Near Doubles

This lesson is where the child solves near-double facts such as 7 + 8 by recalling the double and adjusting by one. Fluency within twenty is not speed for its own sake. Facts that come without thinking free up the working memory that the next four years of mathematics need, and a child recomputing 8 + 6 every time has nothing left over for the problem it sits inside.

Watch for finger counting that has gone underground — a pause, a glance away, lips moving. The strategy has not gone; it has just got quieter.

Short and often beats long and rare. Two minutes of the facts they nearly know is worth more than twenty minutes of the ones they already do.

What makes two numbers near doubles — Two numbers are near doubles when they are one apart, like 6 and 7, or two apart, like 6 and 8. You do not add them from scratch. You find the double hiding inside them, then fix the difference. For 6 + 7, the double is 6 + 6 = 12, and 7 is one more than 6, so the answer is one more: 13.

Two doubles to choose from — For 6 + 7 you could use the double of 6 and add one, or use the double of 7 and take one away: 7 + 7 = 14, then 14 - 1 = 13. Both routes land on 13. Pick whichever double you know better. Getting the same answer two ways is good evidence you are right.

The slip to watch for — The common mistake is adjusting in the wrong direction — using 6 + 6 = 12 and then taking one away instead of adding one. Guard against it by asking whether the answer should be bigger or smaller than the double before you calculate. 6 + 7 has more in it than 6 + 6, so the answer must be bigger. That check takes a second and catches the error every time.

Lean on the double next door — 7 + 8. Not a double, but nearly one. You know 7 + 7 = 14. 8 is one more than 7. So the answer is one more than 14. 7 + 8 = 15