Lesson 19 | Multiplication and Division of Decimals | 5th Grade Mathematics

Objective

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

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.

5.OA.A.1 — Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Operations and Algebraic Thinking

5.OA.A.1 — Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Operations and Algebraic Thinking

5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Criteria for Success

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

Write numerical expressions based on verbal/written descriptions of calculations involving decimals (e.g., write 0.3 ÷ (8 + 7) to express the calculation “the quotient of 3 tenths and the sum of 8 and 7”) (MP.7).
Write descriptions of calculations involving decimals based on numerical expressions (e.g., write “add 8 and 7, then divide 3 tenths by that sum” to describe the expression 0.3 ÷ (8 + 7)) (MP.7).
Evaluate expressions with and without grouping symbols that include decimals using the order of operations (MP.6).
Interpret expressions that include decimals without evaluating them.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson connects the work of adding, subtracting, multiplying, and dividing decimals (5.NBT.7) with writing and interpreting numerical expressions (5.OA.A), connecting content across domains in order to address the note in the Progressions “that the numbers in expressions need not always be whole numbers” (OA Progression, p. 32).

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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

Write an expression to represent the tape diagrams below. In each tape diagram, their units are equal.

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 4 > Topic D > Lesson 10 — Concept Development

Grade 5 Mathematics > Module 4 > Topic D > Lesson 10 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

Write numerical expressions that match the following calculations. Then evaluate them.

a. Subtract 8.5 from 14.03 and multiply the result by 3.5.

b. Subtract 8.5 from 14.03 and multiply the result by 7.

c. Half the sum of 10.4 and 3.42.

Guiding Questions

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Problem 3

Write the following numerical expressions in words. Then evaluate them.

a. 63 × (0.5 – 0.04)

b. (0.02 + 1.6) ÷ 0.4

c. 7 × (5.4 ÷ 0.45)

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

What two expressions did you choose in #1? How do you know they are equivalent?
How did you solve #5? Was anyone able to come up with the answer without having to evaluate Expression A? How?

Target Task

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

Problem 1

Write an equivalent expression in numerical form. Then evaluate it.

Twice as much as the difference between 7 tenths and 5 hundredths

Problem 2

Write an equivalent expression in word form. Then evaluate it.

9 ÷ (0.16 + 0.2)

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 18

Lesson 20

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

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

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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