Lesson 6 | Unit Conversions | 4th Grade Mathematics

Objective

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.

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

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 customary unit of a ton, pound, and ounce.
Understand that a ton is 2,000 times as heavy as a pound and a pound is 16 times as heavy as a ton.
Use these relationships to convert measurements from a larger customary weight unit to a smaller unit (MP.7, MP.8).
Use these relationships to convert measurements from mixed customary weight units to a smaller unit (MP.7, MP.8).
Solve one-step word problems that require customary weight unit conversions (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

It is unclear whether converting from tons to pounds is expected in Grade 4. It is not explicitly mentioned in the CCSS, the Progressions, or standardized test items from the larger testing sources (SBAC, PARCC, MCAS, and NY State Math Test). However, because tons are included on the Grade 5 MCAS reference sheet Massachusetts Comprehensive Assessment System Grade 5 Mathematics Reference Sheet and is therefore assumed to be a conversion students need to be familiar with, it is included in this lesson. It is at your discretion to choose to cut it.
As mentioned in Lesson 2, 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

Balance scale (1 per teacher) — There are other options to use in place of this material. See Anchor Task 1 Notes for more information.
1-ounce weights (16 per teacher) — There are other options to use in place of this material. See 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 Anchor Task 1 Notes 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

Use a balance scale and 1-pound and 1-ounce weights to answer the following question.

What do you notice about the relationship between the weight of a pound and the weight of an ounce?

Guiding Questions

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Problem 2

Fill in the following conversion tables.

Tons	Pounds (lb)
1
2
3
6

Pounds (lb)	Ounces (oz)
1
2
4
15

Guiding Questions

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Problem 3

A birth weight between 5 pounds 8 ounces and 8 pounds 13 ounces is considered normal for a full-term newborn baby. Louis’s daughter weighs 145 ounces. Is Louis’s daughter’s weight considered normal?

Guiding Questions

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Problem 4

Robyn and Danny are truck drivers. They have to haul the following pallets to the same location.

Pallet	Weight
A	4,000 lb
B	4 tons 1,000 lb
C	1 ton 1,625 lb
D	1,000 lb
E	3 tons
F	2 tons 375 lb

Robyn and Danny want to each haul the same amount of weight. They can’t break the pallets apart into smaller packages. Which pallets should they each take? How much weight will they be hauling?

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Did anyone determine how many ounces are in a ton in #3? How did you figure it out?
How many additional one-ounce weights are needed to balance Julius’s three-pound weight in #4? How did you figure that out?
In #5, I think each bottle of glue weighs 2 ounces, since 1 lb. 2 oz. is the same as 12 ounces. Do you agree or disagree? Why?
What strategy did you use to solve #6? Which strategy is most efficient?
When measuring weight, which customary unit could I use? Which metric unit could I use?

Target Task

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

Problem 1

Solve.

a. 9 pounds = __________ ounces

b. 13 pounds 5 ounces = __________ ounces

Student Response

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Problem 2

Sasha’s backpack weighs 15 pounds 9 ounces. Amanda’s backpack weighs 183 ounces. Stefan’s backpack weighs 272 ounces. Order the weight of each backpack from greatest to least.

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 5

Lesson 7

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

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.

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

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

Lesson Map

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