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.

Quarter 1

Quarter 2

Quarter 3

Quarter 4

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.

Divide 2-digit by 1-digit numbers.

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.

Divide 3-digit by 1-digit numbers.

Divide 4-digit by 1-digit numbers.

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.

Divide 3-digit by 1-digit numbers.

Divide 4-digit by 1-digit numbers.

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.

Continue if needed.

* Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

What is the relationship between multiplication and division? Provide examples to show your thinking.

How does knowing 5 x 5 help you to solve 75 ÷ 5? Explain.

How many different ways can you solve 84 ÷ 6?

If the quotient is 15, what could your possible dividend and divisor be?

How does changing the value of your divisor affect the quotient? (e.g. 350 ÷ 5 vs. 350 ÷ 50?)

Using the digits 4, 9, 7, and 5, create a division sentence with the greatest possible quotient.

Which division strategy (partial quotients, rectangular array, area model) do you think is best? Justify your answer.

About the Math

Two types of division problems are sharing (also call partitioning division) and repeated subtraction (also called measurement division.) In partition problems the whole is shared or distributed among a known number of sets to determine the size of each. When the number of sets is unknown but the size of the equal sets is known the problems are measurement division.

Partition Division: Jake has 24 oranges. He wants to share them equally among his 6 friends. How many oranges does each friend get? Measurement Division: Jake has 24 oranges. He puts them into baskets containing 4 oranges each. How many baskets did he use?
Not all division situations come out evenly. Students need to understand the meaning of remainders. Initial instruction should include using counters and arrays to show how sometimes counters are "left over". Remainders can have different effects on answers depending on the context of the problem. Students need to interpret the meaning of the remainder. The remainder may be discarded because it has no affect on the answer. The remainder can force the answer to go to the next whole number.

The Illustrative Mathematics task below demonstrates expectation for this standard.

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

NCTM's Illuminations offers the Quotient Cafe. This virtual tool and demonstration model helps students develop understanding of division with larger numbers. It is a wonderful resource for a lesson seed, practice, and much more.

pg. 93 * How Close Can You Get?-Activity 3.10, pg. 121-124, pg. 121 *Figure 4.16, pg. 124 *Figure 4.17, Learning ABout Division ) pg. 64, The Broken Division Key pg. 65,

Interpreting the Remainder (Reasoning Abstractly and Quantitatively): When solving a word problem, there are three different ways to interpret the remainder. You need to carefully read the word problem to know how to interpret the remainder.

You have to add one to the quotient.

The answer is only the quotient.

The solution is only the remainder.

There were 39 people on a bus when it broke down. People were driven home, 5 in each car. How many cars were used? 39 ÷ 5 = 7 R 4. You need to add the remainder and use 8 cars.

Movie tickets cost $5. How many can be purchased with $39? 39 ÷ 5 = 7 Drop the remainder 4 and the answer is 7 tickets

A total of 39 trophies were purchased for the basketball league. Each box holds 5 trophies. How many trophies will be in the partially filled box? (4 trophies)

## 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.

Divide 2-digit by 1-digit numbers.

Divide 3-digit by 1-digit numbers.

Divide 4-digit by 1-digit numbers.

Divide 3-digit by 1-digit numbers.

Divide 4-digit by 1-digit numbers.

Continue if needed.

Increasing Rigor

Two types of division problems are sharing (also call partitioning division) and repeated subtraction (also called measurement division.) In partition problems the whole is shared or distributed among a known number of sets to determine the size of each. When the number of sets is unknown but the size of the equal sets is known the problems are measurement division.About the MathPartition Division: Jake has 24 oranges. He wants to share them equally among his 6 friends. How many oranges does each friend get?Measurement Division: Jake has 24 oranges. He puts them into baskets containing 4 oranges each. How many baskets did he use?Not all division situations come out evenly. Students need to understand the meaning of remainders. Initial instruction should include using counters and arrays to show how sometimes counters are "left over". Remainders can have different effects on answers depending on the context of the problem. Students need to interpret the meaning of the remainder. The remainder may be discarded because it has no affect on the answer. The remainder can force the answer to go to the next whole number.

The Illustrative Mathematics task below demonstrates expectation for this standard.

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)Teaching Student-Centered Mathematics(Grades 3-5)pg. 93 * How Close Can You Get?-Activity 3.10,pg. 121-124, pg. 121 *Figure 4.16,pg. 124 *Figure 4.17, Learning ABout Division )pg. 64, The Broken Division Key pg. 65,Interpreting the Remainder (Reasoning Abstractly and Quantitatively):When solving a word problem, there are three different ways to interpret the remainder. You need to carefully read the word problem to know how to interpret the remainder.

There were 39 people on a bus when it broke down. People were driven home, 5 in each car. How many cars were used?

39 ÷ 5 = 7 R 4. You need to add the remainder and use 8 cars.

Movie tickets cost $5. How many can be purchased with $39?

39 ÷ 5 = 7 Drop the remainder 4 and the answer is 7 tickets

A total of 39 trophies were purchased for the basketball league. Each box holds 5 trophies. How many trophies will be in the partially filled box? (4 trophies)

## Learnzillion Video Resources (5 Lessons)

## Division Activities

Print Resources:Brain-Compatible Activities for Mathematics 4-5 (29-31)

Number Sense 3-4 92-96

'Lesson 30, 31 & 32' pages 99-104

Web Resources:Division Strategy: Partial Quotients (2)

Division Strategy: Partition the Dividend

(Online resource)

(Teaching channel)

(ppt)

Teacher guide for virtual manipulatives 4.NBT.6

(Teaching channel)

Remainders Count recording sheet

(Teacher resource)

(Games 5 and 6, game/lesson seed)

(Georgia Dept. of Education)

(Game/Lesson)

Who has the Largest Quotient - Version 2

Write It, Solve It, Check It! - Version 2

(Georgia Dept. of Education)

(lesson seed)

Connecting to Children's Literature:Divide and Rideby Stuart J. Murphy## Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.Use and Sharing of HCPSS Website and ResourcesHoward County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.