - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-compound-shapes/1)%20How%20to%20Find%20Area%20of%20Compound%20Shape.webp Diagram explaining how to find the area of a compound shape by breaking it into simpler shapes, then summing or subtracting their areas. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-compound-shapes/2)%20Compound%20Shape%20Two%20Rectangles.webp Diagram showing the area of a compound shape made of two rectangles with dimensions and steps for calculating total area, totalling 12 square metres. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-compound-shapes/3)%20Compound%20Shape%20Rectangle%20and%20Triangle.webp Diagram showing a compound shape composed of a rectangle and a right-angled triangle, with their respective and total areas calculation. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-compound-shapes/4)%20Application%20of%20Area%20of%20Compound%20Shapes.webp Diagram showing the calculation of the shaded area of a wall, excluding a door and window, with a total painting cost of £46 at £5 per square metre. https://maths-angel.com/lessons/decimal-point-movement https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimal-point-movement/movement-of-the-decimal-point-math-angel.webp Decimal point shifting right for multiplication and left for division by powers of 10 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimal-point-movement/movement-of-the-decimal-point-welcome-visual.webp Movement of the Decimal Point - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimal-point-movement/1)%20Movement%20of%20the%20Decimal%20Point.webp Shifting the decimal point in division and multiplication, showing how the decimal point shifts left for division and right for multiplication. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimal-point-movement/2)%20Movement%20of%20the%20Decimal%20Point%20Examples.webp Examples on how to move the decimal point when calculating 5.02*1000, 4.21/100, and 56.7%*10. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimal-point-movement/3)%20Movement%20of%20the%20Decimal%20Point%20in%20Unit%20Conversion.webp Converting 2.8 metres to 280 centimetres by multiplying by 100, and converting 0.0028 kilometres to metres by multiplying by 1000. https://maths-angel.com/lessons/sets-and-venn-diagrams https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/sets-and-venn-diagrams/sets-and-venn-diagrams-math-angel.webp Sets and Venn diagrams lesson thumbnail with overlapping circles showing union and intersection https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/sets-and-venn-diagrams/sets-and-venn-diagrams-welcome-visual.webp Sets and Venn Diagrams - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/sets-and-venn-diagrams/1)%20Sets%20in%20Maths.webp Introduction to sets showing a set A = {1, 3, 5, 7} defined as a collection of distinct objects, with no repeated elements and order doesn't matter. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/sets-and-venn-diagrams/2)%20Venn%20Diagram%20(Notation).webp Venn diagram showing ice cream preferences of 30 students, with 15 liking chocolate, 10 liking vanilla, and 5 not liking either flavour. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/sets-and-venn-diagrams/3)%20Venn%20Diagram%20(Example).webp Venn diagram showing the intersection and union of students who like chocolate and vanilla flavour, with definitions and notations for set operations. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/sets-and-venn-diagrams/4)%20Venn%20Diagram%20(Practice).webp Venn diagram showing ice cream preferences with 4 liking chocolate, 8 liking vanilla, 10 liking both, and 6 not liking either. Total students are 28. https://maths-angel.com/lessons/equation-of-a-straight-line https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equation-of-a-straight-line/finding-the-equation-of-a-straight-line-math-angel.webp Graph of the linear equation y = mx + c showing gradient and y-intercept labelled on a straight line https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equation-of-a-straight-line/finding-the-equation-of-a-straight-line-welcome-visual.webp Finding the Equation of a Straight Line - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equation-of-a-straight-line/1)%20Linear%20Equations.webp Linear equation y = mx + c with m labelled as slope and c as y-intercept, shown on a graph crossing the y-axis. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equation-of-a-straight-line/2)%20Determining%20Linear%20Equations.webp Finding linear equation y = mx + c using two points, and steps to calculate gradient (m) and y-intercept (c) with points (2,3) and (4,7) on a graph. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equation-of-a-straight-line/3)%20Checking%20whether%20point%20on%20Line.webp Verifying if points (3, 5) and (-2, -4) lie on the line y = 2x - 1 by substituting coordinates into the equation illustrating right and wrong results. https://maths-angel.com/lessons/circumference-area-circle-sector https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/circumference-area-circle-sector/circumference-and-area-of-a-circle-and-a-sector-math-angel.webp Circle with radius r labelled, showing circumference formula C = πd = 2πr and area formula A = πr² https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/circumference-area-circle-sector/circumference-and-area-of-a-circle-and-a-sector-welcome-visual.webp Circumference and Area of a Circle and a Sector - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/circumference-area-circle-sector/1)%20Constant%20pi.webp Diagram showing relationship between pi and circumference: a rolling wheel illustrates that circumference equals pi times diameter. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/circumference-area-circle-sector/2)%20Circumference%20of%20a%20Circle.webp Circle with radius 5 cm showing formula for circumference C = 2πr. Example calculation gives circumference ≈ 31.4 cm. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/circumference-area-circle-sector/3)%20Area%20of%20a%20Circle.webp Area of a circle formula Area equals pi r squared., with an example that the radius is 3 cm. The area is calculated as approximately 28.26 cm². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/circumference-area-circle-sector/4)%20Arc%20Length%20and%20Area%20of%20Circle%20Sectors.webp Circle sector diagram with formulas: Arc length equals alpha over 360 times 2 r; area equals alpha over 360 times pi r squared. https://maths-angel.com/lessons/adding-and-subtracting-negative-numbers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/adding-and-subtracting-negative-numbers-math-angel.webp Adding and subtracting negative numbers with sign rules and number line examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/adding-and-subtracting-negative-numbers-welcome-visual.webp Adding and Subtracting Negative Numbers - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/1)%20Understanding%20Negative%20Numbers.webp Number line showing negative and positive numbers from -5 to 5, with zero as neutral, labelled 'Understanding Negative Numbers'. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/2)%20Adding%20and%20Subtracting%20Negative%20Numbers%20Using%20Number%20Line.webp Number line visual for adding and subtracting negative numbers, showing (-7) + 5 = -2 with a move right and (-6) - 3 = -9 with a move left. ​ https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/3)%20Application%20-%20Negative%20Numbers.webp Temperature drops from 3°C to -7°C by subtracting 10°C, shown on a number line to teach negative numbers. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/4)%20Rules%20for%20Removing%20Brackets%20for%20Addition%20and%20Subtraction.webp Rules for removing brackets when adding or subtracting negative numbers using same and different sign combinations. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/5)%20Removing%20Brackets%20with%20Multiple%20Numbers.webp Steps to remove brackets with multiple numbers, solving -12 - (-12 + 5) by solving inside first or applying the rule to change signs. Result is -5. https://maths-angel.com/lessons/x-intercept-y-intercept-intersection https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/x-intercept-y-intercept-intersection/how-to-find-x-intercept-y-intercept-and-intersections-math-angel.webp Linear equation y = 200 - 50x showing where the line crosses the x-axis and y-axis with intercepts labelled https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/x-intercept-y-intercept-intersection/how-to-find-x-intercept-y-intercept-and-intersections-welcome-visual.webp How to Find X-Intercept, Y-Intercept and Intersections - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/x-intercept-y-intercept-intersection/1)%20Intercepts%20of%20Linear%20Equations.webp Diagram explaining the x- and y-intercepts of linear equations using the equation y = 200 - 50x, illustrating where the line crosses the axes. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/x-intercept-y-intercept-intersection/2)%20Intersection%20of%20Linear%20Equations.webp Intersection of two linear equations, y = 200 - 50x and y = 150 - 30x, at point (2.5, 75) with x-axis as hours drove and y-axis as remaining distance. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/x-intercept-y-intercept-intersection/3)%20Determining%20the%20Intersection.webp Steps to find the intersection of two linear equations by setting equations equal and solving for x and y, with equations and example values. https://maths-angel.com/lessons/line-of-symmetry https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/line-of-symmetry/line-of-symmetry-and-reflection-symmetry-math-angel.webp Line of symmetry lesson preview showing shapes with marked lines of symmetry https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/line-of-symmetry/line-of-symmetry-welcome-visual.webp Line of Symmetry and Reflection Symmetry - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/line-of-symmetry/1)%20What%20is%20Line%20of%20Symmetry.webp Heart shape divided by a line of symmetry, showing that folding along the line makes both halves match perfectly. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/line-of-symmetry/2)%20Line%20of%20Symmetry%20in%20Common%20Shapes.webp Lines of symmetry in shapes: rectangle 2, square 4, isosceles triangle 1, equilateral triangle 3, circle infinite. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/line-of-symmetry/3)%20Check%20for%20Reflection%20Symmetry.webp Four road signs are checked for whether they have reflection symmetry. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/line-of-symmetry/4)%20Key%20Feature%20of%20Line%20of%20Symmetry.webp Diagram showing a pentagon with a vertical line of symmetry and demonstrating two key features of a line of symmetry. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/line-of-symmetry/5)%20Complete%20a%20Shape%20Given%20Line%20of%20Symmetry.webp Step-by-step guide to completing a shape using a line of symmetry: measure, locate mirror points, and connect them. https://maths-angel.com/lessons/multiplying-and-dividing-negative-numbers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-and-dividing-negative-numbers/multiplying-and-dividing-negative-numbers-math-angel.webp Sign rules for multiplying and dividing negative numbers with worked examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-and-dividing-negative-numbers/multiplying-and-dividing-negative-numbers-welcome-visual.webp Multiplying and Dividing Negative Numbers - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-and-dividing-negative-numbers/1)%20Sign%20Rules%20of%20Multiplication%20and%20Division.webp Multiplication and division of negative numbers, showing odd negative signs give a negative result and even negative signs give a positive result. