Adding Three Numbers
Three numbers at once. Find the pair that makes ten and start there.
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
Adding three one-digit numbers, and choosing which two to add first.
Two standards, and both were gaps. 1.OA.A.2 (add three whole numbers whose sum is at most 20) was claimed by all-kinds-of-stories, which generated no three-addend item in 96 tries; the claim now sits on the activity that meets it. 1.OA.B.3 (use properties of operations as strategies) was not covered anywhere. The make-ten route is the same one adding-to-twenty already teaches and make-ten-race already drills, so this asks for no new strategy — only for the child to spot where to apply it. No efficacy trial sits behind the three-addend format specifically; it is in the standard, it is in IM Units 2 and 3, and it is what a first grader asked for.
- The underlying idea
- Three addends are where the associative property stops being a fact about arithmetic and becomes a decision the child makes. The sum is fixed; the route is not, and choosing the route is the skill.
- Where this sits in Illustrative Mathematics
- 1st grade Unit 2: Addition and Subtraction Story Problems · 1st grade Unit 3: Adding and Subtracting Within 20
- Sources
- Illustrative Mathematics / Kendall Hunt (2024) · Illustrative Mathematics (2024) · Fuchs et al. (2012) · Codding et al. (2011) all references →
Related measured skills: ARF · Addition facts, ALPACA · Early operations. What this means