Draw the Story
Four bags of six, or six bags of four? Draw the story and you can see which.
For grown-ups
- How long: 10 to 15 minutes is plenty. Short and frequent beats long and occasional — the early-numeracy trials with the largest effects ran eight weeks or less.
- When they get one wrong: the page shows the working. Read it together rather than moving straight on. Feedback that explains is worth several times more than feedback that only marks right or wrong, and that gap is wider in maths than in any other subject.
- Not timed: thinking time is the point of a book. Let silences run.
- Print it too: doing the same problems on paper a few days later is worth more than doing twice as many today.
What this practises
Drawing and reading a tape diagram for equal-groups and sharing stories.
WWC Recommendation 5 — teach the structure of word problems, and use visual representations to expose it — is rated STRONG on 18 studies, and it does not stop at addition. The multiplicative schemas are where the structure and the arithmetic come apart most sharply: 4 × 6 and 6 × 4 are the same product and different stories, so a child who reaches for the numbers can be right about the total and wrong about the problem. Illustrative Mathematics uses the tape diagram for precisely this across grades 3 and 4, and the same fading argument applies as everywhere else (Fyfe 2014) — the diagram is drawn for the child, then read, then completed, then judged.
- The underlying idea
- A multiplicative story has a structure — equal groups, or a total shared out — and the tape diagram makes the structure visible before any arithmetic happens.
- Where this sits in Illustrative Mathematics
- 3rd grade Unit 1: Introducing Multiplication · 3rd grade Unit 4: Relating Multiplication to Division
- Sources
- Institute of Education Sciences / What Works Clearinghouse (2021) · Illustrative Mathematics / Kendall Hunt (2024) · Illustrative Mathematics (2024) · Fyfe et al. (2014) · van der Kleij et al. (2015) all references →
Related measured skills: ALPACA · Elementary operations, ARF · Multiplication facts. What this means