Curriculum
Year 8 (Grade 8)
Ages 13–14 · Linear functions, systems, exponents, transformations, intro to Pythagoras.
Numbers
Under Numbers
- Irrational numbers
Decimals with no pattern, no repeat, no end — like √2 and π.
- Integers
Negative + positive, and how to think about each.
- Prime numbers
Find primes with the Sieve of Eratosthenes — interactive.
- Factors & multiples
GCD, LCM and divisibility rules — the hidden structure of numbers.
- Factorial (n!)
5! = 5×4×3×2×1 = 120. Click and watch the tree fan out.
- Real numbers
Every number on the number line — the big family.
- Absolute value
Distance from zero, ignoring sign — |−7| = 7.
- Scientific notation
6.02 × 10²³ — a tidy way to write very big or very small numbers.
- Rounding numbers
Round to the nearest 10, 100, or decimal place — and the tie-breaker rules.
- Coprime
Two numbers whose only common factor is 1 — they share no factors.
- Evolution of numbers
Counting → naturals → integers → rationals → reals → complex. The story.
Percentages
Under Numbers
Ratios & rates
Under Numbers
- Ratios & proportion
Two cups flour to one cup sugar — scale the recipe and watch the ratio hold.
- Order of operations
PEMDAS — brackets first, then powers, then × and ÷, then + and −.
- Golden ratio (φ)
1 : 1.618 — the rectangle that nests inside itself forever.
- Irrational numbers
Decimals with no pattern, no repeat, no end — like √2 and π.
- Rates
Miles per hour, beats per minute — anything 'per' is a rate.
Measurement
Under Measurement
- Introduction to measurement
What you can measure: length, mass, capacity, time, temperature.
- What is a unit?
A standard chunk you compare other things against — and why standards matter.
- Unit converter
Convert any length, mass, volume, area, speed, or temperature — with the cancel-the-units trick.
- US customary units
Inch, foot, pound, gallon, acre, Fahrenheit — the system that runs the US, with a visual size chart.
- Metric prefixes
kilo, mega, giga, milli, micro, nano — 14 prefixes that scale every metric unit.
- Length
mm, cm, m, km — and inches and feet.
- Metric length
mm, cm, m, km — base 10, easy to convert.
- US customary length
Inch, foot, yard, mile — and the conversions you really need.
- Time
Read clocks, count minutes, work with durations.
- Days, weeks, months, years
How many days in this month? When does the leap year fall?
- Months
Twelve months, names and origins — and how many days each one has.
- Weeks
Seven days, where the names come from, and how the modern week was set.
- Days
Sunrise to sunrise — and the 24 hours in between.
- Years
One trip around the sun — and why it's not exactly 365 days.
- Seasons
Spring, summer, autumn, winter — and the tilt of the Earth that drives them.
- Time units convert
Seconds, minutes, hours, days — convert between any two.
- Stopwatches & timers
Measuring elapsed time — for races, recipes and physics experiments.
- Analog & digital clocks
Two ways to display the same time — read either at a glance.
Showing 18 of 46 — more on the Measurement page.
Geometry (Plane)
Under Geometry
- Similar triangles
Same shape, different size — corresponding sides scale together.
- Congruent triangles
Same shape AND same size — SSS, SAS, ASA, AAS, RHS prove it.
- Triangles
The three angles always sum to 180°. Drag to convince yourself.
- Triangle centers
Centroid, circumcenter, incenter, orthocenter — four points every triangle hides.
- Area & perimeter
Resize a rectangle and see area and perimeter follow.
- Interior angles of polygons
Triangle 180°, quad 360°, pentagon 540° — sum grows by 180° per side.
- Exterior angles of polygons
Walk around a polygon — the turns always add to 360°.
- Triangle inequality
Two sides always add to more than the third — or no triangle.
- Right-angle triangle
One 90° corner — and the home of Pythagoras and trig.
- Equilateral triangle
Three equal sides, three 60° angles — the most symmetric triangle.
- Isosceles triangle
Two equal sides — and the base angles are equal too.
- Scalene triangle
All sides different — no symmetry.
- 3-4-5 triangle
The simplest right triangle in whole numbers — used since ancient Egypt.
- Rectangle
Four right angles, opposite sides equal — the most familiar shape.
- Construct triangles
Three sides, two sides and an angle — build a triangle from any combination.
- Rotational symmetry
Spin a shape — does it look the same before a full turn?
- Shapes
Circle, triangle, square, polygon — names, sides, properties.
- Polygons
Three sides, four, five, six… and the angle each interior corner gets.
Showing 18 of 52 — more on the Geometry page.
Algebra
Under Algebra
- Substitution
Swap a letter for a number. The simplest move in algebra.
- Expressions
Combine like terms — simplify with a tap.
- Like terms
3x and 5x add to 8x. 3x and 5y don't combine. Why like terms matter.
- Expanding
Multiply out the brackets — distribute, FOIL, then simplify.
- Equations
Balance both sides of a scale and solve for the unknown.
- Linear equations
ax + b = c. The cleanest equation — one variable, one solution.
- Equations of a line
Slope-intercept, point-slope, two-point — every form for y = mx + b.
- Remainder & factor theorems
If P(a) = 0, then (x − a) is a factor. The fastest factor check there is.
- Rational expressions
Polynomials in fractions. Add, subtract, multiply, divide — same rules as fractions.
- Factoring
Break x² + 5x + 6 into (x+2)(x+3) — split the middle.
- Factoring quadratics
Find two numbers that multiply to c and add to b — the quadratic factor trick.
- Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a — solves every quadratic.
- Systems of equations
Two equations, two unknowns — substitute, eliminate, or matrix-solve.
- Introduction
Letters stand in for unknown numbers. The first idea — and why it works.
- Brackets
Parentheses, square brackets, braces — when each one is used and why.
- Simplify
Cancel, combine and rewrite — make the expression as small as possible.
- Inequalities
Less-than, greater-than, and number-line shading.
- Solving inequalities
Same moves as equations — except multiplying by a negative flips the sign.
Showing 18 of 69 — more on the Algebra page.
Exponents & roots
Under Numbers
- Square & cube roots
What number times itself is 16? See roots as the inverse of powers.
- Scientific notation
6.02 × 10²³ — a tidy way to write very big or very small numbers.
- Cube root
What number, multiplied by itself three times, gives this?
- Nth root
Square, cube, fourth, fifth — the general inverse of powers.
Inequalities
Under Algebra
Coordinates
Under Geometry
Quadratic equations
Under Algebra
- Factoring quadratics
Find two numbers that multiply to c and add to b — the quadratic factor trick.
- Completing the square
Rewrite ax² + bx + c into a(x − h)² + k — and solve any quadratic.
- Quadratics
Parabola playground — change a, b, c and see the curve respond.
- Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a — solves every quadratic.
Polynomials
Under Algebra
Logic
Under Algebra
No lessons mapped for this group yet — see Algebra for related content.
Functions
Under Algebra
- Direct & inverse proportion
Twice the input, twice (or half) the output — two flavours of proportion.
- Functions & graphs
Slide m and b on y = mx + b and watch the line move.
- Evaluating functions
f(3) means: drop 3 in for x, simplify, read the answer.
- Odd & even functions
Mirror across the y-axis (even) or rotate around the origin (odd).
- Matrix inverse
The matrix that undoes another — like 1/x but for matrices.
Estimation
Under Data
No lessons mapped for this group yet — see Data for related content.
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