Addition and Subtraction Together

This lesson is where the child writes the four related equations for a part-part-whole relationship within 20. 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.

Why the four sentences belong together — A fact family is built from three numbers where two of them combine to make the third, like 5, 8 and 13. Those three numbers can be arranged into two additions and two subtractions. They are not four separate facts to memorize — they are one relationship described from four directions.

The four sentences in full — From 5, 8 and 13: 5 + 8 = 13, 8 + 5 = 13, 13 - 5 = 8, and 13 - 8 = 5. The biggest number, 13, is the whole. It sits alone after the equals sign in the additions, and it starts both subtractions. Spotting which number is the whole is the key to writing the family correctly.

What this buys you — If you know 5 + 8 = 13, you already know 13 - 8 without doing any subtracting. Children who see fact families stop treating subtraction as a separate skill to be dreaded. Subtraction becomes a question about addition: what do I add to 8 to reach 13?

One relationship, four sentences — Parts 6 and 7. Whole 13. 6 + 7 = 13 7 + 6 = 13 13 − 6 = 7 13 − 7 = 6 The three numbers never changed. Only which one you were hunting for.