Fraction Equivalence and Ordering

Lesson 1

Math

Unit 4

4th Grade

Lesson 1 of 15

Objective


Identify multiples and determine if a whole number is a multiple of another number.

Common Core Standards


Core Standards

  • 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.

Criteria for Success


  1. Understand that a multiple is a product of a given number and any other whole number.
  2. Find multiples of whole numbers.
  3. Determine whether a number is a multiple of another number. 
  4. Recognize and analyze patterns in the multiples of a number (e.g., all the multiples of 9 have digits whose sum is a multiple of 9). 

Tips for Teachers


  • Lessons 1—4 focus on gaining familiarity with factors and multiples, which “supports students’ work with multidigit arithmetic as well as their work with fraction equivalence” (PARCC 3-11 Model Content Frameworks for Mathematics).
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Anchor Tasks

25-30 minutes


Problem 1

a.   Mr. Rivera is setting up the auditorium for a presentation by arranging chairs into an array. The chairs are arranged into rows of 4 chairs each. 

  1. Draw arrays to represent what the auditorium will look like after he has built 1, 2, 3, 4, and 5 rows. 
  2. What is the total number of chairs in 1, 2, 3, 4, and 5 rows of chairs? 
  3. What do you notice about your answer to Part (ii)?

b.   Why is 14 chairs not a possible total number of chairs arranged in rows of 4?

c.   If Mr. Rivera kept setting up more rows of chairs, will he ever have 62 chairs set up? How do you know?

d.   Will he ever have 96 chairs set up? How do you know?

Guiding Questions

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Student Response

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Problem 2

a.   Francine says, "I knew 96 was a multiple of 4 because when I divided 96 by 4 I got 24 with no remainder. Since there’s no remainder, I know it’s a multiple." Does Francine’s method of determining whether a number is a multiple of another one work? Explain. 

b.   Determine whether the following numbers are multiples of 6 using a method that makes sense to you. Explain or show how you know. 

A.  0

B.  3

C.  36

D.  56

E.  78

F.  95

Guiding Questions

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Student Response

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Problem 3

I am a two-digit even number. I am a multiple of 5. I am more than 78. What am I?

Guiding Questions

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Student Response

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Problem 4

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. 

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Guiding Questions

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Student Response

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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 Fishtank Learning, Inc.

Problem Set

15-20 minutes


Discussion of Problem Set

  • In #2, which multiples were the easiest to write: the fives, fours, or sixes? Why? 
  • What strategy did you use in #3? 
  • In #6, why doesn’t 42 have 21 as a multiple? 
  • What number did you come up with for #7? Is there more than one correct answer? 
  • Which number is a multiple of every number? 
  • In Anchor Task #1, we found that when counting by fours, the multiples followed a pattern of having 0, 4, 8, 2, and 6 in the ones digit. Does that mean any even number is a multiple of 4? Why or why not?

Target Task

5-10 minutes


Problem 1

Select the list of numbers that are all multiples of 9.

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Student Response

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Problem 2

What numbers have 24 as a multiple?

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Next

Explore patterns in multiples of various whole numbers.

Lesson 2
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Factors and Multiples

Topic B: Equivalent Fractions

Topic C: Comparing and Ordering Fractions

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