Video: Investigating Division and the Distributive Property Using Array Models

Liam is learning strategies to divide. He finds that 21 ÷ 3 = (12 ÷ 3) + (_ ÷ 3). What number is missing from his equation? Use his equation to write the missing addition expression: 21 ÷ 3 = _ + _.

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Video Transcript

Liam is learning strategies to divide. He finds that 21 divided by three equals 12 divided by three plus what divided by three. What number is missing from his equation? Use his equation to write the missing addition expression: 21 divided by three equals what plus what.

This array has three rows. And there are seven hearts in each row. Liam is working on 21 divided by three. This means that there are 21 hearts altogether. Seven times three equals 21; 21 divided by three is seven. Liam has split his division into two parts. He say’s that 21 divided by three is equal to 12 divided by three and something divided by three. We have to find the missing number. If we look closely at the array, we can see the each row has pink hearts and blue hearts. This must be why Liam has two divisions. There are four pink hearts in each row and three blue hearts. So each row has four pink hearts, and there are three rows. Four lots of three or four times three is 12.

This is where Liam got the division 12 divided by three. This is for the pink hearts. Four times three is 12. 12 divided by three is four. There are three blue hearts in each row. There are three rows of three, which makes 9 — 3, 6, 9. So the missing number must be nine. There are nine blue hearts altogether. They’ve been divided into three equal groups, and each group contains three hearts. So the number missing from his equation is number nine. 21 divided by three is equal to 12 divided by three and nine divided by three .12 plus nine is 21. So altogether, we have 21 divided by three.

The second part of the question asks us to complete the missing addition expression. We need to find the two missing numbers. 21 divided by three equals what plus what. We already know that each row of hearts has four pink hearts and three blue hearts. And we know that 21 divided by three is seven. So our two missing numbers need to add together to give us a total of seven. Four plus three is seven. So 21 divided by three equals four plus three. The missing numbers in the addition expression are four and three. Four and three makes seven, and 21 Divided by three is seven. Well, the answer to the first part of the question is nine. And the answer to the second part of the question is four plus three.

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