Methods for Dividing Whole Numbers
In fifth grade, students should be using a combination alternative strategies to complete division problems. These strategies might include an area model, using the relationship between multiplication and division, or using partial quotients (a variation of the standard algorithm). In the fifth grade AC mathematics course, it is our expectation that students will attempt and use the standard algorithm to divide, but they should also be familiar with other strategies as well.
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Students in AC Math are expected to work fluently with the standard algorithm for division, as presented in the first portion of the video to the left. If you need extra support in this area, please see Miss Dobbins.
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Division style problem solvers.
Multiplication and division problems have a predictable pattern to the type of word problems that students will see. Let's examine a few problems to identify their parts.
Alex makes homemade candles, and has agreements with 16 business owners to stock her goods in their stores. She just finished making her latest batch and wants to give every store the same amount of candles. If she made 378 candles, how many candles can she give to each store?
In this problem, we know the total amount of candles that are being distributed is 378. That amount is the amount we have to begin with. This amount then needs to be separated (distributed) into equal groups. In this problem, we know the number of groups we will have is 16. We need to find out the amount in each group.
When we plug it into our number sentence it should look like
Total Amount / Number of Groups = Amount in Each Group.
or
378/16=______
Lucas has 794 promotional stickers. If he wants to give every fan that buys a ticket to his show 5 stickers, how many of his fans will receive stickers with their order?
In this problem, we know the total amount stickers is 794. We also know the amount in each group of stickers will be 5. We need to figure out how many groups of five we can make. This will be the number of fans that get stickers with their ticket.
When we plug it into our number sentence, it should look like:
Total Amount / Amount in Each Group = Number of Groups
or
794/5=______
In this problem, we know the total amount of candles that are being distributed is 378. That amount is the amount we have to begin with. This amount then needs to be separated (distributed) into equal groups. In this problem, we know the number of groups we will have is 16. We need to find out the amount in each group.
When we plug it into our number sentence it should look like
Total Amount / Number of Groups = Amount in Each Group.
or
378/16=______
Lucas has 794 promotional stickers. If he wants to give every fan that buys a ticket to his show 5 stickers, how many of his fans will receive stickers with their order?
In this problem, we know the total amount stickers is 794. We also know the amount in each group of stickers will be 5. We need to figure out how many groups of five we can make. This will be the number of fans that get stickers with their ticket.
When we plug it into our number sentence, it should look like:
Total Amount / Amount in Each Group = Number of Groups
or
794/5=______
Interpreting the Remainder
Some problems in context may require you to think about what the remainder means to the context of the problem. For example, in both of the problems mentioned earlier the remainder was insignificant. We wanted all of our groups to be equal, but think about how that differs from this problem.
Vivian collects old and unique coins. She has 391 in her collection. She wants to display her collection in nice oak boxes. Each box will hold 24 coins. How many boxes will she need if she wants to display all of her coins?
In this problem, the remaining amount should be counted, because she wants to display all of her coins. Instead of purchasing 16 boxes, which would hold 384 of her coins, she needs to purchase 17 boxes, so that the remaining seven can be displayed as well.
In this problem, the remaining amount should be counted, because she wants to display all of her coins. Instead of purchasing 16 boxes, which would hold 384 of her coins, she needs to purchase 17 boxes, so that the remaining seven can be displayed as well.