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.
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Remainders Count

Increasing Rigor

  • 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.
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Quotient Cafe

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Quotient Cafe


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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.
  • 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)

Learnzillion Video Resources (5 Lessons)

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Select image for lessons.

Division Activities

Print Resources:

braincompatible4-5.pngBrain-Compatible Activities for Mathematics 4-5 (19-24)

Brain-Compatible Activities for Mathematics 4-5 (29-31)
developing_base_ten_blocks.pngDeveloping Mathematics with Base Ten p. 71-73
supersource_all.pngSuperSource: Color Tiles (58-61)
hands-on_standards.pngHands on Standards (Grades 3-4), pgs. 38-39 (Dividing with one-digit Divisors
math_intervention_building_number_power.pngMath Intervention: Building Number Power 3-5 (121-123)
math_by_all_means.pngMath By All Means - Division
numbersense.png
Number Sense 3-4 92-96
mental_math_in_middle_grades.png
'Lesson 30, 31 & 32' pages 99-104

Web Resources:

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lessons.jpg
student_resources.jpg
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Games and Centers
Lessons
Student Resources
Video Segments
Division Strategy: Partial Quotients (1)

Division Strategy: Partial Quotients (2)

Division Strategy: Partition the Dividend
The Baker Problem Solving(lesson)
Divisibility Rules
(Online resource)
Reasoning About Division
(Teaching channel)
Remainder
Divide Four-Digit Dividends with Partial Quotients
(ppt)
Virtual Manipulatives

Teacher guide for virtual manipulatives 4.NBT.6
Iditarod Math
(Teaching channel)
Remainder Count(game/lesson seed)
Remainders Count recording sheet
Long Division Made Easy
(Teacher resource)


Dicey Operations
(Games 5 and 6, game/lesson seed)
What is 2500 Divided by 300?
(Georgia Dept. of Education)


Arithmetic Connect Four(online game)
Partial Quotients Strategy Guide


Number Factory (online game)
Leftovers with 100
(Game/Lesson)


Estimate the Quotient
Teaching Long Division With Base 10 Blocks(lesson seed)


Who has the Largest Quotient - Version 1

Who has the Largest Quotient - Version 2



Write It, Solve It, Check It! - Version 1

Write It, Solve It, Check It! - Version 2
Compatible Numbers to Estimate (4.NBT.6 & 4.OA.3)
(Georgia Dept. of Education)



Division Activities



Cuisenaire Rods division
(lesson seed)



Connecting to Children's Literature:

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Divide and Ride by Stuart J. Murphy


Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.


Creative_Commons.pngUse and Sharing of HCPSS Website and Resources
Howard County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.