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-and-dividing-negative-numbers/2)%20Multiplying%20and%20Dividing%203%20Numbers.webp Steps for multiplication and division with rules for odd and even negative signs determining result positivity. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-and-dividing-negative-numbers/3)%20Combining%20Multiplication%20and%20Division.webp Combining multiplication and division with examples showing the rules for odd and even numbers of negative signs, calculating from left to right. https://maths-angel.com/lessons/simple-quadratic-equations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simple-quadratic-equations/simple-quadratic-equations-math-angel.webp Quadratic equation y = ax² with parabolas showing how the coefficient a affects direction and width https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simple-quadratic-equations/simple-quadratic-equations-welcome-visual.webp Simple Quadratic Equations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simple-quadratic-equations/1)%20Simple%20Quadratic%20Equation.webp Quadratic equation formula y = ax² with a not equal to zero, highlighting coefficient 'a'. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simple-quadratic-equations/2)%20Standard%20Parabola.webp Graph of the quadratic equation y = x² with a table of x and y values and a standard parabola on a coordinate plane where a = 1. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simple-quadratic-equations/3)%20Effect%20of%20%27a%27%20in%20quadratic%20equation.webp Graph illustrating how the sign of 'a' affects direction and its absolute value affects the width of the parabola. https://maths-angel.com/lessons/rotational-symmetry https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotational-symmetry/rotational-symmetry-math-angel.webp Rotational symmetry lesson preview showing shapes with different orders of rotational symmetry https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotational-symmetry/rotational-symmetry-welcome-visual.webp Rotational Symmetry - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotational-symmetry/1)%20Rotational%20Symmetry.webp Diagram showing a square with an order of rotation symmetry 4, and explanations of the centre of rotation, angle of rotation, and order of symmetry. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotational-symmetry/2)%20Rotational%20Symmetry%20of%20Common%20Shapes.webp Rotational symmetry of rectangle, equilateral triangle, and regular hexagon, showing their centre of rotation, angle of rotation, order of symmetry. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotational-symmetry/3)%20Check%20for%20Rotational%20Symmetry.webp Illustrating three traffic signs to check for whether they have rotational symmetry, and showing different angles of rotation and orders of symmetry. https://maths-angel.com/lessons/calculating-money https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/calculating-money-math-angel.webp Step-by-step guide to calculating money with pounds and pence examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/calculating-money-welcome-visual.webp Calculating Money - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/1)%20Money%20and%20Prices.webp A cartoon with a sandwich priced at £3.68, illustrating UK currency conversion of pounds to pence, and showing how £3.68 equals £3 plus 68p. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/2)%20Adding%20Prices.webp Calculation of adding £3.68 and £1.49 by separating pounds and pence, demonstrating the result as £5.17. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/3)%20Subtracting%20Prices.webp Subtracting money in UK currency with pounds and pence, and step-by-step calculation of £10 minus £5.17 to find the difference of £4.83. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/4)%20Multiplying%20a%20Price.webp Calculating the price of 8 chocolate bars, each costing £1.20, by multiplying 8 by £1.20, resulting in £9.60. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/5)%20Dividing%20a%20Price.webp Calculating £9.60 divided by 3 step by step using pounds and pence, resulting in £3.20. https://maths-angel.com/lessons/vertex-form https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/vertex-form/vertex-form-and-parabola-transformations-math-angel.webp Vertex form y = a(x - h)² + k showing the vertex point (h, k) on a parabola graph https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/vertex-form/vertex-form-and-parabola-transformations-welcome-visual.webp Vertex Form and Parabola Transformations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/vertex-form/1)%20Vertex%20Form%20of%20Quadratic%20Equations.webp Vertex form of quadratic equation y = a(x - h)² + k, showing the vertex at point (h,k) on a graph of a parabola. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/vertex-form/2)%20How%20to%20Find%20the%20Vertex%20of%20a%20Quadratic%20Function.webp Vertex form of quadratic equation y = a(x - h)² + k showing how horizontal (h) and vertical (k) shifts affect a parabola's position on a graph. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/vertex-form/3)%20Transformations%20of%20Quadratic%20Functions%20Using%20the%20Vertex.webp Graph showing transformation of the quadratic equation from y = -2x² with vertex (0,0) to y = -2(x+2)² + 3 with vertex (-2,3), shifting the parabola. https://maths-angel.com/lessons/reflecting-points-coordinate-plane https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/plotting-and-reflecting-points-on-the-coordinate-plane-math-angel.webp Coordinate plane with points (−3, 2) and (3, 2) reflected across the y-axis, showing how to locate, read, and reflect points https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/plotting-and-reflecting-points-on-the-coordinate-plane-welcome-visual.webp Plotting and Reflecting Points on the Coordinate Plane - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/1)%20Coordinate%20System.webp Coordinate system graph showing positive and negative numbers, with the origin marked at (0,0). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/2)%20Locating%20Points%20on%20Coordinate%20System.webp Locating points on a coordinate system with positive and negative coordinates. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/3)%20Reflecting%20Points%20over%20the%20y-axis.webp Explanation on how to reflect (-3, 2) on a coordinate grid across the y-axis to (3, 2), by changing the sign of x. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/4)%20Reflecting%20point%20over%20x-axis.webp Explanation on how to reflect (-3, 2) on a coordinate grid across the x-axis to (-3, -2), by changing the sign of y. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/5)%20Reflecting%20Point%20over%20the%20origin.webp Explanation on how to reflect (-3, 2) on a coordinate grid across the origin to (3, -2), by changing both the signs of x and y. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/6)%20Reflecting%20Figure%20over%20y-axis.webp Reflecting a triangle over the y-axis by changing the sign of the x-coordinate of all points. https://maths-angel.com/lessons/units-of-length https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-length/converting-and-calculating-units-of-length-math-angel.webp Metric units of length conversion chart showing km, m, cm, and mm with examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-length/units-of-length-welcome-visual.webp Converting and Calculating Units of Length - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-length/1)%20Converting%20Units%20of%20Length.webp Conversion chart for metric units of length showing millimetres, centimetres, metres, and kilometres with examples. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-length/2)%20Converting%20Units%20of%20Length%20Example.webp Converting 47 metres to 4700 centimetres and 5020 metres to 5.020 kilometres using unit conversion rules. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-length/3)%20Calculating%20Units%20of%20Length.webp Adding and subtracting units of length by standardising to one unit first, showing 1.75 m + 40 cm = 2.15 m and 1.75 m - 40 cm = 1.35 m as examples. https://maths-angel.com/lessons/converting-standard-form-and-vertex-form https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/converting-standard-form-and-vertex-form/converting-quadratics-standard-form-and-vertex-form-math-angel.webp Converting a quadratic from general form y = ax² + bx + c to vertex form y = a(x-h)² + k https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/converting-standard-form-and-vertex-form/converting-quadratics-standard-form-and-vertex-form-welcome-visual.webp Converting Quadratics: Standard Form and Vertex Form - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/converting-standard-form-and-vertex-form/1)%20General%20Form%20and%20Vertex%20Form.webp Converting quadratic equations between general form y = ax² + bx + c and vertex form y = a(x - h)² + k, where a ≠ 0. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/converting-standard-form-and-vertex-form/2)%20Converting%20Vertex%20to%20General%20Form.webp Converting a quadratic equation from vertex form, y = 2(x - 3)² - 5, to general form by expanding and simplifying to y = 2x² - 12x + 13. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/converting-standard-form-and-vertex-form/3)%20Converting%20General%20to%20Vertex%20Form.webp Conversion of a quadratic equation from general form y = 3x² + 18x + 25 to vertex form by completing the square, resulting in y = 3(x + 3)² - 2. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/converting-standard-form-and-vertex-form/4)%20Converting%20General%20to%20Vertex%20Form.webp Converting the quadratic equation y = -2x² + 8x - 5 from general to vertex form using completing the square method, resulting in y = -2(x - 2)² + 3. https://maths-angel.com/lessons/translating-shapes https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/translating-shapes/translating-shapes-math-angel.webp Translating shapes lesson preview showing a shape moved on a grid using a column vector https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/translating-shapes/translating-shapes-welcome-visual.webp Translating Shapes - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/translating-shapes/1)%20Translation.webp Column vectors with visual examples. Describes horizontal and vertical shifts using positive and negative values. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/translating-shapes/2)%20Column%20vectors.webp Examples of vectors as ordered pairs, illustrating horizontal and vertical shifts on a grid with arrows and numerical values. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/translating-shapes/3)%20Translating%20with%20a%20column%20vector.webp Shape P is translated to shape Q on a grid by column vector (8, -3), with horizontal shift of 8 units and vertical shift of -3 units. