- 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.

*2 groups of 1.3*. 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. We labeled the sides 2 and 1.3. I asked students to find the product, and they added the base-10 blocks and got 2.6. I pointed out that, as with whole numbers, the product was greater than either of the factors. So far so good.

*factors, whole numbers, mixed numbers,*and

*decimals*to explain the differences in the problem types. That’s a huge advantage of small group instruction–you can really focus on getting the students to use precise mathematical language.

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.

Marlana says

I love this! I struggle with teaching these models. I am going to try your way.

Shelly says

Wow…. We were just working with kiddos today and this was so hopeful!!!! I know how to do it myself, but helping kids work through and understand more than just because I said so and put the decimal here.

Some of my kiddos made me feel like a super hero because they said you make this seem so easy!!! I love your other examples and can’t wait to share with the kids!!

Denise says

I think using a concrete model helps students visualize the meaning of multiplying decimal values. We use models after students estimate products with decimals. Students are given task cards with two decimal factors and the digits of the product WITHOUT the decimal point. Students use estimation to determine where the decimal point belongs in the product. Example: 2.3 X 5.1 gives a product with the digits 1173. Students use estimation to place the decimal. They know the product is a bit more than 10, so there is only one logical place the decimal can go. Therefore, the product is 11.73. Then we move to the area model using base-ten blocks.

Jorey Beamesderfer says

I like this too. I teach 6th grade and may try to get them to estimate prior to using the models.

Angela says

How long did you work with a small group on this?

Donna Boucher says

This lesson, which was an introductory first-teach lesson, was about 25 minutes long.

Stephanie says

This is so helpful! I never learned multiplying decimals visually; I just learned how to adjust the decimal point. This really helps create a clear picture of what is actually happening when multiplying two decimals results in a smaller number. That can be very confusing to explain to kids, so this activity is a great way to prove it to them. I think this would be helpful for middle school students as well who need to practice their multiplication skills!

Rhonda says

Help please! We are working with this model but are not sure what happens when we work with hundredths. It breaks down for us. Do you have an example of that? Rhonda

Donna Boucher says

Right, as far as I know, it won’t work with hundredths times hundredths. At that point, they would probably be using the standard algorithm, but their work with concrete and pictorial models will help them better understand the decimal placement.

Rhonda says

Thanks so much. I do love the concept and I think it helped the students. I admire all of your work and I know I am one of your biggest fans! Thanks for all you do. Rhonda

Alice says

Thanks for this! I have been using these manipulatives to teach decimals but I love how your explanation is set out so clearly! Going to do this lesson today:)

Beverly Thompson says

I am not seeing the share buttons for your blog anymore. I have always been able to share with my fellow teachers. Am I looking in the wrong place?

Donna Boucher says

If you just want to share a particular post, the icons are at the bottom of the post, right before the comments. There are also social share buttons at the top to visit my Facebook, Twitter, etc. Let me know if you still don’t see them!!

Nicole Schuler says

The models can get so confusing to the kids. I noticed my advanced classes struggle with the models more than my regular classes because they just want to do the math. But we spent FOREVER on models this year. But if was at the beginning of the year. By the time it was STAAR review, they had forgotten most of it.

I like the 2 groups of 1.3, saying it that way. Thanks for shantung!

Donna Boucher says

Retention is always a problem, Nicole, and that’s so frustrating. If you’re using a workshop approach, consider having a previous skill activity as one of your workstations to provide that spiraling review throughout the year.

A.T. says

Thank you for this post!

Kadi says

Hoo!! so helpful! then I can help my boy throat this! txs