Ratio & proportional reasoning

A recipe for green paint mixes blue and yellow in the ratio `3 : 5`. You want to make a batch using `40` drops of paint in total, keeping the same shade. How many drops of blue and how many of yellow do you need?

Art hook A colour-mixing canvas: a slider sets the total number of drops; the sketch draws `3` parts blue dots and `5` parts yellow dots side by side, then blends the averaged RGB into a filled swatch. Because the ratio is fixed, the swatch hue never changes as the total grows — proportional colour you can watch.

A train travels `240` km in `3` hours at a steady speed. Work out its speed as a unit rate (km per hour), then say how far it goes in `7` hours.

Art hook A number-line animation: a dot moves along a horizontal line, advancing `80` px per 'hour' tick. Stamp a faint marker at each hour so the equal spacings make constant speed visible as equal jumps.

A map is drawn at scale `1 : 25 000`. Two towns are `6` cm apart on the map. What is the real distance between them in kilometres?

Art hook A zoomable map grid: draw a small route of connected dots, then a 'scale slider' that multiplies every gap by the scale factor. A live label shows the real-world length, so children see the same shape stretch while its proportions stay identical.

A jacket costs `£60`. Its price is changed twice: first it is reduced by `20%`, then that reduced price is increased by `20%`. Is the final price back to `£60`? Work it out.

Art hook A bar-height animation: one vertical bar shrinks by 20% then grows by 20%, with a dotted line marking the original top. The gap between the dotted line and the final bar top makes the 'not equal' result impossible to miss.

Shop A sells `500` g of nuts for `£4.00`. Shop B sells `750` g for `£5.70`. Using price per gram, which shop is better value?

Art hook A dot-density grid: each shop is a rectangle of dots, one dot per 10 g, tinted darker where cost-per-gram is higher. The cheaper shop's grid glows lighter — value made visible as brightness.

In a fruit bowl there are `4` apples for every `3` oranges. Write this comparison as a ratio in the form `a : b`.

Art hook Place `4` red dots and `3` orange dots in a repeating strip across the canvas; each repeat is one 'unit' of the ratio, so the pattern visibly tiles the bowl.

A necklace uses beads in the ratio `2 : 1`, red to gold. If you scale it up keeping the same pattern, how many red beads go with `5` gold beads?

Art hook Draw beads evenly spaced around a circle: for every gold dot placed, add two red dots next to it. Spin the circle slowly so the fixed `2 : 1` rhythm reads as a steady repeating pattern.

`6` identical stickers cost `£1.50`. What is the cost of `1` sticker (the unit rate), and then the cost of `10` stickers?

Art hook A number line where each step of one 'sticker' adds a dot and a `+25p` label; watch the running total climb in equal jumps — the unit rate is the size of one jump.

Spot the mistake. To scale the ratio `2 : 3` up, a friend adds `2` to each part and writes `4 : 5`, saying it is the same mix. Explain why this is wrong and give a correct scaled ratio.

Art hook Two side-by-side dot grids: one built by adding (`4 : 5`), one by multiplying (`4 : 6`). Colour each so equal ratios share a hue — the 'added' grid clashes, showing the relationship broke.

A drink is mixed with squash and water in the ratio `1 : 4`. What fraction of the whole drink is squash?

Art hook A ring of `5` equal arcs (a pie made of dots): fill `1` arc as squash, `4` as water. The single filled arc out of five shows the fraction `1/5` directly.

A model dinosaur is built at scale `1 : 20`. The model's tail is `15` cm long. How long was the real dinosaur's tail, in metres?

Art hook Draw the tail as a chain of dots, then a slider that multiplies every gap by 20; the shape is preserved but stretches across the screen, with a live cm→m readout.

A `£30` game is discounted by `10%`. What is the sale price?

Art hook A single vertical bar of height 30; shave off the top 10% in a different colour, so the discount is a visible slice and the remaining bar is the sale price.

A car travels `150` km using `10` litres of fuel. How many kilometres does it travel per litre, and how far could it go on `25` litres at the same rate?

Art hook A row of fuel-drop icons, each advancing a dot `15` steps along a track; fill more drops to extend the journey — distance scales in equal, proportional strides.

You save `£150` at `4%` simple interest per year. How much interest do you earn in `1` year, and what is the total after `3` years?

Art hook A growing stack of equal-height coin-dots, exactly `£6` added each year — the equal increments show why simple interest grows in a straight line, not a curve.

A photo is `1200` pixels wide and `800` pixels tall. You shrink it keeping the same shape (proportion). If the new width is `300` pixels, what is the new height?

Art hook A rectangle that resizes with a single slider that scales width AND height by the same factor, keeping the `3 : 2` ratio locked; toggle the lock off to show how an un-proportional stretch distorts the picture.

Reasoning challenge. Two paints match in colour only if their red-to-blue ratios are equal. Paint P is `6 : 4` and paint Q is `9 : 6`. Do they match? Show your reasoning.

Art hook Plot each paint as a point at angle `atan2(blue, red)` on a wheel: `6 : 4` and `9 : 6` give the same angle, so both needles point the same way — equal ratios land on the same hue direction.

Open-ended. A `£25` shirt goes up to `£30`. Work out the percentage increase. Then a `£30` shirt drops to `£25` — is that the same percentage change? Explain.

Art hook Two bars, `25→30` and `30→25`, each annotated with its % change. The equal `£5` gap looks the same in height but the % labels differ, dramatising 'relative to the start'.