Guide · strategy
Counting On: The First Addition Strategy
Counting on means starting from the bigger number and counting up the smaller one. For 3 + 8, say 8, then 9, 10, 11. It's the first real strategy after counting everything from 1. It's the right tool for adding 1, 2 or 3, and the wrong tool for bigger numbers.
From counting all to counting on
A child who is counting all solves 5 + 3 by counting five fingers, three fingers, then all eight from the start. Counting on skips the first part: the 5 is already there. To teach it, put 5 blocks under a cup and write 5 on it, then add 3 more blocks. Tap the cup and say five, then count on: 6, 7, 8. The cup helps children trust that the 5 is still there without counting it.
Always start with the bigger number
2 + 9 is a slow count from 2 and a quick count from 9. So teach the turnaround at the same time: order doesn't matter in addition, so pick the bigger number to start. Use the phrase put the big number in your head. A number line makes it visible. A common slip is to count the starting number as the first hop, so 7 + 3 becomes 7, 8, 9. Point at the jumps, not the numbers, and say hop, hop, hop.
When to move on
Counting on is great for the plus 1, 2 and 3 facts. Past that it gets slow, and children lose track of how many they've counted. Once it's secure, start on doubles and pairs that make 10, which give quicker routes. If a child is still counting on 7 for 6 + 7 by the end of first grade, that's a sign to teach those strategies, not to do more drills.
Questions people ask
Is counting on the same as skip counting?
No. Counting on goes up in ones from a starting number. Skip counting goes up in bigger steps, like 2, 4, 6.
Is counting back the same idea?
Yes, for subtraction, and it's fine for taking away 1 or 2. For more than that, think addition.
An app is on its way
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