Year 8 (Grade 8)

Decimals with no pattern, no repeat, no end — like √2 and π.

Negative + positive, and how to think about each.

Find primes with the Sieve of Eratosthenes — interactive.

GCD, LCM and divisibility rules — the hidden structure of numbers.

5! = 5×4×3×2×1 = 120. Click and watch the tree fan out.

Every number on the number line — the big family.

Distance from zero, ignoring sign — |−7| = 7.

6.02 × 10²³ — a tidy way to write very big or very small numbers.

Round to the nearest 10, 100, or decimal place — and the tie-breaker rules.

Two numbers whose only common factor is 1 — they share no factors.

Counting → naturals → integers → rationals → reals → complex. The story.

Per-cent means per-hundred. Slide it and see it.

How much bigger or smaller? And how far off your estimate was.

Three ways to write the same part of a whole — and how to switch between them.

Two cups flour to one cup sugar — scale the recipe and watch the ratio hold.

PEMDAS — brackets first, then powers, then × and ÷, then + and −.

1 : 1.618 — the rectangle that nests inside itself forever.

Decimals with no pattern, no repeat, no end — like √2 and π.

Miles per hour, beats per minute — anything 'per' is a rate.

What you can measure: length, mass, capacity, time, temperature.

A standard chunk you compare other things against — and why standards matter.

Convert any length, mass, volume, area, speed, or temperature — with the cancel-the-units trick.

Inch, foot, pound, gallon, acre, Fahrenheit — the system that runs the US, with a visual size chart.

kilo, mega, giga, milli, micro, nano — 14 prefixes that scale every metric unit.

mm, cm, m, km — and inches and feet.

mm, cm, m, km — base 10, easy to convert.

Inch, foot, yard, mile — and the conversions you really need.

Read clocks, count minutes, work with durations.

How many days in this month? When does the leap year fall?

Twelve months, names and origins — and how many days each one has.

Seven days, where the names come from, and how the modern week was set.

Sunrise to sunrise — and the 24 hours in between.

One trip around the sun — and why it's not exactly 365 days.

Spring, summer, autumn, winter — and the tilt of the Earth that drives them.

Seconds, minutes, hours, days — convert between any two.

Measuring elapsed time — for races, recipes and physics experiments.

Two ways to display the same time — read either at a glance.

Same shape, different size — corresponding sides scale together.

Same shape AND same size — SSS, SAS, ASA, AAS, RHS prove it.

The three angles always sum to 180°. Drag to convince yourself.

Centroid, circumcenter, incenter, orthocenter — four points every triangle hides.

Resize a rectangle and see area and perimeter follow.

Triangle 180°, quad 360°, pentagon 540° — sum grows by 180° per side.

Walk around a polygon — the turns always add to 360°.

Two sides always add to more than the third — or no triangle.

One 90° corner — and the home of Pythagoras and trig.

Three equal sides, three 60° angles — the most symmetric triangle.

Two equal sides — and the base angles are equal too.

All sides different — no symmetry.

The simplest right triangle in whole numbers — used since ancient Egypt.

Four right angles, opposite sides equal — the most familiar shape.

Three sides, two sides and an angle — build a triangle from any combination.

Spin a shape — does it look the same before a full turn?

Circle, triangle, square, polygon — names, sides, properties.

Three sides, four, five, six… and the angle each interior corner gets.

Swap a letter for a number. The simplest move in algebra.

Combine like terms — simplify with a tap.

3x and 5x add to 8x. 3x and 5y don't combine. Why like terms matter.

Multiply out the brackets — distribute, FOIL, then simplify.

Balance both sides of a scale and solve for the unknown.

ax + b = c. The cleanest equation — one variable, one solution.

Slope-intercept, point-slope, two-point — every form for y = mx + b.

If P(a) = 0, then (x − a) is a factor. The fastest factor check there is.

Polynomials in fractions. Add, subtract, multiply, divide — same rules as fractions.

Break x² + 5x + 6 into (x+2)(x+3) — split the middle.

Find two numbers that multiply to c and add to b — the quadratic factor trick.

x = (−b ± √(b² − 4ac)) / 2a — solves every quadratic.

Two equations, two unknowns — substitute, eliminate, or matrix-solve.

Letters stand in for unknown numbers. The first idea — and why it works.

Parentheses, square brackets, braces — when each one is used and why.

Cancel, combine and rewrite — make the expression as small as possible.

Less-than, greater-than, and number-line shading.

Same moves as equations — except multiplying by a negative flips the sign.

What number times itself is 16? See roots as the inverse of powers.

6.02 × 10²³ — a tidy way to write very big or very small numbers.

What number, multiplied by itself three times, gives this?

Square, cube, fourth, fifth — the general inverse of powers.

Less-than, greater-than, and number-line shading.

Same moves as equations — except multiplying by a negative flips the sign.

Shade the half-plane below or above — and the boundary line tells you which.

The three things every other shape is built from.

Plot points, drag dots, watch (x, y) follow your finger.

Pythagoras turned into a coordinate formula.

The point exactly halfway between two given points.

Find two numbers that multiply to c and add to b — the quadratic factor trick.

Rewrite ax² + bx + c into a(x − h)² + k — and solve any quadratic.

Parabola playground — change a, b, c and see the curve respond.

x = (−b ± √(b² − 4ac)) / 2a — solves every quadratic.

Add, subtract and multiply expressions with x², x³ and beyond.

Long division — but the divisor and dividend are polynomials.

Expand (a + b)ⁿ without multiplying — Pascal's triangle does the work.

Twice the input, twice (or half) the output — two flavours of proportion.

Slide m and b on y = mx + b and watch the line move.

f(3) means: drop 3 in for x, simplify, read the answer.

Mirror across the y-axis (even) or rotate around the origin (odd).

The matrix that undoes another — like 1/x but for matrices.

Shade the half-plane below or above — and the boundary line tells you which.

Slide m and b on y = mx + b and watch the line move.

The waves trigonometry draws when you sweep an angle.