Lesson 2 | Unit Conversions | 4th Grade Mathematics

Objective

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.

Common Core Standards

Core Standards

The core standards covered in this lesson

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

The foundational standards covered in this lesson

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.
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.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Establish benchmarks for the metric units of a kilogram and gram.
Use the meaning of the prefix “kilo-” to deduce that a kilogram is 1,000 times as heavy as a gram.
Establish benchmarks for the metric units of a liter and milliliter.
Use the meaning of the prefix “milli-” to deduce that a liter is 1,000 times as capacious as a milliliter.
Use these relationships to convert measurements from a larger metric mass or capacity units to a smaller unit (MP.7, MP.8).
Use these relationships to convert measurements from mixed metric mass or capacity units to a smaller unit (MP.7, MP.8).
Solve one-step word problems that require metric capacity or mass unit conversions (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

As the Geometric Measurement Progression states, “the Standards do not differentiate between weight and mass. Technically, mass is the amount of matter in an object. Weight is the force exerted on the body by gravity. On the earth’s surface, the distinction is not important (on the moon, an object would have the same mass, would weigh less due to the lower gravity)” (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 2). Thus, the term “mass” is used through Lesson 2 in reference to metric mass measurement but the term “weight” is used throughout Lesson 6 in reference to customary weight measurement. Enforcing the correct usage with students isn’t necessary, but it could be discussed if a student raises the issue.

Lesson Materials

1-gram weight (1 per teacher) — There are other options to use in place of this material. See Anchor Task 1 for more information.
1-kilogram weight (1 per teacher) — There are other options to use in place of this material. See Anchor Task 1 for more information.
1-milliliter container (1 per teacher) — There are other options to use in place of this material. See Anchor Task 2 for more information.
1-liter container (1 per teacher) — There are other options to use in place of this material. See Anchor Task 2 for more information.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

a. What do you think the relationship between a gram and a kilogram is? Explain.

b. Use your answer to Part (a) to fill out the following conversion table.

Kilograms (kg)	Grams (g)
1
2
4
7
10

Guiding Questions

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Problem 2

a. What do you think the relationship between a liter and a milliliter is? Explain.

b. Use your answer to Part (a) to fill out the following conversion table.

Liters (L)	Milliliters (mL)
1
2
5
8
20

Guiding Questions

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Problem 3

Jennifer is going on a trip with her two younger siblings, Leon and Veronica. They’re each bringing one suitcase. She wants to carry the heaviest suitcase, since she’s the oldest, and give Veronica, the youngest sibling, the lightest suitcase. Which child should carry which suitcase, based on their masses listed below?

Suitcase	Mass
Blue	26 kg
Black	20 kg 40 g
Gray	23,975 g

Guiding Questions

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Problem 4

Ronan bought a 3-pack of Gatorade. Each bottle in the 3-pack is 1 L 890 mL. How much Gatorade does Ronan have in total?

Guiding Questions

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Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

How did the table in #1 help you to solve #2(a)–(c)?
In #5, what was your strategy for ordering the weight of the students?
What patterns have you noticed about the vocabulary used to measure length, mass, and capacity?
What did you hypothesize the relationship between a gram and a milligram is? What about a liter and a kiloliter? Why?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Fill in the blank to make each equation true.

a. 4 kg 675 g = __________ g

b. 39 kg 74 g = __________ g

c. 62 L 18 mL = __________ mL

d. 80 L 900 mL = __________ mL

Student Response

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Problem 2

Daniel drinks 3,200 milliliters of water per day. Fatima drinks 2 liters 900 milliliters of water per day. Geneva drinks 3 liters 90 milliliters of water per day.Order the quantity of water each person drinks from least to greatest.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 1

Lesson 3

Lesson Map

Topic A: Metric Unit Conversion

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.

4.MD.A.1 4.MD.A.2

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

4.MD.A.1

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

4.MD.A.2

Topic B: Customary Unit Conversion

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.

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.

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.

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.

4.MD.A.1 4.MD.A.2

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

4.MD.A.2

Topic C: Fraction and Decimal Unit Conversions

Express fractional measurements in terms of a smaller unit.

4.MD.A.1 4.MD.A.2

Express decimal measurements in terms of a smaller unit.

4.MD.A.1 4.MD.A.2

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

4.MD.A.2

Unit Conversions

Objective

Common Core Standards

Core Standards

Measurement and Data

Measurement and Data

Foundational Standards

Measurement and Data

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem 4

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Student Response

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

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