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

Objective

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.

Common Core Standards

Core Standards

The core standards covered in this lesson

5.NBT.B.7 — Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Number and Operations in Base Ten

5.NBT.B.7 — Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Foundational Standards

The foundational standards covered in this lesson

5.NBT.A.1

Number and Operations in Base Ten

5.NBT.A.1 — Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.2

Number and Operations in Base Ten

5.NBT.A.2 — Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.A.4

Number and Operations in Base Ten

5.NBT.A.4 — Use place value understanding to round decimals to any place.
5.NBT.B.5

Number and Operations in Base Ten

5.NBT.B.5 — Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NF.B.4

Number and Operations—Fractions

5.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Criteria for Success

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

Multiply a decimal by a decimal in cases that involve basic facts using fraction equivalence.
Multiply a decimal by a decimal in cases that involve basic facts using the whole number basic fact, then moving the decimal point the relevant number of spaces based on the place value of the original values (e.g., 0.4 × 0.02 = 4 × 2 × 0.1 × 0.01 = 8 × 0.1 × 0.01 = 0.8 × 0.01 = 0.008).
Estimate the product of two decimals by rounding each decimal to its largest place.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

a. Helen, Ramiro, and Jackie all have square garden plots in their community garden.

Helen plants 0.1 of her garden with flowers. Of those flowers, 0.1 of them are tulips. How much of Helen’s garden is tulips?
Ramiro plants 0.3 of his garden with flowers. Of those flowers, 0.1 of them are tulips. How much of Ramiro’s garden is tulips?
Jackie plants 0.3 of her garden with flowers. Of those flowers, 0.2 of them are tulips. How much of Jackie’s garden is tulips?

b. Write equations to represent each problem in Part (a) above. What do you notice? What do you wonder?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

a. Select all expressions that are equivalent to $$0.4 \times 0.02$$.

$$4 \times 0.1 \times 2 \times 0.01$$
$$4 \times 0.1 \times 2 \times 0.1$$
$$4 \times \frac{1}{10} \times 2 \times \frac{1}{100}$$
$$4 \times \frac{1}{100} \times 2 \times \frac{1}{1,000}$$
$$4 \times 2 \times 0.01 \times 0.01$$
$$4 \times 2 \times \frac{1}{10} \times \frac{1}{100}$$
$$\frac{4}{10} \times \frac{2}{100}$$

b. Find the value of $$0.4 \times 0.02$$. Show your reasoning.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Open Up Resources Grade 6 Unit 5 Lesson 5 — Activity 5.3 Fractionally Speaking: Multiples of Powers of Ten

Grade 6 Unit 5 Lesson 5 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Sept. 18, 2019, 3:32 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Find the value of each product below. Show or explain your work.

a. 0.09 × 0.3 = _________

b. 0.7 × 0.6 = _________

c. 0.8 × 0.05 = _________

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 4

Estimate the following products. Determine whether the actual product will be greater or less than the estimated product or whether it’s difficult to determine.

a. 6.23 × 8.4

b. 5.4 × 0.79

c. 0.34 × 0.56

d. 0.21 × 0.03

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

I think the area model in #1 represents 0.8 × 0.4, which isn’t one of the options listed. What mistake did I make?
My estimate in #2d is 0.04 because 8 × 5 is 40, and our answer should be to the hundredths place since tenths times tenths are hundredths. Do you agree or disagree? Why?
I think the Boy Scout used 0.5 meter of the rope for the knot in #3. Do you agree or disagree? Why?
How does #4a help you solve #4c?
My estimate in #5f is 0.48 because 6 × 8 is 48, and I know my answer needs to be less than 0.84. Do you agree or disagree with my estimate?

Target Task

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

Problem 1

Which equation shows a correct strategy and product for the expression shown?

$$0.04 \times 0.8$$

Create a free account or sign in to view multiple choice options

Problem 2

Estimate $$0.5 \times 0.63$$.

Student Response

An example response to the Target Task at the level of detail expected of the students.

Create a free account or sign in to view Student Response

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

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

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

Lesson 4

Lesson 6

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

Number and Operations in Base Ten

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations—Fractions

Criteria for Success

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem 4

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

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy