For each of the following, find the total without writing anything down, and without using a calculator or other tool. You can write down your answer so that you don’t forget it!
(a)
(b)
(c)
(d)
(e)
As a group, illustrate your solutions to each problem using a picture. Your pictures can include objects, number lines, or whatever else makes sense to you! Try using different types of pictures for each problem.
As a group, illustrate your solutions to each problem using equations. Be sure to place the equals sign only between things which are actually equal! Did you use any properties of arithmetic in your equations? If so, what were they, and where did you use them? Be as specific as you can.
Mel solves in the following way.

I’m going to start by shifting this problem from to be . This will have the same answer as my original problem because I took away from both numbers. Now I take and get . Then I take away more and get , which is my answer.

Why does Mel’s strategy give us the correct answer? Draw pictures or write equations to help you understand this strategy. Did Mel use any properties of arithmetic in this strategy? Explain your thinking.

2025-08-13 00:41:47