# 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. But, the unit not only incorporates some important Grade 4 understanding, 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)

For guidance on adjusting the pacing for the 2021-2022 school year, see our 4th Grade Scope and Sequence Recommended Adjustments. • Expanded Assessment Package
• Problem Sets for Each Lesson
• Student Handout Editor
• Vocabulary Package

## Assessment

This assessment accompanies Unit 7 and should be given on the suggested assessment day or after completing the unit.

## Unit Prep

### Intellectual Prep

?

#### 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 Post-Unit Assessment.

#### Unit-Specific Intellectual Prep

• Read the following table that includes models used in this unit.
Two-column table
 Gallons Quarts 1 4 2 8 3 12

### Essential Understandings

?

• 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

?

metric unit

metric system of measurement

customary unit

customary system of measurement

To see all the vocabulary for this course, view our 4th Grade Vocabulary Glossary.

### Materials

?

• Meter stick (1 per teacher) — There are other options to use in place of this material. See Lesson 1 Anchor Task 1 Notes for more information.
• 1-kilogram weight (1 per teacher) — There are other options to use in place of this material. See Lesson 2 Anchor Task 1 Notes for more information.
• 1-gram weight (1 per teacher) — There are other options to use in place of this material. See Lesson 2 Anchor Task 1 Notes for more information.
• 1-liter container (1 per teacher) — There are other options to use in place of this material. See Lesson 2 Anchor Task 2 Notes for more information.
• 1-milliliter container (1 per teacher) — There are other options to use in place of this material. See Lesson 2 Anchor Task 2 Notes for more information.
• Yardstick (1 per teacher) — There are other options to use in place of this material. See Lesson 5 Anchor Task 1 Notes for more information.
• 12-inch rulers (1 per teacher) — There are other options to use in place of this material. See Lesson 5 Anchor Task 1 Notes for more information.
• 1-pound weight (1 per teacher) — There are other options to use in place of this material. See Lesson 6 Anchor Task 1 Notes for more information.
• 1-ounce weight (16 per teacher) — There are other options to use in place of this material. See Lesson 6 Anchor Task 1 Notes for more information.
• Balance scale (1 per teacher) — There are other options to use in place of this material. See Lesson 6 Anchor Task 1 Notes for more information.
• 1-gallon container (1 per teacher) — There are other options to use in place of this material. See Lesson 7 Anchor Task 1 Notes for more information.
• 1-quart container (1 per teacher) — There are other options to use in place of this material. See Lesson 7 Anchor Task 1 Notes for more information.
• 1-pint container (1 per teacher) — There are other options to use in place of this material. See Lesson 7 Anchor Task 1 Notes for more information.
• 1-cup container (1 per teacher) — There are other options to use in place of this material. See Lesson 7 Anchor Task 1 Notes for more information.
• Water (About 3 gallons per teacher) — There are other options to use in place of this material. See Lesson 7 Anchor Task 1 Notes for more information.
• Optional: Demonstration analog clock (1 per teacher) — See Lesson 8 Anchor Task 1 Notes for more information. #### Unit Practice

With Fishtank Plus you can access our Daily Word Problem Practice and our content-aligned Fluency Activities created to help students strengthen their application and fluency skills.

View Preview

# 1

4.MD.A.1

4.MD.A.2

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

# 3

4.MD.A.1

Know and relate metric units to place value units in order to express measurements in different units.

# 4

4.MD.A.2

Solve multi-step word problems that requires metric unit conversions of length, mass, and capacity.

# 5

4.MD.A.1

4.MD.A.2

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.

# 6

4.MD.A.1

4.MD.A.2

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

# 7

4.MD.A.1

4.MD.A.2

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

# 8

4.MD.A.1

4.MD.A.2

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

# 9

4.MD.A.2

Solve multi-step word problems involving conversion of customary units of length, weight, capacity, and time.

# 10

4.MD.A.1

4.MD.A.2

Express fractional measurements in terms of a smaller unit.

# 11

4.MD.A.1

4.MD.A.2

Express decimal measurements in terms of a smaller unit.

# 12

4.MD.A.2

Solve word problems involving converting fractional and decimal measurements to a smaller unit.

## Common Core Standards

Key: Major Cluster Supporting Cluster Additional Cluster

### Core Standards

?

##### 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.

?

• 3.MD.A.1

• 3.MD.A.2

• 4.NBT.A.1

• 4.NBT.A.2

• 4.NBT.A.3

• 4.NBT.B.4

• 4.NBT.B.5

• 4.NBT.B.6

• 4.NF.A.1

• 4.NF.B.4

• 4.NF.C.5

• 4.NF.C.6

• 4.OA.A.1

• 4.OA.A.2

• 4.OA.A.3

?

• 5.MD.A.1

• 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.