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/translating-shapes/4)%20Find%20the%20column%20vector%20of%20a%20translation.webp Translation of triangle M to triangle N on a grid using column vector (-10, -4), with -10 units left and -4 units down. https://maths-angel.com/lessons/units-of-mass https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-mass/converting-and-calculating-units-of-mass-math-angel.webp Metric units of mass conversion chart showing tonnes, kilograms, grams, and milligrams https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-mass/converting-and-calculating-units-of-mass-welcome-visual.webp Converting and Calculating Units of Mass - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-mass/1)%20Converting%20Units%20of%20Mass.webp Units of mass conversion chart showing milligrams, grams, kilograms, and tonnes with examples: 10 mg pills, 500 g pasta, 5 kg rice, and 8 t crane. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-mass/2)%20Converting%20Units%20of%20Length%20Example.webp Converting 21 kilograms to 21000 grams and 560 kilograms to 0.56 tonnes using multiplication and division by 1000. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-mass/3)%20Calculating%20Units%20of%20Mass.webp Adding and subtracting units of mass by converting to one unit first, showing 3.25 kg + 30 g = 3.28 kg and 3.25 kg - 30 g = 3.22 kg as examples. https://maths-angel.com/lessons/quadratic-equations-in-vertex-form-standard-form https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-equations-in-vertex-form-standard-form/how-to-write-quadratic-equations-in-vertex-form-and-standard-form-math-angel.webp Quadratic equations in vertex form y = a(x-h)² + k and standard form y = ax² + bx + c https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-equations-in-vertex-form-standard-form/how-to-write-quadratic-equations-in-vertex-form-and-standard-form-welcome-visual.webp How to Write Quadratic Equations in Vertex Form and Standard Form - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-equations-in-vertex-form-standard-form/1)%20Determining%20Quadratic%20Equations.webp Quadratic equations with vertex form y = a(x - h)² + k and general form y = ax² + bx + c, labelled as methods for forming quadratic equations. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-equations-in-vertex-form-standard-form/2)%20Determining%20quadratic%20equations%20through%20vertex%20form.webp Forming a quadratic equation using vertex form with equation y = -2(x - 2)² + 3, where the vertex is (2,3) and the curve passes through (3,1). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-equations-in-vertex-form-standard-form/3)%20Determining%20quadratic%20equations%20through%20General%20Form.webp Forming quadratic equations using the general form y = 2x² - x + 3, solving coefficients with three given points: (0,3), (1,4), and (2,9). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-equations-in-vertex-form-standard-form/4)%20Application%20of%20Quadratic%20Equations.webp Solving the classic tunnel problem. The parabola equation is y = -5/9 · x² + 5 and the vertex is at (0,5). When x = 1, the truck can pass through. https://maths-angel.com/lessons/rotating-shapes https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotating-shapes/rotating-shapes-math-angel.webp Rotating shapes lesson preview showing a shape rotated around a centre of rotation on a grid https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotating-shapes/rotating-shapes-welcome-visual.webp Rotating Shapes - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotating-shapes/1)%20What%20is%20Rotation.webp Diagram explaining rotation in geometry with examples, including the centre of rotation, direction (clockwise or anticlockwise), and angle. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotating-shapes/2)%20Rotate%20Shapes%20with%20a%20Tracing%20Paper.webp Rotating shape P 90 degrees clockwise about point O on a coordinate grid, resulting in shape Q. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotating-shapes/3)%20Rotate%20Shapes%20by%20Drawing%20Lines.webp Rotating shape P 90° anticlockwise about point O using auxiliary lines, resulting in shape Q, shown on a grid with axes. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotating-shapes/4)%20How%20to%20Find%20the%20Centre%20of%20Rotation.webp Rotating triangle P rotated 90° anticlockwise about the (2, 3) to triangle Q, with perpendicular bisectors intersecting at the centre of rotation. https://maths-angel.com/lessons/converting-time https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/converting-time/converting-time-and-calculating-time-math-angel.webp Converting time and calculating time lesson covering hours, minutes, and seconds https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/converting-time/converting-time-and-calculating-time-welcome-visual.webp Converting Time and Calculating Time - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/converting-time/1)%20Converting%20Units%20of%20Time.webp Conversions between units of time showing 1 day equals 24 hours, 1 hour equals 60 minutes, and 1 minute equals 60 seconds. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/converting-time/2)%20Examples%20on%20Converting%20Units%20of%20Time.webp Converting time examples with 2 hours equalling 120 minutes and 300 seconds equalling 5 minutes. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/converting-time/3)%20Adding%20Time.webp Adding time: 35 min 20 s + 20 min 45 s = 55 min + 65 s, then converting 65 s to 1 min 5 s, giving 56 min 5 s https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/converting-time/4)%20Subtracting%20Time.webp STime difference: 56 min 5 s − 54 min 23 s, subtracting minutes and seconds separately with borrowing, result 1 min 42 s https://maths-angel.com/lessons/solving-simple-quadratic-equations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/solving-simple-quadratic-equations-math-angel.webp Solving simple quadratic equations showing x² = k with solutions x = ±√k https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/solving-simple-quadratic-equations-welcome-visual.webp Solving Simple Quadratic Equations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/1)%20Solving%20Simple%20Quadratics.webp Solving the quadratic equation x² = k, showing the general solution x equals plus or minus the square root of k, and example of x² = 9 with solutions. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/2)%20Solving%20Quadratic%20Equations%20Example.webp Solving quadratic equations with the steps to isolate x² and find solutions x sub one equals the positive square root of k. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/3)%20Solving%20Quadratic%20Equations%20No%20Solution.webp Solving quadratic equations, demonstrating x² = k and x² + 50 = 0 leading to no real solution since x² = -25. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/4)%20Solving%20Quadratic%20Equations%20Factorising.webp Solving quadratic equations by factorisation, showing x² - dx = 0 with solutions x sub one equals zero, and x sub two equals d. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/5)%20Solving%20Quadratic%20Equations%20Example.webp Solving quadratic equation x² - dx = 0 with steps to simplify and factorise, showing solutions x₁ = 0 and x₂ = 5. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/6)%20Overview%20Solving%20Simple%20Quadratic%20Equations.webp Solving simple quadratic equations: x² = k gives x = ±√k, and x² − dx = 0 factors to x = 0 or x = d. https://maths-angel.com/lessons/enlargement https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/enlargement/introduction-to-enlargement-math-angel.webp Enlargement lesson preview showing a shape scaled by different factors from a centre of enlargement https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/enlargement/introduction-to-enlargement-welcome-visual.webp Introduction to Enlargement - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/enlargement/1)%20What%20Is%20Enlargement.webp Illustration explaining enlargement as a transformation, showing triangles scaled from widths 2 to 4 to 8. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/enlargement/2)%20Key%20Concepts%20in%20Enlargement.webp Enlarged triangles on a coordinate grid from centre P, showing scale factor 2, 4 and 8 and that factors >1 enlarge and 0-1 reduce https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/enlargement/3)%20How%20to%20Enlarge%20a%20Shape.webp Triangle enlarged by scale factor 3 from point P on a coordinate grid, with rays from P to vertices and new vertices marked three times further away https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/enlargement/4)%20Finding%20the%20Centre%20of%20Enlargement.webp Coordinate grid showing trapezium A enlarged to trapezium B with lines from matching vertices meeting at centre of enlargement (0,0). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/enlargement/5)%20Enlargement%20from%20Trapezium%20A%20to%20B.webp Trapezium A enlarged to trapezium B on a coordinate grid, with lines to centre of enlargement O and scale factor 2 shown by lengths 4 and 8 https://maths-angel.com/lessons/divisibility-rules https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/divisibility-rules/divisibility-and-divisibility-rules-math-angel.webp Divisibility rules for 2, 4, and 8 using last-digit checks, with worked examples for 26, 328, and 6160 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/divisibility-rules/divisibility-and-divisibility-rules-welcome-visual.webp Divisibility and Divisibility Rules - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/divisibility-rules/1)%20Divisibility.webp Divisibility explained with bananas — dividing 9 by 2 leaves a remainder, but dividing by 3 gives no remainder https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/divisibility-rules/2)%20Divisibility%20Rules%20for%202%2C4%2C8.webp Divisibility rules for 2, 4, and 8 based on last digits with examples 26, 328, and 6160 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/divisibility-rules/3)%20Divisibility%20Rules%20for%203%2C6%2C9.webp Divisibility rules for 3, 6, and 9 using digit sum method with examples 543, 198, and 402 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/divisibility-rules/4)%20Divisibility%20Rules%20for%205%2C%2010.webp Divisibility rules for 5 and 10 — last digit must be 0 or 5 for five, and 0 for ten, with examples https://maths-angel.com/lessons/solving-quadratic-equations-factorising https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-quadratic-equations-factorising/solving-quadratic-equations-by-factorising-math-angel.webp Factorising x² + 5x + 6 = 0 into (x + 2)(x + 3) = 0, finding factors that multiply to 6 and add to 5 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-quadratic-equations-factorising/solving-quadratic-equations-by-factorising-welcome-visual.webp Solving Quadratic Equations by Factorising - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-quadratic-equations-factorising/1)%20Factorisation%20Method.webp Solving quadratic equations by factorisation step-by-step, note finding two numbers that multiply to the constant and add up to the coefficient of x. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-quadratic-equations-factorising/2)%20Solving%20Quadratic%20Equations.webp Solving quadratic equations by factorisation, with example x² + 7x + 12 = 0, note steps to find factors 3 and 4, with solutions. