Help with Class 8 Maths at home, one chapter at a time

A queen’s puzzle about lockers leads to square numbers. Your child finds squares and square roots, patterns in their last digits, perfect cubes and cube roots, and estimates roots of numbers that aren’t perfect squares.

• square
• square root
• perfect square
• cube
• cube root
• estimate

Fold a paper 46 times and its thickness would reach the Moon. Your child explores exponents, the laws of exponents, negative and zero powers, powers of 10 and scientific notation for very large and very small numbers.

• exponent
• base
• power
• scientific notation
• laws of exponents

How did people count before our digits? Your child explores tally systems, Egyptian and Roman numerals, the Mayan and Babylonian systems, and why the Indian place-value system with zero is so powerful. They also try counting in other bases.

• place value
• base
• numeral
• Roman
• zero
• symbol

Your child studies rectangles, squares, parallelograms, rhombuses, trapeziums and kites: their sides, angles and diagonals, and how they relate. The angle sum of a quadrilateral is 360°.

• parallelogram
• rhombus
• trapezium
• kite
• diagonal
• bisect
• 360°

Your child investigates sums of consecutive numbers, divisibility patterns, digital roots, and puzzles where algebra explains why a trick works.

• consecutive
• divisible
• digital root
• multiple
• proof
• pattern

Algebra helps multiply quickly. Your child multiplies expressions using the distributive property, learns identities like (a + b)² = a² + 2ab + b² and (a + b)(a − b) = a² − b², and uses them for mental maths like 103² or 98 × 102.

• distributive
• expand
• identity
• square
• product
• like terms

When a photo is resized, width and height change in the same ratio. Your child writes ratios, recognises proportional relationships, uses the unitary method, and scales recipes, maps and images.

• ratio
• proportion
• unitary method
• scale
• equivalent ratios

Percentages are fractions out of 100. Your child converts between fractions, decimals and percentages, finds percentages of amounts, and solves discount, profit and loss, and simple interest problems.

• percent
• discount
• profit
• loss
• marked price
• cost price
• simple interest

Baudhayana described this around 800 BCE: in a right triangle, the square on the longest side equals the sum of squares on the other two. Your child sees it with squares on sides, finds missing sides and checks for right angles.

• hypotenuse
• right triangle
• square
• Pythagorean triple
• converse

More workers finish a job faster: that is inverse proportion. Your child tells direct from inverse proportion, solves time-and-work and speed problems, and divides amounts in a given ratio.

• inverse proportion
• direct proportion
• ratio
• share
• constant product

Your child explores fractals such as the Sierpinski triangle, where a pattern repeats inside itself, and visualises 3D solids: nets, views from different sides and counting faces, edges and vertices (Euler’s formula).

• fractal
• self-similar
• net
• view
• faces
• edges
• vertices

Your child revisits mean and median, sees the mean as a balance point, groups data into class intervals, and reads and draws graphs like histograms and line graphs to tell a story from data.

• mean
• median
• class interval
• frequency
• histogram
• line graph

Number tricks and puzzles become clear with algebra. Your child builds and explains think-of-a-number tricks, calendar tricks and digit puzzles by writing them as expressions.

• expression
• variable
• prove
• simplify
• trick

Your child divides and rearranges shapes to find area formulas: parallelogram = base × height, triangle = ½ × base × height, trapezium = ½ × (sum of parallel sides) × height, and areas of rhombuses and composite shapes.

• area
• base
• height
• parallelogram
• trapezium
• composite shape