Topics · Numbers & Calculations

Ratios and rates

Two of this for every three of that. Ratios keep amounts fair when things grow.

Doubling a recipe without wrecking it is ratio thinking.

Learn: The ratio table →▶ Play Best Buy Challenge ↺ The table

More ways into this idea

Play with itRatio MixerMix red and yellow — equivalent ratios make the same orange
Play with itPrice LabSlice two pack prices into per-item pieces
Step into a storyThe Mural MixThe sky colour is perfect. Now make four times as much.
Make it a gameBest Buy ChallengeBuild a purchase plan that fits the goal — the goal is the judge
Test yourselfA fresh mixed set, whenever you likeExplanations after every question. Nothing is recorded.

Common sticking points

The big sticking point is ADDING instead of scaling: extending 2:3 to 4:5 because both went up by 2. Equivalent ratios MULTIPLY both quantities by the same factor — 2:3 doubled is 4:6.
Another is scaling only one side. A ratio is a relationship between BOTH quantities — whatever factor changes one must change the other.
Order carries meaning: 'red to blue' lists red first. 2:3 and 3:2 describe different mixes.

Try this together

Lay out 2 red counters and 3 blue (coins or paper scraps work). Ask: how could we make TWICE as much without changing the mix? Then three times as much? Watch for the moment both piles scale together.

1–5 minutes, no materials to buy, nothing to hand in.

Ontario curriculum details

B2.9Make and use equivalent ratios and rates

Plain-language summaries. See the full curriculum for every expectation and the official source.