- Whole number factor times mixed number factor (eg., 2 x 1.3)
- Mixed number factor times mixed number factor (eg., 1.3 x 1.5)
- Whole number factor times a decimal factor (eg., 2 x 0.8)
- Mixed number factor times a decimal factor (eg., 1.3 x 0.4)
- Decimal factor times a decimal factor (eg., 0.7 x 0.3)
I think I got them all!
Before getting into the meat of the lesson, we had to cover some basics. First, we needed to establish the value of the base-10 blocks. When using base-10 blocks with whole numbers, the flat typically represents 100, the rod represents 10, and the cube represents 1. But when we shift to decimals, the materials take on new values. With decimals, the flat becomes the whole, meaning that it is now 1. That makes the rod one 10th, and the cube one 100th.
Okay, this was a trickier one. Again, I gave them very little direction. I just kept reminding them that one side had to show 2.3 and the other 1.5. They showed the 2.3 first, quite easily. When trying to show 1.5 on the other side, they initially had the rods placed vertically. I just rotated them so they were horizontal. Then I told them they had to fill it in to make it into a rectangle. They actually figured out on their own that they would need to use 100ths. Pretty cool! Once they had filled out their rectangle, I again asked them to find the product. Notice that this time they had to trade ten 10ths to make a 1. They found the correct solution of 3.45. I asked if the product was greater than or less than the factors. They said greater.
If you are looking for some practice resources for multiplying decimals, check out this product, which contains an I Have/Who Has? game and matching picture/expression cards.