Place Value, Rounding, Addition, and Subtraction

Lesson 12

Objective

Round multi-digit numbers to any place value in more complex cases, including those involving real-world contexts and/or assessing the reasonableness of that estimate. 

Common Core Standards

Core Standards

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  • 4.NBT.A.3 — Use place value understanding to round multi-digit whole numbers to any place.

Foundational Standards

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  • 3.NBT.A.1

Criteria for Success

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  1. Round multi-digit numbers to any place value. 
  2. Know that, by convention, numbers at the midpoint between two benchmarks are rounded to the larger of the two benchmarks. 
  3. Use the $$\approx$$ symbol to record estimations.
  4. Understand the advantages and disadvantages of rounding a value to various place values, including the precision of rounding a number to a smaller place value (MP.6) and ease of working/operating when rounding a number to a larger place value.
  5. Determine the most appropriate place value to round to to have a reasonable estimate, based on the context of the problem (MP.1, MP.3). ​​​​​​

Tips for Teachers

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This whole lesson provides an excellent opportunity for students to construct viable arguments and critique the reasoning of others regarding when to round and to what level of precision, based on the context of the problem (MP.3). “How close an estimate must be to the actual computation is a matter of context,” and thus “the goal of computational estimation is to be able to flexibly and quickly produce an approximate result that will work for the situation and give a sense of reasonableness” (Van de Walle, p. 195). Thus, these tasks offer an opportunity for a rich discussion where one’s decision about the degree of precision of an estimate should be supported by reasoning. 

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (benefits from discussion). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

In the year 2015, there were 935,292 visitors to the White House. They each got a map to guide them around. President Obama said that they can round to the nearest thousand to decide about how many maps to order for next year. Do you agree or disagree with President Obama? Explain. 

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic C > Lesson 10Concept Development

Grade 4 Mathematics > Module 1 > Topic C > Lesson 10 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

2,837 students attend Lincoln Elementary school. How would you estimate the number of chairs needed at the school? 

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic C > Lesson 10Concept Development

Grade 4 Mathematics > Module 1 > Topic C > Lesson 10 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

  • Problem Set

    • Problem Set Answer Key
  • Homework

    • Homework Answer Key

Discussion of Problem Set

  • Look at #5. Why didn’t rounding to the nearest hundred work? What about rounding to the nearest thousand? What does this show you about rounding? 
  • Look at #7. What numbers could you fill the blanks with? How many different possible answers are there? 
  • Look at #8. Can both Jeff and Sara be correct? How? 
  • How do you choose a best estimate? What is the advantage of rounding to smaller and larger units?
  • Why might you round to the larger benchmark even though the numbers tell you to round to the smaller benchmark?
  • What does it mean for an estimate to be precise? What does it mean for an estimate to be reasonable? 

Target Task

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Problem 1

There are 72,053 Google employees in the United States. For Google’s new headquarters, their CEO rounds the number to the nearest thousand to determine how many desks to order. Do you think his estimate is reasonable? Why or why not? Explain. 

References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic C > Lesson 10Exit Ticket, Question #1

Grade 4 Mathematics > Module 1 > Topic C > Lesson 10 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

A company developed a student survey so that students could share their thoughts about school. In 2011, 594,500 students across the United States were administered the survey. In 2012, the company was deciding about how many copies of the survey to make. Round the number and explain why it is a reasonable estimate. 

References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic C > Lesson 10Exit Ticket, Question #2

Grade 4 Mathematics > Module 1 > Topic C > Lesson 10 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.

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