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.

Enduring Understanding

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Remainders Count

Some real world problems can be solved using multiplication and some can be solved using division.

Essential Questions

When is multiplication and division helpful for solving a problem?

Vocabulary (online dictionary)


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.


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
Constructing Ideas About Multiplication and Division Grades 3-6 pg 68-857
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
hands-on_standards.pngHands on Standards (Grades 3-4), pgs. 38-39 (Dividing with one-digit Divisors
supersource_all.pngSuperSource: Color Tiles (58-61)
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'Lesson 30, 31 & 32' pages 99-104

Web Resources:

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lessons.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

Remainders

Remainder Count game/lesson seed


Divisibility Rules Online resource
Learnzillion Video Resources
(5 Lessons)
Arithmetic Connect Four online game
Estimate the Quotient

Iditarod Math (Teacher Channel)

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






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


Snork's Long Division




Teaching Long Division With Base 10 Blocks
blog post lesson seed

Reasoning About Division-for TeachersReasoning about Division (Teacher Resource).png

Compatible Numbers to Estimate (4.NBT.6 & 4.OA.3)
Georgia Dept. of Education

Short Division (Discovery Education)

Division Activities



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.