Lesson 19 | Multiplication and Division of Whole Numbers | 5th Grade Mathematics

Objective

Divide multi-digit numbers by one- and two-digit divisors and assess the reasonableness of the quotient.

Common Core Standards

Core Standards

The core standards covered in this lesson

5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Number and Operations in Base Ten

5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Foundational Standards

The foundational standards covered in this lesson

4.NBT.B.4

Number and Operations in Base Ten

4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.6

Number and Operations in Base Ten

4.NBT.B.6 — Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
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.

Criteria for Success

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

Estimate partial quotients of up to four-digit dividends and up to two-digit divisors with up to three-digit quotients.
Use the estimate to approximate each value in the quotient, adjusting when the estimate is either too high or too low.
Divide up to four-digit dividends by up to two-digit divisors with up to three-digit quotients and remainders in the ones place.
Check that the solution to a division problem is correct by using inverse operations, multiplying the quotient by the divisor and adding the remainder, seeing if it is equivalent to the dividend.
Assess the reasonableness of an answer using estimation and/or the relationship between multiplication and division to check answers (MP.1).
Solve word problems involving division, including those that require interpretation of the remainder (MP.1, MP.4).

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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

Make the largest quotient by filling in the boxes using the whole numbers $${1-9}$$ no more than one time each.

Guiding Questions

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References

Open Middle Dividing Two-Digit Numbers (Elementary)

Dividing Two-Digit Numbers (Elementary) by is made available on Open Middle under the CC BY-NC-SA 4.0 license. Accessed Dec. 5, 2017, 4:13 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Solve. Then assess the reasonableness of your answer.

a. $${8,801\div33}$$

b. $${6,032\div15}$$

c. $${7,414 \div 92}$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Look at #1b. What did you do when you got to the tens place?
Look at #1c. What did you do when you got to the tens place?
What made #1h easier than #1g or #1j?
Look at #1. Were there any problems where your estimate was incorrect and you had to adjust it?
I think the principal now needs to buy 54 cartons of eggs in #3b. I saw a student write that the principal now needs to buy 53 cartons of eggs. Who do you agree with? Why?

Target Task

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

Problem 1

For parts (a) and (b) below,

Solve. Show or explain your work.
Assess the reasonableness of your answer.

a. $$1,534\div6$$

b. $$344\div18$$

Student Response

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Problem 2

Henry says the solution to $${8,{18}8\div19 }$$ is $${43}$$ with a remainder of $${18}$$.

a. Use estimation to explain why Henry’s answer is not reasonable.

b. What error do you think Henry made? Why do you think he made that error?

c. Find the correct quotient of $${8,188\div19 }$$.

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.

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: Writing and Interpreting Numerical Expressions

Evaluate numerical expressions involving addition, subtraction, multiplication, division, and grouping symbols.

5.OA.A.1

Write expressions that record calculations with numbers, and interpret expressions without evaluating them.

5.OA.A.1 5.OA.A.2

Write expressions that represent real-world situations and evaluate them.

5.OA.A.1 5.OA.A.2

Topic B: Multi-Digit Whole Number Multiplication

Multiply multiples of powers of ten. Estimate multi-digit products by rounding numbers to their largest place value.

5.NBT.B.5

Multiply two-digit, three-digit, and four-digit numbers by one-digit numbers.

5.NBT.B.5

Multiply two-digit numbers by two-digit numbers.

5.NBT.B.5

Multiply three-digit numbers by two-digit numbers.

5.NBT.B.5

Multiply four-digit numbers by two-digit numbers.

5.NBT.B.5

Multiply three- and four-digit numbers by three-digit numbers.

5.NBT.B.5

Multiply multi-digit numbers and assess the reasonableness of the product.

5.NBT.B.5

Topic C: Multi-Digit Whole Number Division

Divide multiples of powers of ten by multiples of ten without remainders. Estimate multi-digit quotients by rounding numbers to their largest place value.

5.NBT.B.6

Estimate multi-digit quotients using compatible numbers.

5.NBT.B.6

Divide two-digit, three-digit, and four-digit dividends by one-digit divisors.

5.NBT.B.6

Divide two- and three-digit dividends by multiples of 10 with one-digit quotients and remainders in the ones place.

5.NBT.B.6

Divide two-digit dividends by two-digit divisors with one-digit quotients and remainders in the ones place.

5.NBT.B.6

Divide three-digit dividends by two-digit divisors with one-digit quotients and remainders in the ones place.

5.NBT.B.6

Divide three-digit dividends by two-digit divisors with two-digit quotients, reasoning about the decomposition of a remainder in any place.

5.NBT.B.6

Divide four-digit dividends by two-digit divisors with two- and three-digit quotients, reasoning about the decomposition of a remainder in any place.

5.NBT.B.6

Divide multi-digit numbers by one- and two-digit divisors and assess the reasonableness of the quotient.

5.NBT.B.6

Solve word problems involving multi-digit multiplication and division.

5.NBT.B.5 5.NBT.B.6 5.OA.A.1 5.OA.A.2

Multiplication and Division of Whole Numbers

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

Criteria for Success

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Student Response

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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