# Unit Conversions

## 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

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• 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.

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• 3.MD.A.2

• 4.OA.A.2

## Criteria for Success

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

## Tips for Teachers

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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-kilogram weight
• 1-milliliter container
• 1-liter container

### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Tasks 3 and 4 (benefit from worked examples). Draw connections between prefixes for units to those they encountered in Lesson 1 to establish conversion rates before solving word problems, saving the need to go through Anchor Tasks 1 and 2. Find more guidance on adapting our math curriculum for remote learning here.

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• Problem Set
• Student Handout Editor
• Google Classrom Integration
• Vocabulary Package

## Anchor Tasks

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### Problem 1

1. What do you think the relationship between a gram and a kilogram is? Explain.
2. Use your answer to part (b) to fill out the following conversion table.
 Kilograms (kg) Grams (g) 1 2 4 7 10

#### Guiding Questions

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### Problem 2

1. What do you think the relationship between a liter and a milliliter is? Explain.
2. 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 Grey 23,975 g

#### Guiding Questions

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### Problem 4

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

#### Guiding Questions

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## Problem Set & Homework

• Problem Set Answer Key
• Homework Answer Key

### 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

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### Problem 1

Convert the measurements.

a.   21 kg 415 g = __________ g

b.   2 kg 91 g = __________ g

c.   87 L 17 mL = __________ mL

d.   96 L 200 mL = __________ mL

#### Mastery Response

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 2 > Topic A > Lesson 2Exit Ticket, Question #1

Grade 4 Mathematics > Module 2 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

### Problem 2

To make fruit punch, John’s mother combined 3,500 milliliters of tropical drink, 3 liters 95 milliliters of ginger ale, and 1 liter 600 milliliters of pineapple juice. Order the quantity of each drink from least to greatest.

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 2 > Topic A > Lesson 3Problem Set, Question #4

Grade 4 Mathematics > Module 2 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

## Additional Practice #### Unit Practice

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