Take It Apart

Break a number into two parts. The same picture keeps turning out to be about something new.

Book Add and subtract within 100 2.NBT.B.52.OA.B.21.OA.D.7 ARF · Addition facts ARF · Subtraction facts

Is the equals sign muddling you up? Start here. A short lesson with a balance that tips, so you can see that the equals sign means “the same as” and not “the answer comes next”. About about 3 minutes.

Show me what equals means → What does the equals sign mean again?

▤ Print this All of 2nd grade

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

Splitting a number into parts that make the next step easy, and reading a total-first equation.

Part-whole decomposition is one of the six representations this site keeps constant across grades (docs/EVIDENCE.md), and until now it appeared at Kindergarten and nowhere else. The claim here is narrow and worth stating precisely: WWC 2021 Recommendation 3 reports 0.64 for representation-based intervention across nine studies, and keeping a representation constant across grades is the panel’s advice in its obstacles box rather than something those nine studies measured. The number bond is Izzi Math’s choice of representation, not one the guide names — it contains no occurrence of the phrase. The total-first form (10 = 7 + ___) is practice in the form that reads the equal sign as a relation, which Recommendation 2 on mathematical language gives as its Example 2.2; it is not claimed to change a belief.

The underlying idea: A number bond makes the part-whole relation visible and reversible: the same three numbers answer a missing-part question and a missing-total one, which is what makes the equal sign a relation rather than an instruction to compute.
Where this sits in Illustrative Mathematics: 2nd grade Unit 3: Measuring Length · 2nd grade Unit 4: Addition and Subtraction on the Number Line
Sources: Illustrative Mathematics / Kendall Hunt (2024) · Institute of Education Sciences / What Works Clearinghouse (2021) all references →

Related measured skills: ARF · Addition facts, ARF · Subtraction facts. What this means