Decomposing Numbers to 10
Decomposing numbers — taking them apart and putting them back together — is the foundation of all mental arithmetic. A child who knows that 7 is 5 and 2 more, or that 8 is 2 away from 10, can add and subtract without counting on their fingers. The ten-frame is the most powerful tool for building this understanding because it makes the structure of numbers to 10 visible at a glance.
Part-part-whole thinking
Every number to 10 can be thought of as two parts. 7 is 5 and 2 (connecting to the benchmark 5). 7 is also 4 and 3, 6 and 1, 7 and 0. Each of these ways of seeing 7 is useful in different situations. The goal is flexibility — not one fixed decomposition, but many.
The ten-frame as a thinking tool
A ten-frame is a 2×5 grid. It shows numbers in relation to 5 (top row) and 10 (full frame). 8 on a ten-frame looks like a full top row plus 3 on the bottom — immediately suggesting '8 is 5 and 3' and '8 is 2 away from 10.' These two facts are enormously useful. The ten-frame is so powerful that it should be present in classrooms from Kindergarten onward.
Number talks — thinking together
A number talk is a short (5–10 minute) whole-class routine where students mentally solve a problem and share strategies. In Kindergarten, a number talk might start with: 'I'm showing you 6 dots. What do you see?' Multiple students share their thinking. The teacher records strategies without judgment. This builds mathematical community and surfaces different ways of seeing the same quantity.