Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Division answers two different questions, and third graders learn to recognize both. Take 56 ÷ 8. One reading is sharing: 56 objects are dealt out fairly into 8 shares, and the answer, 7, is how many land in each share. The other reading is grouping: 56 objects are packed into groups of 8, and the answer, 7, is how many groups you can make. The numbers are identical but the story and the drawing are different.
Students should be able to look at a situation and say which kind it is, and they should be able to invent their own context for an expression like 24 ÷ 6. Sharing stories usually tell you the number of groups (6 friends) and ask for the amount in each. Grouping stories tell you the size of each group (6 eggs per carton) and ask how many groups. Knowing both meanings helps children choose division when a word problem does not use the word divide, and it links division tightly to the equal groups they already know from multiplication.
Many children only picture dealing items to people. When a problem asks how many bags of 5 can be filled from 30 apples, they get stuck. Model grouping explicitly with real bags.
Students sometimes share 20 pencils among 4 children by handing out piles of different sizes. Remind them that division always means each share or group is the same size.
Writing 8 ÷ 56 for sharing 56 cards among 8 players is common. The total being split always comes first in a division expression.
In a grouping problem the quotient is a number of groups, not a number of items. Ask students to label their answer: 7 bags, not 7 apples.
Write a sharing story and a grouping story for 24 ÷ 6 and solve each one.
Answer: 24 ÷ 6 = 4 in both stories: 4 strawberries per child, or 4 cartons.
Act out both kinds of problems with the same set of counters on the same day, so students notice that the answer is the same number even though the action is different. A T-chart labeled "number of groups" and "number in each group" helps children see which piece of information the problem gives and which it asks for.
Expect test items that show a picture of counters circled in groups and ask which division it represents, or ask students to choose a situation that matches an expression. This standard prepares students for 3.OA.B.6, where division is seen as finding a missing factor.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 6 (also accepted: 6 stickers)
Sharing 18 into 3 equal shares gives 18 ÷ 3 = 6 stickers each.
Answer: B) 30 crayons go into boxes of 5. How many boxes?
Putting 30 crayons into boxes of 5 tells you the size of each group and asks how many groups, so it is grouping: 30 ÷ 5 = 6 boxes.
Answer: 7 (also accepted: 7 bags)
Groups of 4 from 28: 28 ÷ 4 = 7 bags.
Answer: D) 40 ÷ 8
The total, 40, is split into 8 equal shares, so the expression is 40 ÷ 8 = 5 cookies per plate.
Answer: C) The number of rows
The size of each row (7) is given, so the answer, 35 ÷ 7 = 5, counts rows.
Answer: 5
Think of 45 shared into 9 groups, or 45 packed into groups of 9. Either way there are 5.
Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
A full lesson with slides, activities and an exit ticket on interpreting division as sharing and grouping, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 3.OA.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn interpreting division as sharing and grouping into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Sharing (also called partitive division), where you know the number of groups and find how many are in each, and grouping (measurement or quotative division), where you know the size of each group and find how many groups.
No. Third graders need to recognize and act out both situations. Teachers may use the formal terms, but students can simply say sharing and grouping.