For each of the following, perform the multiplication 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)
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.
Cade solves in the following way.

I’m going to split into and into . Now that I see the , I’m going to split that into . So we take and multiply that by . Now times is , and multiplying that by gives me . If I do I can start with which is . Now multiplying that by I get times which is and which is so all together that’s . Adding the gives me and that’s my answer.

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

2025-08-13 00:47:51