Year 7 (Grade 7)

Divide, multiply, subtract, bring down — the four-step dance, animated.

Share 12 cookies between 3 friends — see division as fair sharing.

Quick tricks to check whether a number is divisible by 2, 3, 4, 5, 6, 9 or 10.

Why your calculator throws an error and what undefined really means.

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.

Why 305 isn't the same as 350 — see digits move between columns.

Tenths, hundredths, thousandths — and why they line up.

Base 16 — A through F take over after 9. Drives all those CSS colours.

1/3 = 0.333…, 1/7 = 0.142857142857… every fraction has a pattern.

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

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.

Cubes, spheres, cylinders — drag a dimension and watch volume grow.

(4/3)πr³ and 4πr² — Archimedes worked these out without calculus.

What's a cube in 4 dimensions? Or 5? You can almost picture it.

Polyhedra, prisms, pyramids, Platonic solids — Euler's V−E+F = 2.

Six squares, twelve edges, eight corners — the simplest 3D solid.

Every point the same distance from the center — the most efficient surface.

Two circles joined by a tube. Cans, pipes, drums.

A circle pulled to a point. Ice-cream, party hats, traffic markers.

A donut. One hole, but a surprising amount of geometry.

Same shape, top and bottom — connected by rectangles.

A polygon base, all sides meeting at one peak.

There are exactly five — tetrahedron, cube, octahedron, dodecahedron, icosahedron.

Unfold a solid into a flat net — a paper template you can cut and rebuild.

Four triangular faces — the simplest 3D solid.

Eight triangular faces — like two pyramids glued base to base.

Twelve pentagonal faces — one of the five Platonic solids.

Twenty triangular faces — the most spherical of the Platonic solids.

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.

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

Maximise (or minimise) a linear thing under linear constraints.

The waves trigonometry draws when you sweep an angle.

Triangles without right angles — two laws that solve them anyway.

sin, cos, tan and the right-triangle ratios behind every angle.

sin² + cos² = 1, and the family of equations that always hold.

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.

Slices of a circle — each one a percentage of the whole.

Bar, pie, line — the same numbers told three ways.

Compare categories at a glance — taller bar means bigger.

Connect points to track change over time.

Pictures stand in for counts — friendly charts for small data.

Bar charts for grouped numerical data — bins on the x-axis.

One dot per data point — see exactly where each value lands.

The fastest way to count by hand — strokes in groups of five.

How often each value (or range) appears — turn a list into a table.

Running total — and the curve it builds.

Two variables, one dot per data point — patterns appear.

An old-school way to see distribution without losing the actual numbers.

Design good questions, gather honest answers, analyse the results.

Mean, median, mode, range — interactive.

Add them all, divide by how many — the everyday average.

Some data points count more — multiply, then divide by total weight.

On average, how far is each value from the mean?

The middle value when sorted — robust against outliers.

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.

Branch out the possibilities — multiply along, add across.

P(A given B) — once you know B happened, A's chances change.

P(not A) = 1 − P(A). The 'everything else' rule.

Roll dice and flip coins as many times as you like.

One coin flip doesn't affect the next — multiply their probabilities.

Can't both happen at once — add their probabilities.

Update your beliefs when new evidence shows up.

Just 23 people — and there's a 50% chance two share a birthday.

On average, how far is each value from the mean?

Add them all, divide by how many — the everyday average.

Some data points count more — multiply, then divide by total weight.

The middle value when sorted — robust against outliers.

The value that appears most often.

Largest minus smallest — the simplest spread.

Range, IQR, standard deviation — how spread out is the data?

Split sorted data into four equal groups — Q1, Q2 (median), Q3.

The 90th percentile means 90% of values fall below — used for ranks.

The typical distance of a value from the mean — spread, summarised.

Data points way outside the pack — notice them, investigate, decide.

The bell curve — why so much of the world clusters around an average.

Mean 0, SD 1 — the bell curve everyone calibrates against.

How lopsided is the distribution? Tail to the left or right.

Wrap a margin of error around an estimate — and quantify your trust.

Test whether observed counts match what you expected.

Compare means with small samples — the workhorse of stats.

Pick a small group to learn about a big one — without bias.

Add up coins and bills.

Cents are decimals of a dollar — every transaction is decimal arithmetic.

Build $1.37 with the fewest coins — a classic problem.

Hourly, salaried, overtime — and how to compare offers fairly.

20% off — what does that actually cost?

What interest is, why borrowers pay it, why savers earn it.

Interest on the original amount only — clean and predictable.

Interest earns interest. Slide the years and watch the curve bend up.

Why A = P(1 + r/n)^(nt) — and where every letter comes from.

Income in, expenses out — build a balanced month.

Convert between dollars, euros, pounds and more.

What a return is, what risk is, and why time helps.

Regular payments — how to value a stream of cash flows.

What a future dollar is worth today — discount it back.

Sum of discounted cash flows — positive means it's worth doing.

The discount rate that makes NPV zero — investing's headline number.

Pool small premiums, pay big claims — risk-sharing as maths.

When does owning beat renting? A comparison you can run with numbers.