Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
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
Once students know what multiplication and division mean, they put that knowledge to work on story problems. The situations come in three main families: equal groups (5 bags of 6 oranges), arrays (4 rows of 9 seats) and measurement quantities (a ribbon 3 feet long cut into pieces, or 8 liters poured into 2-liter jugs). Every problem stays within 100, so the challenge is understanding the situation rather than heavy calculation.
A key skill is representing the problem before solving it. Students draw a quick sketch, a tape diagram or an array, and write an equation with a symbol for the unknown, such as 6 × ? = 42 or ? ÷ 4 = 8. The unknown can be in any position: the total, the number of groups or the size of each group. Problems with the unknown in different places look different but use the same relationship, and students who write the equation first are much less likely to grab the wrong operation just because they spotted a keyword.
Children taught that "each" means multiply will multiply in "24 cards were shared so each child got 6". Insist on a sketch of the situation before any calculation.
Some problems include extra information. A student who multiplies all three numbers in a problem may not have asked which numbers describe the groups.
In "Some boxes hold 7 pens each and there are 42 pens", students may write 42 × 7. Writing ? × 7 = 42 shows that the missing piece is a factor.
Answers like 8 when the question asks for meters or rows lose meaning. Ask students to answer in a full sentence with the unit.
A teacher arranges 48 desks in 6 equal rows. How many desks are in each row?
Answer: There are 8 desks in each row.
Give students sets of problems that use the same three numbers (for example 4, 9 and 36) with the unknown in different positions. Comparing them side by side shows that one fact family covers several stories. Tape diagrams are especially useful for measurement problems such as cutting lengths of rope.
State assessments usually present a short story and ask for the answer or for the equation that represents it. Practise both, and include measurement contexts like liters, centimeters and minutes so students are not surprised.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 36 (also accepted: 36 books)
4 equal groups of 9: 4 × 9 = 36 books.
Answer: 8 (also accepted: 8 pieces)
This is grouping by length: 24 ÷ 3 = 8 pieces of 3 feet.
Answer: D) 7 × ? = 56
7 rows of an unknown size make 56, so 7 × ? = 56. The missing number is 8.
Answer: 9 (also accepted: 9 packs)
45 ÷ 5 = 9, because 9 × 5 = 45. She needs 9 packs.
Answer: B) 63 marbles are put into 9 equal bags.
Splitting 63 into 9 equal bags is 63 ÷ 9 = 7 marbles per bag.
Answer: 18 (also accepted: 18 muffins)
The question asks about ONE tray, so the 4 trays are extra information. One tray is 3 × 6 = 18 muffins.
Answer: D) 9
8 × 9 = 72, so the missing factor is 9.
A full lesson with slides, activities and an exit ticket on multiplication and division word problems, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 3.OA.A.3 with an answer key, ready in about a minute.
Make a worksheet →Turn multiplication and division word problems into a quiz students answer online that marks itself, with a class summary for you.
Build a test →The standard asks students to represent problems with drawings and equations that use a symbol for the unknown. Writing the equation is part of showing understanding, not just finding the answer.
They are amounts like length, liquid volume or time. For example, pouring 20 liters into 5-liter buckets, or cutting a board into 2-foot pieces.