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-quadratic-equations-factorising/3)%20Practice%20Solving%20Quadratic%20Equations%20by%20Factorising.webp Solving quadratic equations by factorisation: find two numbers that multiply to be the constant (-18) and add up to be the coefficient of x (3). https://maths-angel.com/lessons/constructing-triangles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/constructing-triangles/constructing-triangles-math-angel.webp Constructing triangles lesson preview showing ASA, SAS, and SSS methods with compass and ruler https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/constructing-triangles/constructing-triangles-welcome-visual.webp Constructing Triangles - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/constructing-triangles/1)%20Triangle%20Components.webp A triangle with vertices A, B, and C, sides a, b, and c, and angles alpha, beta, and gamma. The vertices are labelled anticlockwise. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/constructing-triangles/2)%20Construct%20Triangle%20(ASA).webp Constructing a triangle ABC with angles 60° and 70°, side c = 6 cm using compass and ruler. The sides and angles are labelled. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/constructing-triangles/3)%20Construct%20Triangle%20(SAS).webp Constructing a triangle ABC with sides 5 cm and 6 cm, and angle 50°, including labelled diagram. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/constructing-triangles/4)%20Constructing%20Triangles(Common%20Pitfall).webp Constructing a triangle ABC with sides a = 7 cm, b = 5 cm, and angle beta = 40°, showing two possible triangles with different angles at vertex C. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/constructing-triangles/5)%20Construct%20Triangle%20(SSS).webp Constructing triangle ABC with sides 4 cm, 5 cm, and 6 cm using compass and ruler, including labelled angles alpha, beta, and gamma. https://maths-angel.com/lessons/prime-numbers-prime-factorisation https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/prime-numbers-prime-factorisation/prime-numbers-and-prime-factorisation-math-angel.webp Prime numbers under 20 and prime factorisation of 126 = 2 × 3² × 7 using a factor tree https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/prime-numbers-prime-factorisation/prime-numbers-and-prime-factorisation-welcome-visual.webp Prime Numbers and Prime Factorisation - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/prime-numbers-prime-factorisation/1)%20Prime%20Numbers.webp Explanation and example of prime numbers, stating that 2 is the smallest prime number. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/prime-numbers-prime-factorisation/2)%20Prime%20Numbers%20below%2020.webp Cartoon dolphin showing prime numbers under 20, which are 2, 3, 5, 7, 11, 13, 17, and 19. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/prime-numbers-prime-factorisation/3)%20Prime%20Factorisation%20Division%20Method.webp Prime factorisation of 90 using the division method step by step. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/prime-numbers-prime-factorisation/4)%20Prime%20Factorisation%20Tree%20Method.webp Prime factorisation of 126 using the factor tree method step by step. https://maths-angel.com/lessons/quadratic-formula https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-formula/solving-quadratic-equations-quadratic-formula-math-angel.webp Quadratic formula applied to 3x² − 5x + 2 = 0 with step-by-step substitution, discriminant = 1, roots x = 1 and x = ⅔ https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-formula/solving-quadratic-equations-quadratic-formula-welcome-visual.webp Solving Quadratic Equations: Quadratic Formula - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-formula/1)%20The%20Quadratic%20Formula.webp Quadratic formula for solving quadratic equations, and the discriminant for determining the number of real roots. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-formula/2)%20Example%20of%20How%20to%20Use%20the%20Quadratic%20Formula.webp Quadratic formula example with a = 3, b = 5, c = 2 solving 3x² − 5x + 2 = 0, giving roots x₁ = 1 and x₂ = 2/3. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-formula/3)%20How%20to%20Apply%20the%20Quadratic%20Formula.webp Solving a quadratic equation using the quadratic formula, with step-by-step breakdown and final solutions. https://maths-angel.com/lessons/congruent-triangles https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/congruent-triangles-math-angel.webp Congruent triangles lesson preview showing SSS, SAS, ASA, and RHS rules with labelled triangle pairs https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/congruent-triangles-welcome-visual.webp Congruent Triangles - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/1)%20Congruent%20Triangles%20Definition.webp Diagram showing the criteria for identifying congruent triangles: SSS, SAS, ASA, and RHS with corresponding labelled triangles. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/2)%20Congruent%20Triangles%20Rules.webp Diagram showing the criteria for identifying congruent triangles: SSS, SAS, ASA, and RHS with corresponding labelled triangles. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/3)%20Congruent%20Triangles%20(Side-Side-Side).webp Identifying congruent triangles using SSS (side, side, side) criteria with two triangles both having sides of 3 cm, 5 cm, and 6 cm. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/4)%20Congruent%20Triangles%20(Side-Angle-Side).webp Identifying congruent triangles using SAS (Side, Angle, Side) rule with two triangles having sides of 3 cm, 5 cm, and an included angle of 70 degrees. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/5)%20Congruent%20Triangles%20(Angle-Side-Angle).webp Identifying congruent triangles using ASA (Angle, Side, Angle) with two example triangles showing two angles and the included side as the same. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/6)%20Congruent%20Triangles%20(RHS).webp Identifying congruent triangles using RHS criteria with examples of right-angle triangles having the same hypotenuse and one identical side. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/7)%20Congruent%20Triangles%20(Common%20Pitfall).webp Illustrating that two triangles are not necessarily congruent if they share two equal sides and a non-included angle. https://maths-angel.com/lessons/hcf-and-lcm https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/hcf-and-lcm/how-to-find-hcf-and-lcm-math-angel.webp Step-by-step guide showing how to find HCF and LCM using prime factorisation with worked examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/hcf-and-lcm/how-to-find-hcf-and-lcm-welcome-visual.webp How to Find HCF and LCM - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/hcf-and-lcm/1)%20What%20is%20HCF%20and%20LCM.webp Explanation that HCF is the biggest factor shared and LCM is the smallest multiple shared. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/hcf-and-lcm/2)%20Finding%20HCF%20and%20LCM%20by%20Listing.webp Method for finding Highest Common Factor (HCF) and Lowest Common Multiple (LCM) by listing factors and multiples, with HCF of 6 and LCM of 36. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/hcf-and-lcm/3)%20Finding%20HCF%20and%20LCM%20by%20Prime%20Factorisation.webp Using prime factorisation to find HCF and LCM for numbers 180 and 168, with step-by-step calculations and final results. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/hcf-and-lcm/4)%20Finding%20HCF%20and%20LCM%20-%20Further%20Example.webp Prime factorisation of 56 and 100 to find HCF as 2² = 4 and LCM as 2³ × 5² × 7 = 1400. https://maths-angel.com/lessons/equations-with-2-variables https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equations-with-2-variables/solving-equations-with-two-variables-math-angel.webp Solving the equation x + 2y = 20 with multiple solutions showing different pairs of x and y values https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equations-with-2-variables/solving-equations-with-2-variables-welcome-visual.webp Solving Equations with 2 Variables - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equations-with-2-variables/1)%20Equations%20with%202%20Variables.webp Using the equation x + 2y = 20 to illustrate prices of items with various solutions for variables x and y, illustrating multiple solutions. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equations-with-2-variables/2)%20Solving%20Equation%20with%202%20variables.webp Solving the equation 10 + 2y = 20 by plugging in x = 10 and finding y = 5, illustrating linear equations in two variables. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equations-with-2-variables/3)%20Solving%20Equations%20with%202%20Variables%20Graphically.webp Graphical solution of the system of equations y = -0.5x + 10 and x + 2y = 20 with highlighted intersection point (8, 6). https://maths-angel.com/lessons/perpendicular-bisectors-and-circumcircle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-bisectors-and-circumcircle/perpendicular-bisectors-and-circumcircle-math-angel.webp Perpendicular bisector dividing a line segment in half at a 90° angle, with the midpoint labelled https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-bisectors-and-circumcircle/perpendicular-bisectors-and-circumcircle-welcome-visual.webp Perpendicular Bisectors and Circumcircle - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-bisectors-and-circumcircle/1)%20Perpendicular%20Bisector.webp Perpendicular bisector dividing a line segment at a 90-degree angle with midpoint marked. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-bisectors-and-circumcircle/2)%20Drawing%20a%20Perpendicular%20Bisector.webp Instructions for drawing a perpendicular bisector with a ruler and a compass. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-bisectors-and-circumcircle/3)%20Key%20Property%20of%20the%20Perpendicular%20Bisector.webp Triangle with perpendicular bisectors meeting at the circumcentre, inside a circumcircle passing through all three vertices. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-bisectors-and-circumcircle/4)%20Triangle%20Circumcentre.webp Diagram of a triangle’s circumcentre, showing the circumradius, circumscribed circle (circumcircle), and the intersection of perpendicular bisectors. https://maths-angel.com/lessons/introduction-to-fractions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/introduction-to-fractions-math-angel.webp Introduction to fractions showing numerator and denominator with pizza slice examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/introduction-to-fractions-welcome-visual.webp Introduction to Fractions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/1)%20Introduction%20to%20Fractions.webp Explanation of fractions with a pizza divided into eight slices, illustrating one-eighth and three-eighths fractions. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/2)%20What%20is%20a%20Fraction.webp Explanation of fractions with numerators and denominators, showing a pizza divided into eight equal parts. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/3)%20Understanding%20Fractions.webp Understanding fractions with examples, showing 4 out of 9 coloured parts in a circle and an unequally divided rectangle. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/4)%20Fractions%20Examples.webp Applying fractions to real-world examples, including finding 3/4 of 20 cm using a ruler and 5/6 of 2 hours using a clock. