Lesson Video: Remainders Using Models Mathematics • 4th Grade

In this video, we will learn how to model division of two-digit numbers by one-digit numbers, when they do not divide evenly.

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Video Transcript

Remainders Using Models

In this video, we’re going to learn how to model division of two-digit numbers when they do not divide evenly. These children have 17 gel pens. They want to share them equally. How can we share these 17 gel pens between three children? We need to divide them. Let’s give everyone one gel pen each, two each. Now they have three gel pens each. Now they have four gel pens each. Each child has five gel pens, and we have two gel pens left over. We can’t share these equally between three children because one child wouldn’t get a gel pen.

To record how we worked this out, we would say there were 17 pens to begin with. We shared them equally or divided them between the three friends, which gave the children five gel pens each. And there were two gel pens left over. When we divide, we have to divide into equal groups. If we have an amount left over, we call this the remainder. So the “r” in our number sentence stands for remainder. There were 17 gel pens. We divided them or shared them equally between three children. Each child got five gel pens. There were two left over. 17 divided by three equals five remainder two. Let’s practice what we’ve learned about dividing with remainders by answering some questions now.

Each of the milk bottles are sold in crates of four. How many complete crates are there and how many bottles are left over?

This is a division problem. We have to divide the milk bottles into crates of four. In other words, we have to divide the milk bottles into equal groups of four. We have to count how many crates or groups of four there are and how many bottles are left over. This group has already been done for us. It contains four milk bottles. Let’s continue dividing the milk bottles into groups of four. Now we’ve got two groups of four, three groups of four, four groups of four, and there’s one milk bottle left over. We made four equal groups, and there’s one milk bottle left over. If the milk bottles were sold in crates of four, we could make four complete crates, and there would be one milk bottle left over.

10 children want to play a game. They need to be in teams of two. Find how many teams of two there will be and whether any child will be left out. Is it four teams, no one will be left out; four teams, one will be left out; five teams, no one will be left out; or five teams, one will be left out?

This question is all about dividing. There are 10 children and they’re trying to make teams of two. We have to work out two things: how many teams of two they can make and whether or not any child will be left out. We could model the number of children using blocks. We’ve got 10 blocks to represent the 10 children. Now, we can divide our 10 children or our 10 blocks into teams or groups of two: one, two groups of two, three groups of two, four groups of two, five groups of two. We had 10 counters and we’ve shared them or divided them equally into groups of two.

Can you see how many groups we made? There are five, so we can cross out these two possible answers. We didn’t make four teams. We made five. We made five groups, and there are no bricks left over. So this is the correct answer. There are five teams, and no one will be left out. If 10 children want to play a game and they need to be in teams of two, they could make five teams, and no one will be left out. To find the answer, we used 10 bricks and divided them into equal groups of two. And we found that there will be no bricks left over.

A teacher has 22 pencils that they want to share equally between four children. What is the maximum number of pencils each child will receive? Some pens might be left over.

This problem is all about sharing equally, which means it’s a division problem. The teacher wants to share 22 pencils equally between four children. We have to work out how many pencils each child will receive. We’ve modeled the number 22 using these bricks. Can you think of a way of sharing these pencils equally between four children? That means each group has to contain an equal number of bricks. There we go. We’ve made four groups, and each group contains an equal amount of bricks. Can you see how many bricks are in each group? We’ve made four groups of five, and there are two bricks left over.

If we have 22 pencils and shared them equally between four children, each child will have five pencils and there will be two left over. 22 divided by four equals five remainder two. So the maximum number of pencils each child will receive is five. We can’t share the two that are left over equally between four children. So the most pencils the children can get is five each.

What have we learned in this video? In this video, we have learned how to divide with remainders using models.

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