Lesson 23 | Multiplication and Division of Decimals | 5th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Measurement and Data

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

The foundational standards covered in this lesson

4.MD.A.1

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), …

Criteria for Success

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

Convert from smaller units to larger ones, including decimal units (e.g., 60.7 cm is how many meters?).
Convert from smaller units to larger ones, including fractional units (e.g., $$5\frac{1}{4} $$ ft is how many yards?).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

5.MD.1 could be interpreted to be inclusive of problems like today’s, but they are relatively rare to see in real-world situations involving unit conversions. Thus, this lesson is optional.

Lesson Materials

Grade 5 MCAS Reference Sheet (1 per student) — Teachers in different states will need to find and use their own state's reference sheet

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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

Fill in the blanks to make the following statements true.

a. 945.6 mL = ________ L

b. 530.8 cm = _________ m

c. 60.34 mm = _________ cm

Guiding Questions

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Problem 2

Fill in the blanks to make the following statements true.

a. $$\frac{1}{4}$$ ft = ________ yd

b. $$ 7\frac{1}{2}$$ oz = ________ lb

c. $$2\frac{3}{4}$$ pt = ________ gal

d. $$4 \frac{1}{2}$$ hrs = ________ days

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

In #1, were you able to solve without having to multiply by the conversion factor? How?
What conversion problem did you come up with for #2? Is there more than one possible answer?
What conversion problem did you come up with for #4? Is there more than one possible answer?

Target Task

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

Problem 1

Convert cups to quarts.

7.5 cups = ___________ quarts

Problem 2

Convert feet to yards.

$$11\frac{1}{4}$$ feet = ___________ yards

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

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

Lesson 22

Lesson 24

Lesson Map

Topic A: Multiplying Decimals

Multiply a single-digit whole number by a decimal in cases that involve basic facts. Estimate the product of a single-digit whole number with a decimal by rounding numbers to their largest place.

5.NBT.B.7

Multiply a single-digit whole number by a decimal.

5.NBT.B.7

Construct viable arguments and critique the reasoning of others regarding the placement of the decimal point in computations that involve multiplying a single-digit whole number by a decimal.

5.NBT.B.7

Multiply a multi-digit whole number by a decimal.

5.NBT.B.7

Multiply a decimal by a decimal in cases that involve basic facts. Estimate the product of two decimals by rounding numbers to their largest place.

5.NBT.B.7

Multiply a decimal by a decimal.

5.NBT.B.7

Multiply with decimals in all cases, reasoning about the placement of the decimal point.

5.NBT.B.7

Topic B: Dividing Decimals

Divide a decimal by a single-digit whole number in cases that involve basic facts. Estimate quotients with single-digit divisors by rounding numbers to compatible numbers.

5.NBT.B.7

Divide a decimal by a single-digit whole number.

5.NBT.B.7

Divide a decimal by a single-digit whole number that requires decomposition in the smallest place.

5.NBT.B.7

Divide a decimal by a two-digit whole number.

5.NBT.B.7

Divide a decimal by a two-digit whole number that requires decomposition in the smallest place.

5.NBT.B.7

Divide a whole number or a decimal by 1 tenth or 1 hundredth.

5.NBT.B.7

Divide a whole number or a decimal by a decimal in cases that involve basic facts. Estimate quotients with decimal divisors by rounding numbers to compatible numbers.

5.NBT.B.7

Divide a whole number or a decimal by a decimal.

5.NBT.B.7

Divide with decimals in all cases, reasoning about the placement of the decimal point.

5.NBT.B.7

Topic C: Decimal Expressions and Real-World Problems

Solve real-world problems that require interpretation of the remainder involving all possible cases, including further decomposition into a decimal.

5.NBT.B.7

Solve real-world problems involving multiplication and division with decimals.

5.NBT.B.7 5.OA.A.2

Write and evaluate numerical expressions involving multiplication and division with decimals.

5.NBT.B.7 5.OA.A.1 5.OA.A.2

Topic D: Measurement Conversion and Real-World Problems

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

5.MD.A.1

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

5.MD.A.1

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

5.MD.A.1

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

5.MD.A.1

Solve real-world problems involving measurement conversions.

5.MD.A.1

Multiplication and Division of Decimals

Objective

Common Core Standards

Core Standards

Measurement and Data

Foundational Standards

Measurement and Data

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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