![]() ![]() ![]() I said Yes, but twenty-one what? And he told me twenty-one hundredths. Immediately, one student said, “Oh! 7 x 3 = 21!”. They counted up the squares and got 0.21. I pointed out the area where the two colors overlap and explained that was the product of 0.7 x 0.3. Then I showed them how to use the other color to shade 0.3 (blue), and we labeled it. ![]() We labeled that side to show that it had a length of 0.7. This I had to show them a little more directly. I reminded them that one side needed to show 0.7 and the other 0.3. They told me that both factors were decimals. I wrote 0.7 x 0.4 on the whiteboard and asked what was different now. I really played up the drama, telling them with great flourish that next I was going to show them something that would blow their minds! Time to move to grid paper and attempt multiplying a decimal by another decimal. So much better than just teaching tricks!įinally, we were ready to move on to a decimal by a decimal. When we get ready to connect the manipulatives to the standard algorithm, they can draw their models and see why we place the decimal where we do in the product. I asked if the product was greater than or less than the factors. Notice that this time they had to trade ten 10ths to make a 1. Pretty cool! Once they had filled out their rectangle, I again asked them to find the product. They actually figured out on their own that they would need to use 100ths. Then I told them they had to fill it in to make it into a rectangle. I just rotated them so they were horizontal. When trying to show 1.5 on the other side, they initially had the rods placed vertically. I just kept reminding them that one side had to show 2.3 and the other 1.5. Again, I gave them very little direction. That’s a huge advantage of small group instruction–you can really focus on getting the students to use precise mathematical language. They had to use vocabulary like factors, whole numbers, mixed numbers, and decimals to explain the differences in the problem types. Oh, BTW, with each new problem I asked them what had changed. Moving down the list, I asked them to try 2.3 x 1.5. I pointed out that, as with whole numbers, the product was greater than either of the factors. I asked students to find the product, and they added the base-10 blocks and got 2.6. That helped quite a bit and one of my pairs figured it out which, of course, led to a light bulb moment for the other group. I restated the problem as 2 groups of 1.3. They struggled a little, but were actually very interested in the problem. I wanted to see what they would do with it. I really didn’t give them much more direction than that. We labeled the sides and discussed that one side showed a length of 3 and the other showed 2. So I asked them to use their base-10 blocks to create an area model showing 2 x 3. Next, I needed to make sure that the students understood how to make an area model to represent multiplication. That makes the rod one 10th, and the cube one 100th. With decimals, the flat becomes the whole, meaning that it is now 1. But when we shift to decimals, the materials take on new values. When using base-10 blocks with whole numbers, the flat typically represents 100, the rod represents 10, and the cube represents 1. First, we needed to establish the value of the base-10 blocks. Decimal factor times a decimal factor (eg., 0.7 x 0.3)īefore getting into the meat of the lesson, we had to cover some basics.Mixed number factor times a decimal factor (eg., 1.3 x 0.4).Whole number factor times a decimal factor (eg., 2 x 0.8).Mixed number factor times mixed number factor (eg., 1.3 x 1.5).Whole number factor times mixed number factor (eg., 2 x 1.3).As I was planning for my lesson, I thought through all the variations related to multiplying with decimals, and here’s what I came up with: There is no additional cost to you, and I only link to books and products that I personally use and recommend. This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. Shifting from multiplying whole numbers to multiplying decimals is a huge shift, so that means that the learning needs to be concrete. In Texas, multiplying decimals with products to the hundredths was added to the 5th grade curriculum last year, and today I tackled it with some of our 5th graders. ![]()
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