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?.


Carnegie Art Museum Visit


On my recent trip to the Carnegie Art Museum in Pittsburgh I came across this work or art by Mel Bochner.  The opportunity to connect mathematics and art are often missed and this presents a wonderful problem.

While there are many ways to use this in the classroom but I would simply present the work to small groups and ask them to interpret it and then create their own work of art.  They could also trade diagrams and allow other groups to create their work.

Are there other ways to make a diagram of a block structure?