### For the last couple of weeks, we’ve been multiplying and dividing decimals. I came across this great way of showing a pictorial representation of multiplying decimals. Of course it didn’t come with the grids, so I made a page up for you to use in your classes. Here is the download so that you can follow along as I go……

## Follow along as I work through the handout.

### The first problem is 0.8 x 0.6. This is like finding the area of a rectangle. The length is 0.8 (or eight out of ten squares), and the width is 0.6 (or six out of ten squares). Remind them that area is the number of square units in a rectangle. Have them shade in a rectangle that is 0.8 x 0.6. Count the number of squares in that rectangle. They should have 48 squares. I teach my students fractions, decimals, and percents using Base 10 blocks (for those lessons, click here) so they know that out of this whole block is out of 100, so each of the small squares are 0.01. I ask them how many squares they have, they would reply with 48, and I ask what each small square represents, and they say hundredths. So I ask them what they have, and they respond with 48 hundredths. I ask them how they write that, and they say 0.48.

### The second problem is 0.3 x 0.7. Students should shade in a rectangle that is 0.3 (or three out of the ten squares) wide and 0.7 (or seven out of the ten squares) long. Have them count how many squares are shaded. At some point, they should be understanding that they are just multiplying the two numbers together. Ask how many squares are shaded? 21. That would be 21 out of 100 which would be 21 hundredths or 0.21.

### This one is to show for more than a tenth times a tenth. Hopefully, they start to get the picture. I couldn’t make a graph that was 100 units long, so we had to improvise a little (it’s the thought that counts right?). They should shade in 13 out of the one hundred squares wide and 7 out of the ten squares long. When they count their squares (or by now have figured out to just multiply), they should get 91. Ask them how many total squares there should be in the whole picture (remember….pretending that you have the full 100 units wide), they should say that they have 10 rows of 100 squares which would be 1000. They have shaded in 91 out of the 1000 squares. How would you write 91 thousandths? 0.091. I then go on and show them that 0.4 x 0.8 would be ten by ten or hundredths. 0.98 x 0.3 would be one hundred by ten which would be 1000. 0.84 x 0.32 would be one hundred by one hundred, or 10,000. After they’ve gotten this concept down, they you can maybe just throw in that you count the number of decimal places, but I feel it’s important for them to grasp the number sense of decimals.

## I hope you find this post useful and enjoy the freebie!!

### Here is the great activity that I used after teaching this lesson. I actually used it for rounding and estimating products of decimals and then kept it up to use with multiplying decimals by a whole number. You could actually add to it in many ways depending on the level of your students. You could tell them that tax is 8.5% and have them compute the tax and the total that they would pay. For dividing decimals, you could have them use the spinner to tell them how many items are included with each price and for them to calculate the cost per unit. Either way, it is a super cute and fun way for students to practice an important skill.

## Click here or on the image to go to my Teachers Pay Teachers store to purchase this activity for only $4.00!

thank u for the help it really helped me alot!!! Thanks

I am confused with the decimal multiplication examples. I am getting ready to teach this next week and am looking for meaningful activities. You are saying that 1 small square out of 100 is 0.01 (one hundredth), yet you are using it as a tenth when coloring it in. For example, 0.3 x 0.7 was shown as 3 squares colored in by 7 squares, and the rest filled in; basically an array. You also use the small squares as both tenths and hundredths in the third picture. I understand how you got the answers, but I’m not sure if the pictures show the true representations of each number in the equations. Let me know if there is something I am missing, because I would really like to use this in class, but I’m not sure my students would understand it.

It’s three out of each ten (in the row of ten) times seven out of each ten (in he column of ten) is twenty-one out of the whole hundred. Does that make more sense? Thanks for the question!

I respectfully disagree. You have created an array, hence why you get the correct answer. The visual doesn’t show three tenths –otherwise you’d have 30 squares shaded in. It also doesn’t show seven tents because that would require 70 squares. What you forgot is that you are multiplying .3 of .7. You could’ve shaded 3 tents vertically, seven tents horizontally and the common shaded area would be your 21 tenths.

Yes, I agree with Gus. What you have showing in that pink grid for .70 x .30 is only where the two decimals would intersect on the graph. The 0.70 should show 7 columns with 10 squares each colored. Then the 0.30 should show 3 rows of 10 cubes in each row colored. After you color the 7 columns of 10 rows you go back to the top right corner of that graph and color 3 rows of 10 cubes. The intersecting portion is the answer .21 as Gus was saying.

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