Multi-Digit Multiplication

Lesson 8

Objective

Solve contextual problems that involve factors, multiples, prime, composite, and/or square numbers.

Common Core Standards

Core Standards

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  • 4.OA.B.4 — Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.

Foundational Standards

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  • 3.OA.C.7

Criteria for Success

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  1. Solve contextual problems involving factors, multiples, prime, composite, and/or square numbers. 

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Anchor Tasks

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Problem 1

A restaurant is open 24 hours a day. The manager wants to divide the day into work shifts of equal length. Show the different ways this can be done. The shifts should not overlap, and all shifts should be a whole number of hours long.

Guiding Questions

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References

Kentucky Department of Education Operations and Algebraic Thinking: Number Puzzles Grade 4 Formative Assessment LessonStudent materials, Question #1

Problem 2

Kaitlyn was playing with her little brother Declan, building towers with his blocks. Declan’s colored blocks are each a different size. The chart below shows the color and size of each block.

Color Size
Blue 4 inches
Red 7 inches
Yellow 9 inches
Green 5 inches
Orange 6 inches

Kaitlyn built a tower that used only red blocks. Which of the following could be the height of the tower? Select all that apply. 

A. 36 inches

B. 56 inches

C. 49 inches

D. 28 inches

E. 62 inches

F. 84 inches

Guiding Questions

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References

Howard County Public School System 4.OA.4 - About the Math, Learning Targets, and RigorAssessment Task #8

4.OA.4 - About the Math, Learning Targets, and Rigor is made available by the Howard County Public School System under a CC BY-NC-SA 4.0 license. © 2013-2014 Elementary Mathematics Office Howard County Public School System. Accessed Dec. 14, 2018, 2:55 p.m..

Modified by The Match Foundation, Inc.

Problem 3

In North America, we have a kind of cicada that only emerges from the ground every 17 years. What kind of advantage does that give the cicadas in the wild? 

Guiding Questions

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References

Yummy Math Cicada Swarmaggedon

Cicada Swarmaggedon by Brian Marks and Lesie Lewis is made available on YummyMath. Copyright © 2017 Yummy Math. All Rights Reserved. Accessed Jan. 8, 2018, 1:37 p.m..

Modified by The Match Foundation, Inc.

Problem Set & Homework

Discussion of Problem Set

  • How did you decide on which answers were correct in #1? What do they all have in common?
  • How many ants might Nathan’s mom have seen in #3? Is there more than one possible answer?
  • Which lockers were still open at the end of the game in #8? What do they all have in common? What about lockers only touched by two students? What do those have in common? What about three students? The most students?
  • What is the fewest number of packages of hot dogs and buns Avery can buy in #9 to have exactly the same number of both? What made this problem more challenging than the others? 
  • When would all three clocks sound at the same time in #10? What made this problem more challenging than the others?

Target Task

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During art class last week, Carmen put crayons into cups for her art teacher. She put exactly 9 crayons into each cup. 
Altogether, Carmen put more than 20 crayons, but fewer than 30 crayons, into the cups. 

Part A
What is the total number of crayons that Carmen put into the cups?

Part B
Is your answer to Part A a prime number or a composite number? Explain your reasoning.

Part C
This week, Carmen’s art teacher has a total of 28 crayons to put into cups. She wants Carmen to put the same number of crayons into each cup. 

Write all factor pairs of 28 that show possible ways Carmen can divide 28 crayons equally to put into cups.

References

Massachusetts Department of Elementary and Secondary Education Spring 2017 Grade 4 Mathematics TestQuestion #5

Spring 2017 Grade 4 Mathematics Test is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed Jan. 8, 2018, 1:39 p.m..

Mastery Response

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Additional Practice

Unit Practice

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