Unit Conversions

Lesson 10

Math

Unit 7

4th Grade

Lesson 10 of 12

Objective


Express fractional measurements in terms of a smaller unit.

Common Core Standards


Core Standards

  • 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

  • 3.MD.A.1
  • 4.NF.A.1
  • 4.NF.B.4

Criteria for Success


  1. Convert customary measurements from a larger unit written as a fraction or mixed number to a smaller unit. 

Tips for Teachers


  • 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 $$13\times5,280$$, 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).

Lesson Materials

  • Ruler (1 per teacher) — There are other options to use in place of this material. See Anchor Task 1 Notes for more information.
  • Yardstick (1 per teacher) — There are other options to use in place of this material. See Anchor Task 1 Notes for more information.
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Anchor Tasks


Problem 1

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

  1. Ms. Cole says that 1 foot is equivalent to $$\frac{1}{3}$$ yard. Do you agree or disagree? Explain. 
  2. Using similar reasoning, determine what fraction of a foot an inch is. 

b.   Use your reasoning from Part (a) to solve the following conversions. 

  1. $$\frac{2}{3}$$ yard = ______ feet
  2. $$2\frac{1}{3}$$ yards = ______ feet
  3. $$\frac{5}{12}$$ foot = ______ inches
  4. $$3\frac{1}{4}$$ feet = ______ inches
  5. $$4\frac{1}{2}$$ yards = ______ inches

Guiding Questions

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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 = $${70}$$ ounces.

Guiding Questions

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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

Guiding Questions

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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

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • How could your answer to #3(c) help you solve #3(d)?
  • 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?

Target Task


Problem 1

Show or explain how you know $${2{3\over4}}$$ gallons = $${11}$$ quarts.

Problem 2

Solve.

a.   $${1{2\over3}}$$ yd = _____ ft

b.   $${3{3\over8}}$$ lb = _____ oz

c.   $${4{5\over6}}$$ ft = _____ in

d.   $${1{1\over2}}$$ hr = _____ min

Student Response

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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.

Extra Practice Problems

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 9

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Lesson 11

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Metric Unit Conversion

Topic B: Customary Unit Conversion

Topic C: Fraction and Decimal Unit Conversions

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