Think Addition to Solve Subtraction

I wrote about combining procedural with conceptual knowledge using John Van de Walle's idea of ten-frame cards for addition facts just a few days ago. There's a link in that post for a set of flash cards with ten frames on them, and suggestions for how to use them.

This set (that you can also download the PDF for free by clicking here) is a little different. Van de Walle suggests using these to count up through ten. Seeing the ten frame with 7, for example, encourages students to think 3 more (to get to ten) then another 3 more (to get to 13). That makes 6. Easy!

I think one of the mistakes I make as a math teacher of young children is to move to "formal recording" too quickly. Letting them make sense of this counting up strategy, to solve a subtraction problem, is one of the biggest ideas they need to develop in elementary school. This falls under the umbrella of inverse operations...not just telling us that addition is the opposite of subtraction. Every 1st grader in California can tell you that. But actually using addition to solve a subtraction problem? Well that takes some finesse.

What does it mean when students are fluently, flexibly, and comfortably using these cards to count up to solve subtraction? Well, they aren't counting on their fingers. They are using the relationship to 10 to count up in parts. How many to get to ten? Now how many more to get from ten to the start number? And this can be recorded in the following way:

Another activity could be to have the students match a subtraction fact card to the corresponding addition card. For example, a student could match this 13-7 card to the 7+6 card in the other set.

Now, if I'm offering an organizational tip, I can just about guarantee it came from somebody else. This one is from Miss Peaslee (1999). She taught me that if I make 7 sets of cards, I should make each set on a different color of paper. Then, when students are working together with their cards, at the end of the day, you simply separate by colors and know that you have a complete set again. Yay!