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/5)%20Applying%20Fractions.webp Splitting £50 using fractions: the calculation shows it is divided into 10 parts, 1 part = £5, your share = 3 parts, total = £15. https://maths-angel.com/lessons/solving-simultaneous-equations-graphically https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simultaneous-equations-graphically/solving-simultaneous-equations-graphically-math-angel.webp Simultaneous equations x + y = 20 and x − y = 10 modelling Sebastian's and Sarah's ages as a system of linear equations https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simultaneous-equations-graphically/solving-simultaneous-equations-graphically-welcome-visual.webp Solving Simultaneous Equations Graphically - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simultaneous-equations-graphically/1)%20Simultaneous%20Equations.webp System of linear equations representing Sebastian's and Sarah's ages with equations x + y = 20 and x - y = 10. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simultaneous-equations-graphically/2)%20Finding%20the%20Solution%20of%20System%20of%20Equations.webp Solving a system of equations graphically, transforming and plotting the equations y = -x + 20 and y = x - 10 to find their intersection at (15, 5). https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simultaneous-equations-graphically/3)%20Possible%20Solutions%20in%20Simultaneous%20Equations.webp Three graphical linear equations showing one solution (intersection), no solution (parallel lines), and infinite solutions (overlapping lines). https://maths-angel.com/lessons/angle-bisectors-and-incircle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-bisectors-and-incircle/angle-bisectors-and-incircle-math-angel.webp Constructing an angle bisector two ways: with a protractor splitting 40° into 20° halves, and with a compass using arcs https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-bisectors-and-incircle/angle-bisectors-and-incircle-welcome-visual.webp Angle Bisectors and Incircle - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-bisectors-and-incircle/1)%20Angle%20Bisector.webp Angle bisector dividing an angle into two equal parts, with one half labelled alpha over two and the other half also labelled alpha over two. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-bisectors-and-incircle/2)%20Drawing%20Angle%20Bisectors.webp Constructing an angle bisector using a protractor and compass, showing steps for accurate measurement and drawing. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-bisectors-and-incircle/3)%20Angle%20Bisector%20Property.webp Key property of angle bisectors shown with diagram: every point on the angle bisector is equidistant from the angle's sides. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-bisectors-and-incircle/4)%20Triangle%20Incircle.webp Explanation of a triangle's in-centre and in-circle, showing the largest circle that can fit inside the triangle, with in-radius and angle bisectors. https://maths-angel.com/lessons/equivalent-fractions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/equivalent-fractions-math-angel.webp Equivalent fractions — simplifying 18/63 to 2/7 and expanding 2/7 to 18/63 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/equivalent-fractions-welcome-visual.webp Equivalent Fractions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/1)%20Expanding%20Fractions.webp Expanding fractions example showing 1/2 multiplied by 8 to get 8/16 with visual representation of equivalent fractions 1/2, 2/4, 4/8, and 8/16. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/2)%20Simplifying%20Fractions.webp Illustration shows simplifying fractions with examples of 8/16 simplified to 1/2 and equivalent fractions 1/2, 2/4, 4/8, and 8/16 using shaded boxes. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/3)%20Expanding%20and%20Simplifying%20Fractions%20Examples.webp Simplifying 18/63 to 2/7 by dividing by 9 and expanding 2/7 to 18/63 by multiplying by 9. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/4)%20Expanding%20and%20Simplifying%20Fractions%20Practice.webp Expanding fractions by multiplying and simplifying fractions by dividing using the example of 12/20 and 72/120. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/5)%20Fully%20Simplified%20Fractions.webp Fully simplified fractions example, showing the fraction 480/1260 simplified to 8/21 by dividing both numerator and denominator by common factors. https://maths-angel.com/lessons/equal-values-and-substitution-method https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equal-values-and-substitution-method/simultaneous-equations-equal-values-and-substitution-method-math-angel.webp Equal values method solving 2x + y = 8 and x - y = 1, showing steps to find x = 3 and y = 2 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equal-values-and-substitution-method/simultaneous-equations-equal-values-and-substitution-method-welcome-visual.webp Simultaneous Equations: Equal Values and Substitution Method - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equal-values-and-substitution-method/1)%20Equal%20Value%20Methods.webp Equal Values Method steps to solve equations by isolating the same variable, with example 2x + y = 8 and x - y = 1, resulting in x = 3 and y = 2. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equal-values-and-substitution-method/2)%20Substitution%20Method.webp Steps to solve a system of equations using the substitution method, expressing one variable in terms of another and verifying the solution. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equal-values-and-substitution-method/3)%20Equal%20Values%20vs%20Substitution%20Method.webp Methods for solving linear systems using Equal Values and Substitution methods, showing steps to isolate variables and solve equations. https://maths-angel.com/lessons/medians-and-centroid-of-a-triangle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/medians-and-centroid-of-a-triangle/medians-and-centroid-of-a-triangle-math-angel.webp Medians and centroid of a triangle lesson preview showing three medians meeting at the centroid https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/medians-and-centroid-of-a-triangle/medians-and-centroid-of-a-triangle-welcome-visual.webp Medians and Centroid of a Triangle - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/medians-and-centroid-of-a-triangle/1)%20Median%20of%20a%20Triangle.webp The definition of a median of a triangle is that it connects a vertex to the midpoint of the opposite side, dividing it into two equal-area triangles. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/medians-and-centroid-of-a-triangle/2)%20Centroid%20of%20a%20Triangle.webp The definition of the centroid of a triangle is the point where the three medians intersect, dividing each median in a 2:1 ratio. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/medians-and-centroid-of-a-triangle/3)%20Median%20and%20Centroid%20of%20a%20Triangle.webp The median and centroid of a triangle apply to the problem. https://maths-angel.com/lessons/comparing-fractions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-fractions/comparing-fractions-math-angel.webp Comparing fractions with same denominator (5/8 > 3/8) and same numerator (4/5 > 4/9) using chocolate bar and pizza visuals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-fractions/comparing-fractions-welcome-visual.webp Comparing Fractions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-fractions/1)%20Rules%20for%20Comparing%20Fractions.webp Comparing fractions, showing 5/8 is greater than 3/8 with chocolate bars, and 4/5 is greater than 4/9 with pizza slices. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-fractions/2)%20Common%20Denominator%20Method.webp Steps to compare fractions by finding the lowest common multiple (LCM) of denominators and converting fractions to have the same denominator. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-fractions/3)%20Practise%20Comparing%20Fractions%20part%201.webp Comparing fractions by finding the lowest common multiple (LCM) of denominators, converting fractions, and identifying the larger numerator. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-fractions/4)%20Practise%20Comparing%20Fractions%20part%202.webp Step-by-step method comparing 4/11 and 5/12 by finding LCM 132, converting fractions to 48/132 and 55/132, showing 4/11 < 5/12. https://maths-angel.com/lessons/elimination-method https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/elimination-method/elimination-method-for-solving-simultaneous-equations-math-angel.webp Elimination method steps: adding simultaneous equations to remove one variable https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/elimination-method/elimination-method-for-solving-simultaneous-equations-welcome-visual.webp Elimination Method for Solving Simultaneous Equations - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/elimination-method/1)%20The%20Elimination%20Method.webp The definition of the elimination method is that it removes one variable (x or y) by adding or subtracting two equations. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/elimination-method/2)%20Elimination%20through%20Addition.webp Demonstrating the elimination method in solving simultaneous equations by adding or subtracting variables x and y. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/elimination-method/3)%20Elimination%20through%20Transform%20and%20Addition.webp Solving simultaneous equations using the elimination method with subtraction steps. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/elimination-method/4)%20Elimination%20Through%20Subtraction.webp Steps for solving simultaneous equations using the elimination method with subtraction, illustrated with equations. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/elimination-method/5)%20Addition%20vs%20Subtraction%20Method.webp Elimination method for solving simultaneous equations, and steps of transform, eliminate, and solve with addition and subtraction examples. https://maths-angel.com/lessons/solids-units-of-volume https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/solids-units-of-volume/solids-and-units-of-volume-math-angel.webp Units of volume chart comparing mm³, cm³, mL, L, and m³ with edge lengths and real-life examples like a dice and milk carton. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/solids-units-of-volume/solids-and-units-of-volume-welcome-visual.webp Solids and Units of Volume - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/solids-units-of-volume/1)%20Solids.webp Rectangular prism with labelled dimensions for length, width, and height, representing a 3D solid shape in geometry. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/solids-units-of-volume/2)%20Cuboid%20and%20Cubes.webp Showing the properties of solids, focusing on cuboids and cubes, with details on vertices, edges, and faces, comparing rectangle and square faces. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/solids-units-of-volume/3)%20Volume.webp Diagram showing volume of a cube: 27 unit cubes (1 cm³ each) form a 3×3×3 cube with total volume of 27 cm³. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/solids-units-of-volume/4)%20Units%20of%20Volume.webp Volume units chart showing cubic millimetre, cubic centimetre, litre, and cubic metre with examples and corresponding edge lengths. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/solids-units-of-volume/5)%20Converting%20between%20Units%20of%20Volume.webp Converting units of volume between cubic millimetres, cubic centimetres, millilitres, litres, and cubic metres with examples. https://maths-angel.com/lessons/adding-and-subtracting-fractions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-fractions/adding-and-subtracting-fractions-math-angel.webp Adding and subtracting like and unlike fractions with common denominators and worked examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-fractions/adding-and-subtracting-fractions-welcome-visual.webp Adding and Subtracting Fractions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-fractions/1)%20Adding%20Subtracting%20Like%20Fractions.webp Explanation of the addition of fractions with the same denominator using pizza slices to illustrate. