Lesson 1 | Unit Conversions | 4th Grade Mathematics

Objective

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.

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

2.MD.A.1

Measurement and Data

2.MD.A.1 — Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.A.2

Measurement and Data

2.MD.A.2 — Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
2.MD.A.3

Measurement and Data

2.MD.A.3 — Estimate lengths using units of inches, feet, centimeters, and meters.
2.MD.A.4

Measurement and Data

2.MD.A.4 — Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
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 kilometer, meter, centimeter, and millimeter.
Understand that a kilometer is 1,000 times as long as a meter, a meter is 100 times as long as a centimeter, and a centimeter is 10 times as long as a millimeter.
Use these relationships to deduce conversion rates in the metric system of measurement not otherwise mentioned, e.g., there are 100,000 centimeters in a kilometer (MP.7, MP.8).
Use these relationships to convert measurements from a larger metric length unit to a smaller unit (MP.7, MP.8).
Use these relationships to convert measurements from mixed metric length units to a smaller unit (MP.7, MP.8).
Solve one-step word problems that require metric length unit conversions (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Before starting the whole unit, it may be helpful to get a sense of students’ benchmarks for various measurement units. You can use select tasks from this NRICH task to do so: Discuss and Choose.
Note that in this lesson and the following one, only the units mentioned in the Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement document are included, such as km, m, cm, and mm, but not other units such as hectometers, decameters, or decimeters. You may decide to modify Lessons 1 and 2 to include those units. But, since they are not explicitly mentioned as part of the Grade 4 expectations and are used in much lower frequency in everyday life compared to the ones included in this lesson, they have been excluded.
The work that students do with measurement conversion (4.MD.1) in Lessons 1, 2, 5, 6, and 7 is connected to the idea of “times as much” in multiplication (4.OA.1). Thus, many tasks and guiding questions below draw attention to this language specifically to make that connection more apparent.

Lesson Materials

Meter stick (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 meter stick to answer the following questions.

a. What do you notice about the relationship between the length of a millimeter and the length of a centimeter?

b. What do you notice about the relationship between the length of a centimeter and the length of a meter?

c. What do you notice about the relationship between the length of a millimeter and the length of a meter?

Guiding Questions

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Problem 2

Fill in the following conversion tables.

Kilometers (km)	Meters (m)
1
2
3
6

Meters (m)	Centimeters (cm)
1
2
4
10

Centimeters (cm)	Millimeters (mm)
1
3
10
40

Guiding Questions

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Problem 3

Mr. Duffy wants to buy a new pair of skis. Skis are sold based on their length in centimeters. If Mr. Duffy wants to buy a pair of skis that are his exact height, and he is 1 meter 83 centimeters tall, what length skis should Mr. Duffy buy?

Guiding Questions

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Problem 4

Two sisters stand back to back to see how much taller the older sister is than the younger sister.

The older sister is 1 m 30 cm tall. The younger sister is 24 cm 2 mm shorter than her. How tall is the younger sister?

Guiding Questions

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References

Questioning My Metacognition Lil' Sister

Lil' Sister by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed June 13, 2018, 12:52 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

What pattern did you notice in the equivalences for #2 and #4? How did converting 1 kilometer to 1,000 meters in #1(a) help you to solve #2(a)?
How long is the ribbon in #3 in centimeters? In millimeters?
How does the ruler in #8 show that a centimeter is ten times as large as a millimeter?
What is wrong with Jason’s reasoning in #10? How much larger is a kilometer than a millimeter? How do you know?

Target Task

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

Problem 1

Complete the conversion table.

Distance

6 km	_____ m
40 km	_____ m
3 m	_____ cm
17 m	_____ cm
50 cm	_____ mm
13 m	_____ mm

Problem 2

Fill in the blank to make the equation true.

21 km 80 m = ___________ m

Problem 3

The female world record for high jump is 2 meters and 9 centimeters. How high is that in centimeters?

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 2

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

Measurement and Data

Measurement and Data

Measurement and Data

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

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Problem 3

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

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