Derived Facts

When one encounters a problem such as the one above there are four main strategies for solving.

1. Counting All – Begin at the first object and count all.    Most children use this strategy as they learn to count.

2. Counting On -As students develop they will notice the first number and then count on from that number, using it as a starting point to count on from.

3. Known Facts – Sometimes we just know the fact because it has been committed to memory.

4. Derived Facts – Another strategy for solving problems is to manipulate the numbers in the problem to make them easier to manage.  Students who use this strategy might make a group of ten and then see that there are two and three left which makes five.  They might also see that the numbers are close to 7+7 and since that is one less, and the known double 14, the answer must be 15.

Knowing that this is how students approach problems is important but it wasn’t until I was reading Jo Boaler’s book, What’s Math Got to Do with It? did I realize just HOW important it was.

Here I used the Create A Graph tool from NCES to show the frequency with which students 8 and older use these strategies to solve addition problems.


I encourage you to pick up a copy of Jo Boaler’s book, What’s Math Got to Do with It?.