Curriculum  /  Math  /  4th Grade  /  Unit 4: Fraction Equivalence and Ordering  /  Lesson 2

Fraction Equivalence and Ordering

Lesson 2

Math

Unit 4

4th Grade

Lesson 2 of 15

Objective

Explore patterns in multiples of various whole numbers.

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. Look for structure (MP.7) to find patterns in multiples of various factors, such as:
    1. All multiples of 2 are even numbers (i.e., end in 0, 2, 4, 6, or 8).
    2. All multiples of 3 have digits that add up to 3, 6, or 9.
    3. All multiples of 4 with an odd digit in the tens place have the digit 2 or 6 in the ones place, while all multiples of 4 with an even digit in the tens place have the digit 0, 4, or 8 in the ones place. 
    4. All multiples of 5 end in 0 or 5.
    5. All multiples of 6 end in 0, 2, 4, 6, 8 (i.e., are even/divisible by 2) and have digits that add up to 3, 6, or 9 (including adding the digits of subsequent sums together, e.g., 48 → 4 + 8 = 12 and 1 + 2 = 3).
    6. All multiples of 9 have digits that add up to 9 (including adding the digits of subsequent sums together, e.g., 99 → 9 + 9 = 18 and 1 + 8 = 9).
    7. All multiples of 10 have a 0 in the ones place.
  2. Make use of structure (MP.7) by using the divisibility rules stated above to determine whether a number larger than 100 is a multiple of 2, 3, 5, 6, 9, or 10. 

Tips for Teachers

  • This lesson explores divisibility properties for the numbers 1–10. This is slightly beyond the scope of the standard, but because knowing these properties will help students to determine whether numbers are factors or multiples more quickly, it is included here. It is at your discretion to keep or cut. 
  • Note that the lesson, including the objective, does not contain the language of “divisible” or “divisibility.” This is because it is not language called for in the standards. You may decide to use it, though.
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Anchor Tasks

25-30 minutes

Problem 1

a.   Take 60 seconds to list as many multiples of 2 as you can. 

b.   What do you notice about the values in that list? What do you wonder?

c.   Is 3,498 a multiple of 2? How do you know? 

Guiding Questions

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Student Response

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Problem 2

a.   Make a list of the first fifteen multiples of 3.

b.   Which of the numbers in your list are multiples of 6? What pattern do you see in where the multiples of 6 appear in the list?

c.   Which numbers in the list are multiples of 7? Can you predict when multiples of 7 will appear in the list of multiples of 3? Explain your reasoning.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Multiples of 3, 6, and 7

Multiples of 3, 6, and 7, accessed on Dec. 14, 2018, 2:36 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Discussion of Problem Set

  • What do all multiples of 2 have in common? 
  • How can you determine if a number is a multiple of 3? What must be true about it? 
  • What do all multiples of 4 have in common? Is every even number a multiple of 4? What about every other? 
  • How can you determine if a number is a multiple of 5? What must be true about it? 
  • How can you determine if a number is a multiple of 6? How is this related to knowing whether a number is a multiple of 2? A multiple of 3? 
  • How can you determine if a number is a multiple of 9?
  • What do all multiples of 10 have in common? How is this related to the work we did in Unit 1? (This question connects two domains in the grade, 4.OA.B and 4.NBT.A.) 

Target Task

5-10 minutes

Problem 1

What do all multiples of 9 have in common?

Student Response

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Problem 2

Use your answer to #1 above to show or explain how you know your answer to yesterday’s Target Task is correct: 

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

A. 1, 3, 9

B. 9, 18, 45, 62

C. 9, 49, 72, 90

D. 27, 63, 81, 99

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

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors.

Lesson 3
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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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