Unit Conversions

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

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Unit Summary

The scope and sequence for 4th Grade Math was adjusted in August 2021. We moved Shapes and Angles to the end of the 4th grade sequence, so while this was previously Unit 8, it is now Unit 7. Learn more about this update.

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.

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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.

Additional Unit Practice

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.

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Lesson Map

Topic A: Metric Unit Conversion

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.

2

4.MD.A.1

4.MD.A.2

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

Topic B: Customary Unit Conversion

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.

Topic C: Fraction and Decimal Unit Conversions

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), …

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.

Measurement and Data

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

Measurement and Data

3.MD.A.1

Measurement and Data

3.MD.A.1 — Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
3.MD.A.2

Measurement and Data

3.MD.A.2 — Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Excludes multiplicative comparison problems (problems involving notions of "times as much"; Excludes compound units such as cm³ and finding the geometric volume of a container.

Number and Operations in Base Ten

4.NBT.A.1

Number and Operations in Base Ten

4.NBT.A.1 — Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
4.NBT.A.2

Number and Operations in Base Ten

4.NBT.A.2 — Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
4.NBT.A.3

Number and Operations in Base Ten

4.NBT.A.3 — Use place value understanding to round multi-digit whole numbers to any place.
4.NBT.B.4

Number and Operations in Base Ten

4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.5

Number and Operations in Base Ten

4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
4.NBT.B.6

Number and Operations in Base Ten

4.NBT.B.6 — Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations—Fractions

4.NF.A.1

Number and Operations—Fractions

4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.B.4

Number and Operations—Fractions

4.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.C.5

Number and Operations—Fractions

4.NF.C.5 — Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
4.NF.C.6

Number and Operations—Fractions

4.NF.C.6 — Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Operations and Algebraic Thinking

4.OA.A.1

Operations and Algebraic Thinking

4.OA.A.1 — Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.A.2

Operations and Algebraic Thinking

4.OA.A.2 — Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.A.3

Operations and Algebraic Thinking

4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Future Standards

Measurement and Data

5.MD.A.1

Measurement and Data

5.MD.A.1 — Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Ratios and Proportional Relationships

6.RP.A.1

Ratios and Proportional Relationships

6.RP.A.1 — Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

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.

Unit Conversions

Unit Summary

Assessment

Unit Prep

Intellectual Prep

Intellectual Prep for All Units

Unit-Specific Intellectual Prep

Essential Understandings

Vocabulary

Materials

Additional Unit Practice

Unit Practice

Lesson Map

Topic A: Metric Unit Conversion

1

2

3

4

Topic B: Customary Unit Conversion

5

6

7

8

9

Topic C: Fraction and Decimal Unit Conversions

10

11

12

Common Core Standards

Core Standards

Measurement and Data

Measurement and Data

Measurement and Data

Foundational Standards

Measurement and Data

Measurement and Data

Measurement and Data

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations—Fractions

Number and Operations—Fractions

Number and Operations—Fractions

Number and Operations—Fractions

Number and Operations—Fractions

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Future Standards

Measurement and Data

Measurement and Data

Ratios and Proportional Relationships

Ratios and Proportional Relationships

Standards for Mathematical Practice

Unit 6

Decimal Fractions

Unit 8

Shapes and Angles