Curriculum  /  Math  /  5th Grade  /  Unit 6: Multiplication and Division of Decimals  /  Lesson 19

Multiplication and Division of Decimals

Lesson 19

Math

Unit 6

5th Grade

Lesson 19 of 23

Objective

Express measurements in a whole number of larger units or mixed units in terms of a smaller unit.

Common Core Standards

Core Standards

  • 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.

Foundational Standards

  • 4.MD.A.1

Criteria for Success

  1. Understand the meaning of different prefixes for metric units and how they relate to the base unit (e.g., kilo- means 1,000, so a kilogram is 1,000 times as large as a gram).
  2. Understand that a conversion factor is the factor in a multiplication sentence that renames one measurement unit as another equivalent unit.
  3. Convert from larger metric whole-number units to smaller ones, including mixed units (e.g., 6 kg 5g is how many grams?).
  4. Convert from larger customary whole-number units to smaller ones, including mixed units (e.g., 6 lb. 7 oz. is how many ounces?).
  5. Convert from larger whole-number units of time to smaller ones, including mixed units (e.g., 3 hr. 4 min. is how many seconds?).

Tips for Teachers

  • Lessons 20–24 have been designed with the Massachusetts Reference Sheet in mind. You should find the reference sheet that will be used on your state assessment so that you know the conversions students will need to memorize and those they will be given. Then revise Lessons 20–24 accordingly.
  • Lesson 20 encompasses learning students did in Grade 4 and is therefore optional. It is included in the unit, though, because later work is dependent on students’ understanding of the conversion factors and their ability to convert in simple cases. Because students do not receive a reference sheet in Grade 4 for state testing in Massachusetts, this lesson will also help students understand how to use this new resource for Grade 5.
  • “Students are not expected to know e.g. that there are 5280 feet in a mile. …It is worth having them realize that they need that information rather than giving it to them upfront; having students identify what information they need to have to solve the problem and knowing where to go to find it allows them to engage in Standard for Mathematical Practice 5, Use appropriate tools strategically” (MP.5) (Converting Fractions of a Unit into a Smaller Unit, Illustrative Math). Thus, provide students with a reference sheet only after they are able to identify the information they need but do not have, namely, the conversion factors.

Lesson Materials

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Anchor Tasks

25-30 minutes

Problem 1

Look at the following table regarding metric measurement prefixes:

SI Prefixes
Prefix Decimal English Word
Name Symbol
kilo k 1 000 thousand
    1 one
centi c 0.01 hundredth
milli m 0.001 thousandth

What do you notice? What do you wonder?

Guiding Questions

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Student Response

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Problem 2

Fill in the blanks to make the following statements true.

a.   6 L = ________ mL

b.   34 kg = _________ g

c.   408 km = _________ cm

d.   53 cm 8 mm = ___________ mm

Guiding Questions

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Student Response

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Problem 3

Fill in the blanks to make the following statements true.

a.   3 lb = ________ oz

b.   12 gal = _________ pt

c.   6 yd = _________ in

d.   3 qt 7 fl oz = ___________ fl oz

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Student Response

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Problem 4

Fill in the blanks to make the following statements true.

a.   4 yr = ________ days

b.   1 wk = _________ min

c.   2 hr 8 min = ___________ sec

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How could #1(b) have helped you solve #1(h)?
  • How are #3(d) and #3(e) similar? How are they different?

Target Task

5-10 minutes

Problem 1

Convert pounds to ounces.

3 pounds = _________ ounces

Student Response

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Problem 2

Convert kilograms to grams.

18 kilograms = _________ grams

Student Response

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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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Express measurements in a fractional or decimal number of larger units in terms of a smaller unit.

Lesson 20
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Multiplying Decimals

Topic B: Dividing Decimals

Topic C: Decimal Real-World Problems

Topic D: Measurement Conversion

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