Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
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 can read multiplication as a comparison, they put the idea to work in story problems. Three kinds appear: the larger amount is unknown (a puppy weighs 4 times as much as a 3-pound kitten, so how much does it weigh?), the smaller amount is unknown (a bike costs $96, which is 3 times as much as a scooter, so what does the scooter cost?), and the multiplier is unknown (a tree is 48 feet tall and a fence is 6 feet tall, so how many times as tall is the tree?). The first needs multiplication; the other two need division.
Students model each problem with a drawing and an equation that uses a symbol for the unknown, such as 3 × s = 96. A big part of the standard is telling these problems apart from additive ones. "Times as many" calls for multiplying or dividing, while "more than" or "fewer than" calls for adding or subtracting. Deciding which operation fits, and explaining why, is as important as getting the number right.
Students see "times" and multiply 96 by 3 even when 96 is the larger amount already. Ask them to sketch the bars first and decide which one is longer before choosing an operation.
A student who reads "6 more than" as "6 times" will multiply when they should add. Pair problems that use the same numbers with different wording so the contrast is visible.
Without a symbol for the unknown, students may answer with the wrong quantity, giving the total instead of the smaller amount. Writing an equation like 4 × n = 32 keeps the question in view.
A blue whale toy costs $72. That is 4 times as much as a dolphin toy. How much does the dolphin toy cost?
Answer: The dolphin toy costs $18.
Sort problems before solving them. Give students a stack of word problem cards and ask them to group the cards into "times as many" and "more than" piles, then draw a diagram for one of each. Only then compute. This slows students down enough to read for structure instead of grabbing numbers.
Tests commonly hide the unknown in different positions, so practice all three forms. A useful habit is to state the answer in a full comparison sentence, such as "The tree is 8 times as tall as the fence," which exposes answers that do not make sense.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 21 (also accepted: 21 pounds)
The dog's weight is 7 copies of 3 pounds: 7 × 3 = 21 pounds.
Answer: 32 (also accepted: $32)
3 × s = 96, so s = 96 ÷ 3 = 32. The scooter costs $32.
Answer: D) 8
6 × ? = 48. Since 6 × 8 = 48, the tree is 8 times as tall. 42 is the difference, which answers a "how much taller" question instead.
Answer: A) k = 4 × 5
Kai read 4 copies of Lena's 5 books, so k = 4 × 5 = 20.
Answer: B) Ty has 9 cards. Mo has 6 times as many cards as Ty. How many does Mo have?
Only "6 times as many" is a multiplicative comparison. The others use more than, fewer than, or take away, which call for adding or subtracting.
Answer: 7 (also accepted: 7 inches)
9 × g = 63, so g = 63 ÷ 9 = 7 inches.
Answer: 60 (also accepted: $60)
5 copies of $12: 5 × 12 = 60 dollars.
A full lesson with slides, activities and an exit ticket on multiplicative comparison word problems, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.OA.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn multiplicative comparison word problems into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Divide when you know the larger amount and need either the smaller amount or the number of times. For example, if 40 is 5 times as many as some number, that number is 40 ÷ 5 = 8.
4.OA.A.1 is about reading and writing comparison equations. 4.OA.A.2 asks students to solve full word problems with those comparisons, including ones where division is needed.