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-fractions/2)%20Adding%20Subtracting%20Unlike%20Fractions.webp Adding and subtracting fractions with different denominators. Showing the steps to make the denominators the same and subtract fractions 5/6 and 1/4. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-fractions/3)%20Proper%2C%20Improper%2C%20Mixed%20Fractions.webp Different types of fractions in a diagram showing proper fractions, improper fractions, and mixed fractions with examples. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-fractions/4)%20Improper%20Fractions%20to%20Mixed%20Fractions.webp Converting between improper fractions and mixed numbers with step-by-step calculations. https://maths-angel.com/lessons/volume-of-a-cuboid https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-of-a-cuboid/volume-of-a-cuboid-and-cube-math-angel.webp Volume of a cuboid and cube lesson preview showing 3D shapes with labelled length, width, and height https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-of-a-cuboid/volume-of-a-cuboid-and-cube-welcome-visual.webp Volume of a Cuboid and Cube - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-of-a-cuboid/1)%20Volume%20of%20Cuboids%20an%20Cubes.webp Diagram showing the volume formulas of a cuboid and a cube. Cuboid: 5 cm x 3 cm x 2 cm, volume 30 cm³. Cube: 5 cm sides, volume 125 cm³. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-of-a-cuboid/2)%20Volume%20of%20Cuboids%20Calculation.webp Solving for width of a cuboid using volume equals length times width times height formula, with given volume 120 m³, length 10 m, height 2 m. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-of-a-cuboid/3)%20Volume%20of%20Complex%20Solids.webp Diagram shows the volume calculation of a complex shape divided into two cuboids A and B, with their respective dimensions and total volume summation. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-of-a-cuboid/4)%20Volume%20of%20Cuboid%20Application.webp The application of cuboid volume formula to calculate water container problem, with dimensions 50 cm x 30 cm x 20 cm, using a flow rate of 10 L/min. https://maths-angel.com/lessons/multiplying-fractions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-fractions/multiplying-fractions-math-angel.webp Multiplying fractions lesson covering cross-cancelling, whole numbers, and mixed number examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-fractions/multiplying-fractions-welcome-visual.webp Multiplying Fractions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-fractions/1)%20Multiplying%20Fractions%20and%20Cross-Cancelling.webp Step-by-step method for multiplying fractions: multiply numerators, multiply denominators, then simplify the result https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-fractions/2)%20Practising%20Cross-Cancelling.webp Cross-cancelling example showing how to simplify before multiplying fractions for an easier calculation https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-fractions/3)%20Fraction%20times%20Number.webp Multiplying a fraction by a whole number: 88 times 13/22 using cross-cancelling to find 52 black piano keys https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-fractions/4)%20Multiplying%20Mixed%20Fractions.webp Converting mixed numbers to improper fractions before multiplying, with worked example and final answer https://maths-angel.com/lessons/surface-area https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/surface-area/surface-area-of-solids-math-angel.webp Surface area of solids lesson preview showing a cuboid with labelled faces and dimensions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/surface-area/surface-area-of-solids-welcome-visual.webp Surface Area of Solids - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/surface-area/1)%20Surface%20Area%20of%20Solids.webp Surface area calculation of a cuboid with labelled dimensions: length (l), width (w), and height (h). Illustration highlights 6 faces in 3 pairs. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/surface-area/2)%20Surface%20Area%20of%20Cuboids%20and%20Cubes.webp Illustration showing surface area formulas for a cuboid and a cube. The cuboid formula is 2lw + 2lh + 2hw, and the cube formula is 6a². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/surface-area/3)%20Calculating%20Surface%20Area%20of%20a%20Cuboid.webp Diagram illustrating how to find the surface area of a cuboid with dimensions, by breaking down the calculations for each face and sum up. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/surface-area/4)%20Calculating%20the%20surface%20area%20of%20a%20Prism.webp A trapezoidal prism with labelled dimensions used to calculate its surface area. The faces include front and back triangles, base, top, and side. https://maths-angel.com/lessons/dividing-fractions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/dividing-fractions/dividing-fractions-math-angel.webp Dividing fractions lesson showing reciprocal method with whole numbers and mixed number examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/dividing-fractions/dividing-fractions-welcome-visual.webp Dividing Fractions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/dividing-fractions/1)%20Division%20with%20Fractions.webp Step-by-step dividing fractions method: change division to multiplication, flip the second fraction, and simplify https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/dividing-fractions/2)%20Dividing%20Fractions%20by%20a%20Whole%20Number.webp Dividing a fraction by a whole number: writing it as a fraction, flipping to the reciprocal, and cross-cancelling https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/dividing-fractions/3)%20Handling%20Mixed%20Fractions.webp Dividing mixed numbers: converting 2⅖ to an improper fraction and dividing by ⅖ using the reciprocal method https://maths-angel.com/lessons/volume-prisms-cylinders https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-prisms-cylinders/volume-of-prisms-and-cylinders-math-angel.webp Volume of prisms and cylinders lesson preview showing the formula V = base area × height https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-prisms-cylinders/volume-of-prisms-and-cylinders-welcome-visual.webp Volume of Prisms and Cylinders - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-prisms-cylinders/1)%20Volume%20of%20Prisms%20and%20Cylinders.webp Volume formulas for prisms and cylinders showing the equation V = B × h, where B is the base area and h is the height. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-prisms-cylinders/2)%20Volume%20of%20Prisms.webp Calculating the volume of a triangular prism using the formula V = B × h, with base dimensions 4 cm by 3 cm, and height 5 cm, resulting in 30 cm³. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-prisms-cylinders/3)%20Volume%20of%20Cylinders.webp Volume calculation of a cylinder with a radius of 2 cm and height of 5 cm, using the formula V = B × h. The final volume is approximately 62.8 cm³. https://maths-angel.com/lessons/decimals-and-fractions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimals-and-fractions/decimals-and-fractions-math-angel.webp Decimal place value chart and step-by-step decimal to fraction conversion with examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimals-and-fractions/decimals-and-fractions-welcome-visual.webp Decimals and Fractions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimals-and-fractions/1)%20Decimal%20and%20Decimal%20Point.webp Place value chart introducing decimals, sort digits from hundreds to thousandths, with the number 12.345 split into whole number and fractional parts. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimals-and-fractions/2)%20Converting%20Decimals%20to%20Fractions.webp Showing decimal to fraction, 0.1 as 1/10, 0.01 as 1/100, 0.001 as 1/1000, 0.4 as 4/10 or 2/5, 0.75 as 75/100 or 3/4, and 0.028 as 28/1000 or 7/250. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimals-and-fractions/3)%20Converting%20Decimals%20greater%20than%201%20to%20Fractions.webp Decimals greater than 1 to fractions, showing conversion of 8.25 to 825/100, 165/20, and 33/4, and breaking 8.25 into 8 and 0.25 as 8 + 1/4. https://maths-angel.com/lessons/cavalieris-principle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cavalieris-principle/principle-of-cavalieri-math-angel.webp Cavalieri's Principle lesson preview showing two solids with equal cross-sections and volumes https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cavalieris-principle/cavalieris-principle-welcome-visual.webp Cavalieri's Principle - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cavalieris-principle/1)%20An%20Example%20of%20Cavalieri%27s%20Principle.webp Two equal-height stacks of 10 slices, one straight and one slanted, illustrating Cavalieri's Principle. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cavalieris-principle/2)%20What%20is%20Cavalieri%27s%20Principle.webp Two identical stacks of bread slices illustrate Cavalieri's principle, showing that even if one stack is tilted, the total volume remains unchanged. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cavalieris-principle/3)%20Calculating%20Volume%20of%20Inclined%20Solids%20Using%20Cavalieri%27s%20Principle.webp Comparison of a rectangular prism and a cylinder, both 10 cm tall, illustrating Cavalieri's principle with equal volumes. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cavalieris-principle/4)%20Check%20Whether%20Two%203D%20Shapes%20Have%20Same%20Volume%20With%20Cavalieri%27s%20Principle.webp Cavalieri’s principle diagram comparing two solids with equal height and cross-sectional areas at every level, explaining they have the same volume. https://maths-angel.com/lessons/comparing-and-rounding-decimals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-and-rounding-decimals/comparing-and-rounding-decimals-math-angel.webp Decimal place value of 12.348 showing 1st, 2nd, and 3rd decimal places as tenths, hundredths, and thousandths https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-and-rounding-decimals/comparing-and-rounding-decimals-welcome-visual.webp Comparing and Rounding Decimals - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-and-rounding-decimals/1)%20Decimal%20Places%20and%20Decimal%20Place%20Value.webp Decimal places and place value chart showing number 12.348 with illustrations highlighting tenths, hundredths, and thousandths. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-and-rounding-decimals/2)%20Rounding%20Decimals%20Rules.webp Rounding decimals, showing rules for rounding up if the digit is 5 or greater, and rounding down if the digit is less than 5, with examples. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-and-rounding-decimals/3)%20How%20to%20Compare%20Decimals.webp Comparison of two decimals, 12.431 and 12.441, with steps to align decimal points, check digits from left to right, and determine the greater decimal. https://maths-angel.com/lessons/volume-surface-area-pyramids-cones-spheres https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/volume-and-surface-area-of-pyramids-cones-spheres-math-angel.webp Volume of a pyramid V = ⅓ × B × h and surface area A = B + L, with labelled 3D diagram and net https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/volume-and-surface-area-of-pyramids-cones-spheres-welcome-visual.webp Volume and Surface Area of Pyramids, Cones, Spheres - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/1)%20What%20is%20a%20Pyramid.webp Diagram showing volume and surface area formulas for a pyramid. Includes base area, height, and the net of the pyramid. