Unit Conversions

Lesson 5

Objective

Express customary length measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require customary length unit conversion.

Common Core Standards

Core Standards

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  • 4.MD.A.1 — Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …

  • 4.MD.A.2 — Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Foundational Standards

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  • 3.MD.A.2

  • 4.OA.A.1

Criteria for Success

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  1. Establish benchmarks for the customary units of a mile, yard, foot, and inch. 
  2. Understand that a mile is 5,280 times longer than a foot, a yard is 3 times longer than a foot, and a foot is 12 times longer than an inch. 
  3. Use these relationships to deduce conversion rates in the customary system of measurement not otherwise mentioned, e.g., there are 36 inches in a yard (MP.7, MP.8).
  4. Use these relationships to convert measurements from a larger customary length unit to a smaller unit (MP.7, MP.8).
  5. Use these relationships to convert measurements from mixed customary length units to a smaller unit (MP.7, MP.8).
  6. Solve one-step word problems that require customary length unit conversions (MP.4).

Tips for Teachers

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  • The following materials are needed for today's lesson: Yardstick rulers
  • As mentioned in the Progressions, “relating units within the traditional system provides an opportunity to engage in mathematical practices, especially ‘look for and make use of structure’ (MP.7) and ‘look for and express regularity in repeated reasoning’ (MP.8)” (GM Progression, p. 20).
  • It is unclear whether converting from miles to yards and feet is expected in Grade 4. It is not explicitly mentioned in the CCSS, the Progressions, or standardized test items from the larger testing sources (SBAC, PARCC, MCAS, and NY State Math Test). However, because of the unit’s obvious ubiquity combined with lots of evidence that students need to know conversion rates for miles in Grade 5, it is included in this lesson. It is at your discretion to choose to cut it. 

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (benefits from worked example) and Anchor Task 4 (can be done independently). You might decide not to give Anchor Task 4 independently, in which case it can be consolidated with Anchor Task 2 to be one Anchor Task. Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

Using a yardstick and a 12-inch ruler, answer the following questions. 

  1. What do you notice about the relationship between the length of a yard and the length of a foot? 
  2. What do you notice about the relationship between the length of a foot and the length of an inch? 

Guiding Questions

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Problem 2

Fill in the following conversion tables.

Guiding Questions

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Problem 3

Janella wants to go on an amusement park ride. She sees this sign before she gets in line for it:

Janella knows that she’s 1 yard 8 inches tall. Is she tall enough to go on the amusement ride? 

Guiding Questions

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References

flickr Photo: You must be 48" tall to ride by Adam Fagen

You must be 48" tall to ride by Adam Fagen is made available on flickr under a CC BY-NC-SA 2.0 license. Accessed June 29, 2018, 10:17 a.m..

Problem 4

Show students this image from a CNN article with the information below.

The world's tallest man met the world's shortest man.

Kosen, who is 31, is 8 feet and 3 inches tall. Dangi, who is 74, is 21 inches tall.

How much taller is the tallest man than the shortest man?

Guiding Questions

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Problem Set & Homework

Discussion of Problem Set

  • How could the tables in #2 have helped you solve #4(a)? 
  • How could you determine how many inches are in a mile to solve #4(e)? 
  • Which statements in #5 were false? How did you alter them to make them true? 
  • How long is Emma’s jump rope in #8? What made this problem especially difficult? 
  • Who is right in #10, Caled, Layla, neither or both of them? Why? 
  • When measuring length, which customary unit could I use? Which metric unit could I use?

Target Task

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Problem 1

Solve. 

a. 8 feet = ______ inches 

b. 4 yards 2 feet = ______ feet 

References

EngageNY Mathematics Grade 4 Mathematics > Module 7 > Topic A > Lesson 1Exit Ticket, Question #1

Grade 4 Mathematics > Module 7 > 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

Answer “true” or “false” for the following statements. If the statement is false, change the right side of the comparison to make it true. 

a. 12 yards < 40 feet __________________

b. 7 feet 1 inch > 70 inches __________________

References

EngageNY Mathematics Grade 4 Mathematics > Module 7 > Topic A > Lesson 1Exit Ticket, Question #2

Grade 4 Mathematics > Module 7 > 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.

Mastery Response

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