Multiplication and Division of Whole Numbers

Lesson 4

Objective

Multiply multiples of powers of ten. Estimate multi-digit products by rounding numbers to their largest place value. 

Common Core Standards

Core Standards

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  • 5.NBT.B.5 — Fluently multiply multi-digit whole numbers using the standard algorithm.

Foundational Standards

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  • 4.NBT.B.5

  • 5.NBT.A.1

  • 5.NBT.A.2

Criteria for Success

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  1. Multiply multiples of powers of ten with multiples of powers of ten (e.g., 6,000 x 50). (Note: They will not encounter examples that have multiple units, e.g., 6,400 x 50.) 
  2. Look for patterns in multiplication of multiples of powers of ten (MP.8).
  3. Estimate products by rounding values to their largest place value.

Tips for Teachers

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Throughout Lesson 4—10, students see and make use of structure (MP.7) and attend to precision (MP.6) as they decompose numbers into sums of multiples of base-ten units to multiply them.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Tasks 1 and 3 (benefit from worked examples). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

1. Solve. 

a.   4 x 3 = _______

b.   4 x 30 = ______

c.   40 x 30 = ______

d.   40 x 300 = ______

e.   400 x 300 = ______

2. What do you notice about Problem 1? What do you wonder?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic A > Lesson 1Concept Development

Grade 5 Mathematics > Module 2 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Solve.

  1.    60 x 5 = ________
  2.    60 x 50 = ________
  3.    60 x 500 = ________
  4.    60 x 5,000 = ________

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic A > Lesson 1Concept Development

Grade 5 Mathematics > Module 2 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 3

Estimate the following products.

a.     46 x 42

b.     463 x 42

c.     463 x 421

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 2 > Topic A > Lesson 2Concept Development

Grade 5 Mathematics > Module 2 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem Set & Homework

Discussion of Problem Set

  • Look at #1. What strategies did you use to solve? 
  • Look at #3c. How could I estimate this by rounding only one factor? Why might someone do this given the factors in this problem? Are there other numbers that are easy to use in computations without needing to round, like 25? 
  • Look at #5. What are some other factors whose product would be about 200,000? 
  • Look at #7. What language in the problem indicates that an estimate is an acceptable answer, rather than an exact one? 

Target Task

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Which pairs of factors have a product between 2,000 and 3,000?

Select the three pairs that apply.

  1.   8 x 200
  2.   9 x 300
  3.   70 x 30
  4.   90 x 20
  5.   700 x 3
  6.   800 x 4

Which two pairs of factors have a product of about 2,700?

Select the two pairs of factors that apply.

  1.   9 x 313
  2.   9 x 382
  3.   84 x 21
  4.   86 x 39
  5.   912 x 3

Mastery Response

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Unit Practice

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