What is this skill?
This skill teaches third graders to tell what kind of equal-groups story they are reading, so they know whether to multiply or divide. Every one of these stories has three numbers: how many groups there are, how many are in each group, and how many there are in all. "6 bags with 4 apples in each" gives the groups and the size, and asks for the total, so it is multiplication. "24 apples shared equally into 6 bags" gives the total and the number of groups, and asks for the size of each group. "24 apples, 4 in each bag" gives the total and the size, and asks how many bags.
The last two are both division, but they are different situations. The first is sharing: dealing things out one at a time until they are gone. The second is grouping: making groups of a set size and counting the groups. Arrays, such as chairs set out in rows or stamps on a sheet, work the same way, with rows in place of groups. The practice asks which operation fits, what the question is asking for, whether a division story is sharing or grouping, which number sentence or bar model matches, and then the answer, with facts up to 10 × 10.
Why it matters
Times tables are only useful if a child knows when to use them. Many children can recite 6 × 4 = 24 but freeze at a story, or multiply any two numbers they see. Learning to name the three quantities (groups, size, total) turns every equal-groups story into the same simple question: which of the three is missing?
This is also where keyword lists start to fail badly. The word "each" appears in both multiplication and division stories. "Shared" can appear in a story that is solved by multiplying: "6 friends shared some crackers, and each friend got 4. How many crackers were there?" The total is the missing number, so the answer is 6 × 4. A bar model cut into equal parts shows this at a glance, and the same drawing is used for fractions in third and fourth grade.
Common mistakes
- Multiplying whenever there are two numbers. Asking "do we already know how many in all?" catches most of these: if the total is given, the answer is a division.
- Treating "shared" or "each" as an instruction. These words describe the situation; they do not choose the operation. Have your child point to the total in the story, or say that it is missing.
- Confusing sharing with grouping. Both are 24 ÷ 4 or 24 ÷ 6, but the answer means something different: the number in each group, or the number of groups. Saying the answer with its label ("6 apples in each bag", "4 bags") keeps the meaning attached.
- Drawing the groups but not the total. Encourage a bracket under the whole bar with the total, or a question mark if the total is the unknown.
How to help at home
- Use cups and a handful of beans. Deal 18 beans into 3 cups for a sharing story, then start again and put 3 beans in each cup for a grouping story. Talk about which question each one answered.
- Spot arrays around the house: egg cartons, muffin pans, window panes, tiles. Ask "how many rows, how many in each row, how many in all?"
- Read a story aloud and ask your child to tell you which of the three numbers is missing before they calculate anything.
- Make a trap story together where the word "shared" goes with multiplying, then swap and let your child try to trick you.
Worked examples
These are real questions from the Tutorsaurus multiply or divide stories practice, with the answers worked out.
Example 1
A garden has 5 rows of carrots, with 6 carrots in each row. How many carrots are there? What is the question asking for?
Choices: How many in each row, The total, How many rows
Answer: The total. It asks for the total. This is an array story. 5 × 6 = 30.
Example 2
There are 35 muffins in all. Each tray holds 5. How many trays are needed? Which number sentence matches the story?
Choices: 35 × 5 = ?, 35 ÷ 5 = ?, ? ÷ 35 = 5, 35 − 5 = ?
Answer: 35 ÷ 5 = ? 35 ÷ 5 = 7 is true, and it follows the story. This is an equal-groups story. The words in all tell you the total, which you already know, so divide. 35 ÷ 5 = 7.
Example 3
7 friends shared some raisins. Each friend got 2. How many raisins did they share?
Answer: 14. This is an equal-groups story. The word shared is a clue, not a rule: we know 7 equal shares of 2 and need the total, so multiply. 7 × 2 = 14.
Printable worksheet (PDF) — one page of multiply or divide stories problems from the same practice, easier ones first, with an answer key on page 2. Free to print, no sign-up. See all 3rd grade math worksheets.