Unit Conversions

Students build their competencies in measurement, relating multiplication to the conversion of measurement units and exploring strategies for solving measurement problems.

Unit Summary

In this unit, students relate multiplication, particularly their understanding of “times as many” developed throughout Grade 4, to the conversion of measurement units. Students will also solve word problems involving measurement and measurement conversion.

In previous grades, students have worked with many of the metric and customary units (2.MD.1—6, 3.MD.1—2). They’ve noticed the relationship between some units to help them understand various measurement benchmarks but have not yet done any unit conversions. Not only does this unit build on measurement work from previous grades, but it also relies on myriad skills and understanding developed throughout Grade 4. As the Progressions state, “relating units within the metric system is another opportunity to think about place value” (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 20). Further, “students also combine competencies from different domains as they solve measurement problems using all four arithmetic operations, addition, subtraction, multiplication, and division” (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 20). Lastly, as directly stated in the language of 4.MD.2, students will convert units and solve problems involving fraction and decimal numbers. Thus, while the unit focuses on supporting cluster standards, their instruction enhances much of the major work of the grade, including place value (4.NBT.A), arithmetic operations (4.NBT.B), word problems (4.OA.A), and fractions (including decimal fractions) (4.NF). 

As NCTM’s position statement on the metric system states, “Students need to develop an understanding of metric units and their relationships, as well as fluency in applying the metric system to real-world situations. Because some non-metric units of measure are common in particular contexts, students need to develop familiarity with multiple systems of measure, including metric and customary systems and their relationships" (The Metric System, NCTM). Thus, students will explore both metric and customary systems of measurement, starting with unit conversions from larger to smaller metric units in Topic A, and then similarly with customary units in Topic B. Then, in Topic C, students deal with more complex cases of fractional and decimal unit conversions. At the end of each topic, students apply their new learning in the context of solving multi-step word problems involving unit conversions. 

The unit provides rich opportunities for students to engage with the mathematical practice standards. As the Progressions state, “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)” (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 20). Further, when students solve word problems that involve unit conversions, they "may use tape or number line diagrams for solving such problems (MP.1)" (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 20).

As mentioned previously, the unit summarizes and applies much of the major work of the grade in the fresh context of measurement, serving as a nice culmination for the year. But, the unit not only looks back on the year in review, it also prepares students for work in future grades, including the very direct link to converting from smaller units to larger ones in Grade 5 (5.MD.1) and also to ratios and proportions in the middle grades (6.RP.1) as well as many other areas to come. 

Pacing: 14 instructional days (12 lessons, 1 flex day, 1 assessment day)

Assessment

This assessment accompanies Unit 8 and should be given on the suggested assessment day or after completing the unit.

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Unit Prep

Essential Understandings

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  • The metric system of measurement is related to our place value system, with each larger unit consisting of 10 of the next smallest unit. 
  • One can only add and subtract like units. This goes for measurement units just as it does with place value units, fractional units, etc. Thus, measurement conversion of one or more units is often necessary in order to add or subtract them.

Vocabulary

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customary system of measurement

customary unit

metric system of measurement

metric unit

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Unit Materials, Representations and Tools

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  • Metric and customary weights (optional)
  • Gallon, quart, pint, and cup containers (optional)
  • Liter container (optional)
  • Meter stick (optional)
  • Yard stick (optional)
  • 12-inch rulers (optional)
  • Number line
  • Tape diagram
  • Two-column table

Intellectual Prep

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Intellectual Prep for All Units

  • Read and annotate “Unit Summary” and “Essential Understandings” portion of the unit plan. 
  • Do all the Target Tasks and annotate them with the “Unit Summary” and “Essential Understandings” in mind. 
  • Take the unit assessment.

Lesson Map

Topic A: Metric Unit Conversion

Topic B: Customary Unit Conversion

Topic C: Fraction and Decimal Unit Conversions

Common Core Standards

Key: Major Cluster Supporting Cluster Additional Cluster

Core Standards

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Measurement and Data
  • 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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Measurement and Data
  • 3.MD.A.1

  • 3.MD.A.2

Number and Operations in Base Ten
  • 4.NBT.A.1

  • 4.NBT.A.2

  • 4.NBT.A.3

  • 4.NBT.B.4

  • 4.NBT.B.5

  • 4.NBT.B.6

Number and Operations—Fractions
  • 4.NF.A.1

  • 4.NF.B.4

  • 4.NF.C.5

  • 4.NF.C.6

Operations and Algebraic Thinking
  • 4.OA.A.1

  • 4.OA.A.2

  • 4.OA.A.3

Future Standards

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Measurement and Data
  • 5.MD.A.1

Ratios and Proportional Relationships
  • 6.RP.A.1

Standards for Mathematical Practice

  • CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

  • CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

  • CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

  • CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

  • CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

  • CCSS.MATH.PRACTICE.MP6 — Attend to precision.

  • CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

  • CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.