Multiplication Word Problems Worksheet: Set Size Unknown

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Reteach: Multiplicative Comparison Set Size Unknown

 In some multiplicative comparison word problems, the part that is unknown is the number of items in one set. You are given the amount of the second set, which is a multiple of the unknown first set, and the “multiplier” amount, which tells you how many times bigger (or more) the second set is than the first. “Bigger” can also mean “longer,” or “wider,” “older,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed. These problems in which you know both the number in the second set, and the multiplier are called “Set Size Unknown” comparisons, because the number in one set is the part that is unknown. In order to answer the question you are being asked, you need to use the inverse operation of multiplication: division. This kind of division is “partition” or “sharing” division. Dividing the number in the second set by the multiplier will tell you the number in one set, which is the question you are being asked in this kind of problem.

Reteach: Guided Practice

 Let’s look at a “Set Size Unknown” problem: Stacy and Vicky both collect stickers. Vicky has seven times as many stickers as Stacy. If Vicky has 63 stickers, how many stickers does Stacy have? Start by clarifying what you understand, and what you are being asked to solve. The words “as many as” tell us that we are comparing. Vicky has 7 times as many as Stacy, so the multiplier is seven. It also tells us that Vicky’s amount, 63, is the second set, since she has more than Stacy. The part we are missing is the number in one set. To solve the problem we have to use the inverse operation of multiplication: division. We divide Vicky’s number of stickers, 63, by the multiplier, 7.  Since 63 ÷  7 = 9, Stacy has nine stickers. This answer is reasonable because the problem tells us that Vicky has more stickers than Stacy. We know that the second set is a multiple of the first set, so we can think, “how many stickers need to be in each of the seven sets to equal 63?”  7 x  9 = 63, so this answer makes sense.

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Independent Practice: Multiplicative Comparison Set Size Unknown

Solve each problem below by identifying the multiplier, and the number in the second set, which is a multiple of the first, unknown set. Divide the second set by the multiplier to find your answer.  Go back to the problem to make sure you have answered the question being asked, and that your answer makes sense.

It costs \$500 to take a bus tour of Europe. This is four times as much as it costs to take a bus tour of Mexico City. How much is the bus tour of Mexico City?

The multiplier is   4  . The number in the second set is   500  .

500   ÷   4   =   125

The tour of Mexico City costs \$ 125  . If you multiply the multiplier by your answer, you should get the cost of the European tour. Is your answer reasonable?

There are 256 students outside on the playground. This is eight times as many students as there are inside the cafeteria. How many students are inside the cafeteria?

The multiplier is   8  . The number in the second set is   256  .

256   ÷   8   =   32

There are   32   students inside the cafeteria. If you multiply the multiplier by your answer, you should get the number of students who are outside on the playground. Is your answer reasonable?

Franklin Middle School has 1,593 students. It has three times as many students as the nearest elementary school, Roosevelt Elementary. How many students attend Roosevelt Elementary School?

The multiplier is   3  . The number in the second set is   1,593  .

1,593   ÷   3   =   531

There are   531   students attending Roosevelt Elementary School. If you multiply the multiplier by your answer, you should get the number of students who are attending Franklin Middle school. Is your answer reasonable?

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Related Resources

The various resources listed below are aligned to the same standard, (4OA02) taken from the CCSM (Common Core Standards For Mathematics) as the Word problems Worksheet shown above.

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.1

Worksheet

Multiplication and Division

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Use the four operations with whole numbers to solve problems