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/2)%20Volume%20and%20Surface%20Area%20of%20Pyramids.webp Illustrating the volume and surface area of a square-based pyramid, including calculations for volume and surface area along with the pyramid's net. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/3)%20Volume%20and%20Surface%20Area%20of%20Pyramids%20Example.webp Square pyramid with base 10 cm, height 12 cm, slant 13 cm; net shown; volume 400 cm³, surface area 360 cm². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/4)%20Volume%20and%20Surface%20Area%20of%20Cones.webp The volume and surface area of a cone, showing formulas for volume (V = 1/3 × B × h) and surface area (A = B + L), with net representation. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/5)%20Volume%20and%20Surface%20Area%20of%20Cones%20Example.webp Cone with radius 3 cm, height 5 cm, slant height 6 cm. Volume is calculated to be 15π cm³ and surface area is 27π cm². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/6)%20Volume%20and%20Surface%20Area%20of%20Spheres.webp Cross-section of a sphere with a radius of 3 cm, showing formulas for volume and surface area. https://maths-angel.com/lessons/convert-fraction-to-decimal https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/convert-fraction-to-decimal/convert-fraction-to-decimal-using-long-division-math-angel.webp Step-by-step long division converting fraction 21/16 to terminating decimal 1.3125 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/convert-fraction-to-decimal/convert-fraction-to-decimal-using-long-division-welcome-visual.webp Convert Fraction to Decimal Using Long Division - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/convert-fraction-to-decimal/1)%20Converting%20Fractions%20to%20Decimals.webp Converting fractions like 2/5 and 3/4 to decimals using equivalent fractions and prompting 21/16 as a challenge. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/convert-fraction-to-decimal/2)%20Fractions%20to%20Decimals%20Using%20Long%20Division.webp Convert fractions to decimals using long division with step-by-step example 21 ÷ 16 = 1.3125 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/convert-fraction-to-decimal/3)%20Terminating%20and%20Recurring%20Decimals.webp Comparison of terminating and recurring decimals with examples 0.3 and 0.33333… https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/convert-fraction-to-decimal/4)%20Fractions%20to%20Decimals%20using%20Long%20Division.webp Conversion of fractions to decimals using long division, highlighting terminating decimals (21/16 = 1.3125) and recurring decimals (41/12 = 3.416…). https://maths-angel.com/lessons/pythagoras-theorem https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/pythagoras-theorem/pythagoras-theorem-math-angel.webp Pythagoras' Theorem lesson preview showing a² + b² = c² with a labelled right-angled triangle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/pythagoras-theorem/pythagoras-theorem-welcome-visual.webp Pythagoras' Theorem - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/pythagoras-theorem/1)%20Pythagoras%20Theorem.webp Diagram explaining Pythagoras' theorem using two right-angled triangles, showing the equation a² + b² = c², and an example showing 3² + 4² = 5². https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/pythagoras-theorem/2)%20Pythagoras%20Theorem%2C%20missing%20side%20triangle.webp Right-angled triangle with sides 5 cm, 13 cm, and unknown side x. Using Pythagoras' theorem, x is calculated as 12 cm with steps shown. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/pythagoras-theorem/3)%20Pythagoras%20Theorem%2C%20distance%20two%20points.webp Pythagoras' theorem example showing a right-angled triangle with sides 6, 8, and hypotenuse x. Equation 6² + 8² = x² solves for x = 10. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/pythagoras-theorem/4)%20Pythagoras%20Theorem%2C%20room%20diagonale%20cuboid.webp 3D Pythagoras theorem example in a cuboid: x² = 4² + 2² + 3², giving diagonal length x = √29. https://maths-angel.com/lessons/adding-subtracting-fractions-and-decimals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-subtracting-fractions-and-decimals/adding-and-subtracting-fractions-and-decimals-math-angel.webp Adding and subtracting fractions and decimals using both decimal and fraction conversion methods https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-subtracting-fractions-and-decimals/adding-and-subtracting-fractions-and-decimals-welcome-visual.webp Adding and Subtracting Fractions and Decimals - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-subtracting-fractions-and-decimals/1)%20Decimal%20and%20Fraction%20Method.webp The addition and subtraction of fractions and decimals, demonstrating both methods with worked-out solutions using 2.5 + 1/4 and 3/5 - 1.2. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-subtracting-fractions-and-decimals/2)%20Decimal%20vs%20Fraction%20Method.webp Diagram comparing the decimal and fraction methods for adding and subtracting numbers with examples and conversion steps and tips. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-subtracting-fractions-and-decimals/3)%20Examples%20and%20Tips.webp Adding and subtracting fractions and decimals with conversion of decimals to fractions, finding a common denominator, and solving for the sum. https://maths-angel.com/lessons/trigonometry-sine-cosine-tangent https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/trigonometry-sine-cosine-tangent/trigonometry-sine-cosine-tangent-math-angel.webp Trigonometry lesson preview showing sine, cosine, and tangent ratios in a right-angled triangle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/trigonometry-sine-cosine-tangent/trigonometry-sine-cosine-tangent-welcome-visual.webp Trigonometry: Sine, Cosine, Tangent - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/trigonometry-sine-cosine-tangent/1)%20Trigonometry%2C%20Sine%2C%20Cosine%2C%20Tangent.webp Definitions, ratios, and visuals of sine, cosine, and tangent shown in a right triangle. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/trigonometry-sine-cosine-tangent/2)%20Trigonometry%2C%20Sine%20for%20Finding%20Side.webp A right triangle with 30° angle, opposite side 4 cm. Using the ratio of sin 30°, solve the hypotenuse, which is 8 cm. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/trigonometry-sine-cosine-tangent/3)%20Trigonometry%2C%20Tangent%20for%20Finding%20Side.webp The application of using tangent to find the missing side of a right triangle with a 50-degree angle and a known side of 5 cm. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/trigonometry-sine-cosine-tangent/4)%20Trigonometry%2C%20Cosine%20for%20Finding%20Angle.webp Finding the angle using cosine in a right triangle with sides 4 cm and 8 cm, showing the calculation cos theta = 1/2 and theta = cos⁻¹(1/2) = 60°. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/trigonometry-sine-cosine-tangent/5)%20Trigonometry%2C%20Common%20values%20Sine%2C%20Cosine%2C%20Tangent.webp Common values of sine, cosine, and tangent for 30°, 60°, and 45° with right triangles and ratios. https://maths-angel.com/lessons/multiplying-decimals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-decimals/multiplying-decimals-math-angel.webp Multiplying decimals lesson showing the three-step method with worked examples and decimal point placement https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-decimals/multiplying-decimals-welcome-visual.webp Multiplying Decimals - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-decimals/1)%20Multiplying%20Decimals%20Method.webp Three-step method for multiplying decimals: ignore decimal points, multiply as whole numbers, then place the decimal https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-decimals/2)%20Multiplying%20Decimals%20Practice.webp Multiplying decimals method: 0.34 × 2.5 solved by ignoring decimals (34 × 25 = 850), counting 3 decimal places, then placing the point https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-decimals/3)%20Multiplying%20Decimals%20Application.webp Real-world multiplying decimals problem: calculating cost using £6.5 per km times 8.12 km step by step https://maths-angel.com/lessons/cosine-rule https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cosine-rule/cosine-rule-math-angel.webp Cosine rule lesson preview showing the formula and a labelled non-right-angled triangle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cosine-rule/cosine-rule-welcome-visual.webp Cosine Rule - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cosine-rule/1)%20What%20is%20the%20Cosine%20Rule.webp Cosine Rule formula a² = b² +c² -2bc·cos(A) explained with a triangle diagram labelled with sides a, b, c, and angle A. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cosine-rule/2)%20How%20to%20Apply%20the%20Cosine%20Rule%20to%20Find%20Sides%20in%20Triangles.webp Using the cosine rule to find a side in a triangle with sides 3 cm and 5 cm and an angle of 60 degrees between them. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cosine-rule/3)%20The%20Cosine%20Rule%20Formula.webp Cosine rule formulas for finding angles in a triangle, with labelled triangle and angle A highlighted in pink. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cosine-rule/4)%20Applying%20the%20Cosine%20Rule%20to%20Find%20Angles%20in%20Triangles.webp Triangle GEF with sides 4 cm, 3 cm, and 2 cm, applying the cosine rule to find angle F as 47 degrees using a calculator. https://maths-angel.com/lessons/calculating-fractions-and-decimals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/calculating-fractions-and-decimals-math-angel.webp Worked example: calculating fractions and decimals by rearranging 1.1 + ³⁄₇ + 0.4 + ⁴⁄₇ with commutative and associative laws https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/calculating-fractions-and-decimals-welcome-visual.webp Calculating Fractions and Decimals - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/1)%20Properties%20of%20Arithmetic%20(Formulas).webp Commutative, associative, and distributive law formulas for simplifying fractions and decimals https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/2)%20Commutative%20and%20Associative%20Law%20in%20Addition.webp Commutative and associative laws applied to addition with decimals and fractions, showing regrouping https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/3)%20Commutative%20and%20Associative%20Law%20in%20Multiplication.webp Associative law in multiplication with fractions, decimals, and whole numbers worked example https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/4)%20Distributive%20Law%20with%20Decimals%20and%20Fractions%20.webp Distributive law applied to multiply and simplify fractions and decimals with step-by-step worked example https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/5)%20Distributive%20Law%20with%20More%20Terms.webp Distributive law with multiple terms: factoring out common fractions and simplifying decimals step by step https://maths-angel.com/lessons/sine-rule https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/sine-rule/sine-rule-math-angel.webp Sine Rule lesson preview showing the formula a/sin A = b/sin B with a labelled triangle https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/sine-rule/sine-rule-welcome-visual.webp Sine Rule - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/sine-rule/1)%20Sine%20Rule.webp Sine Rule Formulas for finding missing sides or angles. