# Unit Conversions

## Objective

Express fractional measurements in terms of a smaller unit.

## Materials and Resources

• Yardstick  — (Optional: 1 per teacher/student)

## 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.

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• 3.MD.A.1

• 3.MD.A.2

• 4.NF.A.1

• 4.NF.B.4

## Criteria for Success

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1. Understand that ${{1\over3}}$ yard is equivalent to a foot and ${{1\over12}}$ foot is equivalent to an inch.
2. Understand that ${{1\over16}}$ pound is equivalent to an ounce.
3. Understand that ${{1\over4}}$ gallon is equivalent to a quart, ${{{{1\over2}}}}$ quart is equivalent to a pint, ${{{{1\over2}}}}$ pint is equivalent to a cup, and ${{1\over8}}$ cup is equivalent to a fluid ounce.
4. Understand that ${{{{1\over2}}}}4$ day is equivalent to an hour, ${{{{1\over60}}}}$ hour is equivalent to a minute, and ${{{{1\over60}}}}$ minute is equivalent to a second.
5. Use these relationships as well as multiplication to convert customary measurements from a larger unit written as a fraction to a smaller unit.

## Tips for Teachers

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• In general, metric measurements that aren’t whole numbers are usually expressed as decimals rather than fractions. Thus, only customary units are used in today’s lesson. But, you could give students a few examples with metric units, e.g.,

${3{1\over2}}$ m = ________ cm

${2{3\over10}}$ L = ________ mL

${7{6\over100}}$ kg = ________ mg, etc.

• Tons and miles are not included in today’s lesson, since their conversion rates are so large and thus would involve more complicated computations or fractions with denominators that are beyond the scope of 4.NF. You could, however, choose to include some examples with these units, such as ${5{1\over2}}$ miles = ________ feet, but make sure the examples you use are relatively simple and especially not beyond the scope of the computations they have encountered in Grade 4 (e.g., having students compute how many feet are in $13\frac{3}{4}$ miles, which would involve the computation 13 x 5,280, beyond the 4-digit by 1-digit multiplication called for in 4.NBT.5).
• The work of Lesson 10 and 11 connects the work of measurement conversion (4.MD.1, 4.MD.2) to their work with fraction and decimal fraction operations (4.NF).

#### Fishtank Plus

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### Problem 1

1. Look at your yardstick and 12-inch ruler again.

a.  Ms. Cole says that 1 foot is equivalent to $\frac{1}{3}$ yard. Do you agree or disagree? Explain.

b.  Using similar reasoning, determine what fraction of a foot an inch is.

2. Use your reasoning from #1 to solve the following conversions.

a.  $\frac{2}{3}$ yard = ______ feet

b.  $2\frac{1}{3}$ yards = ______ feet

c.  $\frac{5}{12}$ foot = ______ inches

d.  $3\frac{1}{4}$ feet = ______ inches

e.  $4\frac{1}{2}$ yards = ______ inches

### Problem 2

a.  Show or explain how you know ${{1\over16}}$  pound = $1$ ounce.

b.  Show or explain how you know ${1\over4}$  pound = $4$ ounces.

c.  Show or explain how you know $4{3\over8}$  pounds = ${67}$ ounces.

### Problem 3

Solve.

a.  ${{1\over4}}$ gallon = ________ quart

b.  ${{3\over2}}$ quarts = ________ pints

c.  ${4{1\over2}}$ pints = ________ cups

d.  ${7{3\over4}}$ cups = ________ fluid ounces

### Problem 4

Solve.

a.  ${{1\over24}}$ day = ________ hour

b.  ${{13\over60}}$ hour = ________ minutes

c.  ${2{1\over4}}$ minutes = ________ seconds

d.  ${3{1\over2}}$ days = ________ minutes

## Discussion of Problem Set

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• How can knowing that 8 gallons is equal to 32 quarts help you check to make sure your answer to #3(f) is reasonable?
• Which car should Ms. Needham buy in #6? Why?
• When have you heard someone talk about a fractional unit before?

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### Problem 1

Show or explain how you know ${4{3\over4}}$ gallons = ${19}$ quarts.

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 7 > Topic C > Lesson 13Exit Ticket, Question #1

Grade 4 Mathematics > Module 7 > Topic C > Lesson 13 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.

 a.  ${1{1\over4}}$ pounds = _____ ounces b.  ${2{3\over4}}$ hr. = _____ min. c.  ${5{1\over2}}$ feet = _____ inches d.  ${1{1\over3}}$ yd. = _____ ft.

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 7 > Topic C > Lesson 13Exit Ticket, Question #2

Grade 4 Mathematics > Module 7 > Topic C > Lesson 13 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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