Basic Addition and Proof

Evelyn can do basic addition mentally. She occasionally utilizes finger counting to check her work, but prefers to simply count on in her head. (for example, she thinks 3 + 2, so 3, 4, 5. 5!)

When it comes to explaining how she knows her answer is correct, she struggles. I want her to be able to explain her strategies and thinking in mathematics, so today we worked on an activity to help her prove her answers when she completes addition problems.

Here was our set up.

The notebook has number sentences for basic addition ("2 + (numbers 0-12) =")

I color coded the addends so that one addend was blue and one addend was yellow. Then I drew green lines underneath the blank space for the sum.

I also provided silicon muffin cups in blue, yellow, and green. (Makes sense because yellow and blue make green, right?)

I added a plus sign and an equals sign to help keep the number sentence structure consistant.

For the addition problem 2 + 4 =, the set up looks as follows:

Then Evelyn would combine the blue and yellow containers by pouring both into the green container.

She could then count the number of pennies in the green container to prove her sum she discovered mentally was correct.

 Tomorrow, Evelyn will rewrite the math sentences to practice writing numbers and math symbols.

Bonuses of this activity:

• I was able to observe different addition strategies being used. Sometimes Evelyn would use her "count on strategy" by using one addend she knew ("there are 6 pennies in the yellow, so if I add the other two...7, 8, then my answer must be 8!"). When making 10 pennies to put in an addend container Evelyn put two sets of five because she knew five and five made ten, etc.
• This lesson lends itself to understanding the commutative property of addition since it is easy to realize that it doesn't matter what order you dump your addends in the green container, you still arrive at the same sum.
• There is a lot of opportunity to talking about conservation of number. You cannot add or take away any pennies when pouring from your addends to your sum. Only the pennies in the addend containers can go into the sum container. 
• It provides a hands-on way to prove basic addition problems while relating them to written number sentences.