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/sine-rule/2)%20Applying%20the%20Sine%20Rule%20to%20find%20Missing%20Sides.webp Sine Rule applied to a triangle with angles 30°, 70°, and one unknown angle, showing how to find the opposite side of 4 cm using the sine rule. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/sine-rule/3)%20Applying%20the%20Sine%20Rule%20to%20find%20Missing%20Angles.webp Applying the sine rule to find angles with a triangle, with the equation sin(135°)/10 cm = sin(theta)/5 cm. https://maths-angel.com/lessons/recurring-decimals-to-fractions https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/recurring-decimals-to-fractions/convert-recurring-decimals-to-fractions-math-angel.webp Step-by-step method for converting recurring decimals to fractions with worked examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/recurring-decimals-to-fractions/convert-recurring-decimals-to-fractions-welcome-visual.webp Convert Recurring Decimals to Fractions - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/recurring-decimals-to-fractions/1)%20Converting%20Recurring%20Decimals%20to%20Fractions%20(Method).webp Step-by-step guide converting 0.333 recurring decimal to fraction 1/3 by multiplying by 10, subtracting equations, and solving for x. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/recurring-decimals-to-fractions/2)%20Converting%20Recurring%20Decimals%20to%20Fractions%20(Example).webp Converting the recurring decimal 0.4545... into a fraction, multiplying both sides by 100, subtracting the equations, and solving for x = 5/11. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/recurring-decimals-to-fractions/3)%20Converting%20Recurring%20Decimals%20to%20Fractions%20(Practice).webp Converting the recurring decimal 0.1666... into a fraction, showing multiplication by powers of 10, subtraction of equations, and solving to get 1/6. https://maths-angel.com/lessons/powers-indices https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/powers-and-indices-math-angel.webp Powers and indices: 3⁴ with base and index labelled, expanded as 3 × 3 × 3 × 3 to show repeated multiplication https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/powers-and-indices-welcome-visual.webp Powers and Indices - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/1)%20Introduction%20to%20Powers%20(indices).webp Introduction to powers by showing the relationship that 3+3+3+3 equals 4 times 3, and 3 x 3 x 3 x 3 equals 3 to the power of 4. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/2)%20Notation%20of%20Powers.webp Explanation of the base 3 and index 4 in 3^4 that it is pronounced 'three to the power of four'. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/3)%20Properties%20of%20Powers.webp Explaining key characteristics of powers, e.g., 3^4 is not the same as 4^3, a^1 is a, and for a different to 0, a^0 is 1. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/4)%20Common%20Powers%20(Indices).webp Common indices chart showing square and cube numbers with examples. For example, square numbers 1, 4, 9, 16, and cube numbers 1, 8, 27, 64, 125. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/5)%20Simplifying%20Expressions%20with%20Powers.webp Cartoon blue bird explaining how to simplify 4 × 3 × 3 × 4 × 4 to 4³ × 3² using commutative and associative laws. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/6)%20Calculating%20Expressions%20with%20Indices.webp BIDMAS calculation rules with indices shown by comparing (2 × 5)^2 and 2 × 5^2, resulting in 100 and 50 respectively. https://maths-angel.com/lessons/standard-form https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/standard-form-math-angel.webp Standard form (scientific notation): expressing numbers as A × 10ⁿ where 1 ≤ A < 10, with example 26,000 = 2.6 × 10⁴ https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/standard-form-welcome-visual.webp Standard Form - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/1)%20Standard%20Form.webp Standard form explained as a method of expressing large or small numbers in the form A × 10ⁿ. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/2)%200.007%20to%20standard%20form.webp Converting 0.007 to standard form: 7 × 10⁻³ by moving the decimal three places right https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/3)%20384000%20to%20standard%20form.webp Converting 384,000 to standard form: 3.84 × 10⁵ by moving the decimal five places left https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/4)%20Calculating%20with%20Standard%20Form%20Example%201.webp Multiplying in standard form: (2 × 10⁷) × (8 × 10⁻¹²) worked step by step https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/5)%20Calculating%20with%20Standard%20Form%20Example%202.webp Calculating in standard form: 3 × 10⁻⁵ × 40,000,000 = (3 × 4) × 10⁻⁵⁺⁷ = 12 × 10² = 1.2 × 10³ https://maths-angel.com/lessons/basics-of-square-roots https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basics-of-square-roots/basics-of-square-roots-math-angel.webp Square roots lesson thumbnail with definition and examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basics-of-square-roots/basics-of-square-roots-welcome-visual.webp Basics of Square Roots - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basics-of-square-roots/1)%20What%20is%20a%20Square%20Roots.webp Square roots of 9 and 25 explained as non-negative values that, when squared, give the original number https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basics-of-square-roots/2)%20Square%20Roots%20Definition%20%26%20Properties.webp Square root properties: always non-negative, and negative numbers have no real square roots https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basics-of-square-roots/3)%20Practicing%20Square%20Roots.webp Practising square roots with examples √0 = 0, √400 = 20, √144 = 12 and their squares shown alongside. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basics-of-square-roots/4)%20List%20of%20Common%20Square%20Roots.webp Practising square roots with examples including 0, 400, and 144, and a list of perfect squares from 0 to 15. https://maths-angel.com/lessons/multiplying-dividing-square-roots https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-dividing-square-roots/multiplying-and-dividing-square-roots-math-angel.webp Multiplying and dividing square roots lesson with step-by-step formulas and examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-dividing-square-roots/multiplying-and-dividing-square-roots-welcome-visual.webp Multiplying and Dividing Square Roots - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-dividing-square-roots/1)%20Multiplying%20and%20Dividing%20Roots.webp Square root rules for multiplication and division showing √a × √b = √(ab) and √a ÷ √b = √(a/b) https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-dividing-square-roots/2)%20Example%20Multiplication.webp Multiplying square roots step by step: √18 simplified to 3√2 and √4.8 × √10 simplified to 4√3 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-dividing-square-roots/3)%20Example%20Division.webp Dividing square roots examples: √(36/25) = 6/5 = 1.2 and √50 ÷ √2 = √25 = 5 https://maths-angel.com/lessons/laws-of-indices-same-base-or-index https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/laws-of-indices-same-base-or-index/laws-of-indices-(same-base-or-same-indices)-math-angel.webp Laws of indices lesson covering same base and same index rules with worked examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/laws-of-indices-same-base-or-index/laws-of-indices-same-base-same-indices-welcome-visual.webp Laws of Indices (Same Base, Same Indices) - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/laws-of-indices-same-base-or-index/1)%20What%20are%20Indices.webp Laws of indices showing rules for multiplying and dividing powers with same base or same index. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/laws-of-indices-same-base-or-index/2)%20Laws%20of%20Indices%20(Same%20Base).webp Same base laws of indices: add exponents when multiplying and subtract when dividing, with examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/laws-of-indices-same-base-or-index/3)%20Laws%20of%20Indices%20(Same%20Index).webp Laws of indices with same index: aⁿ × bⁿ = (ab)ⁿ for multiplying and aⁿ ÷ bⁿ = (a÷b)ⁿ for dividing, with worked examples https://maths-angel.com/lessons/negative-exponents-power-of-a-power https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/negative-exponents-and-power-of-a-power-math-angel.webp Negative exponents and power of a power lesson with reciprocal and exponent rules https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/negative-exponents-and-power-of-a-power-welcome-visual.webp Negative Exponents and Power of a Power - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/1)%20Law%20of%20Indices.webp Laws of indices showing a⁻ᵐ = 1/aᵐ and (aᵐ)ⁿ = aᵐⁿ for negative indices and power of a power https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/2)%20Applying%20Negative%20Indices%20Rule%20on%20Fractions.webp Negative indices rules shown with examples. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/3)%20Power%20of%20a%20Power%20Rules.webp Power of a power rule with examples using positive and negative exponents. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/4)%20Power%20of%20a%20Power%20Examples.webp Power of a power rule illustrated with examples using positive, negative and fractional exponents. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/5)%20Law%20of%20Indices%20and%20Power%20Rules.webp Laws of indices showing negative indices and power of a power, with examples including negative powers and simplification of expressions. https://maths-angel.com/lessons/nth-root-fractional-indices https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/the-nth-root-and-fractional-indices-math-angel.webp nth root and fractional indices lesson with cube root and fourth root worked examples https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/the-nth-root-and-fractional-indices-welcome-visual.webp The nth Root and Fractional Indices - Introduction https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/1)%20The%20nth%20Root.webp Square, cube, and fourth root examples showing nth root calculations and corresponding powers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/2)%20Characteristics%20of%20the%20nth%20Root.webp Cube root of 8 equals 2, showing nth root rule: multiplying n roots of a number returns the original value. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/3)%20Basic%20Fractional%20Indices.webp Cube root of 8 equals 2, showing ∛8·∛8·∛8 = 8 and fractional indices rule a^(1/n) = ⁿ√a. https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/4)%20Basic%20Fractional%20Indices%20Example.webp Cube root of 125 using fractional indices: 125 to the power ⅓ = ³√125 = 5, since 5³ = 125 https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/5)%20Fractional%20Indices.webp Fractional indices rule a^(m/n) with worked example 125^(2/3) = 25 using roots and powers https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/6)%20Fractional%20Indices%20Example.webp Fractional indices example: 16^(3/4) step by step — fourth root of 16 is 2, then 2^3 = 8