Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
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
Multiplication starts with a picture in the mind: a number of groups, each holding the same number of things. When a third grader sees 5 × 7, the goal is for them to read it as 5 groups with 7 in each group, a total of 35 objects. The first factor tells how many groups there are and the second tells the size of each group, although the total stays the same if the roles are swapped.
Students show this meaning with bags of counters, rows of chairs, arrays of stickers or jumps on a number line. They also go the other way: given 4 × 6, they invent a story where it fits, such as 4 packs of juice boxes with 6 boxes in a pack. Being able to tell a story for a product is the real test of understanding, because it shows the child knows what the symbols stand for and is not just reciting a fact. Repeated addition (7 + 7 + 7 + 7 + 7) is a useful bridge, but the aim is to think in equal groups so that bigger products and division make sense later.
Some students see 5 × 7 and write 12 because they combine the two numbers. Ask them to build 5 groups of 7 cubes so they can see the total is far larger.
A drawing with 3 bags holding 4, 5 and 3 apples is not 3 × 4. Multiplication only describes situations where every group has the same amount, so check that each group matches.
When asked how many cookies are on 6 plates of 3, a child may answer 6 because they counted plates. Have them say what the total is counting before they answer.
For 4 × 6 a student might write about 4 children and 6 more children arriving, which is addition. Prompt for the word each: 4 children, each with 6 stickers.
Write a story for 4 × 6, draw it, and find the total.
Answer: Maya has 24 markers: 4 groups of 6 make 24.
Use real objects first: egg cartons, cups of beans, rows of desks. Ask students to say the sentence frame aloud, such as "3 groups of 5 is 15", before writing 3 × 5 = 15. Then move to arrays, which line up equal groups in rows and set up later work on area and the commutative property.
Assessment items for this standard often show a picture and ask which expression matches, or give an expression and ask which situation fits. Students who can explain both directions are ready for 3.OA.A.2, where the same groups are used to understand division.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: D) 6 × 4
There are 6 equal groups (baskets) with 4 in each group, so the expression is 6 × 4.
Answer: 15 (also accepted: 15 students)
5 groups of 3 is 5 × 3 = 15. Count by threes: 3, 6, 9, 12, 15.
Answer: B) Ben has 3 boxes with 8 crayons in each box.
3 boxes with 8 crayons in each are 3 equal groups of 8, which is 3 × 8. The other stories are addition, subtraction or division.
Answer: 14
7 groups of 2 is 7 × 2. Count by twos seven times: 2, 4, 6, 8, 10, 12, 14.
Answer: D) 5 + 5 + 5 + 5
4 × 5 means 4 groups of 5, so you add 5 four times: 5 + 5 + 5 + 5 = 20.
Answer: 18 (also accepted: 18 plants)
2 rows of 9 is 2 × 9 = 18 plants.
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.
Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
A full lesson with slides, activities and an exit ticket on interpreting multiplication as equal groups, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 3.OA.A.1 with an answer key, ready in about a minute.
Make a worksheet →Turn interpreting multiplication as equal groups into a quiz students answer online that marks itself, with a class summary for you.
Build a test →It means your child understands what multiplication is, not just the facts. They can explain that 5 × 7 means 5 groups of 7 and can make up a story or drawing that shows it.
For the meaning, the first number is usually the number of groups and the second is the size of each group. The total is the same either way, which students explore further in 3.OA.B.5.