Enhanced Instructional Transition Guide
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Unit 04: Multiplication and Division Foundations (14 days)
Possible Lesson 01 (7 days)
Possible Lesson 02 (4 days)
Possible Lesson 03 (3 days)
POSSIBLE LESSON 02 (4 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing
with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and
districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your
child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and
Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students use concrete models and objects to investigate how multiplication and division are inverse operations.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas
law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
3.4
Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations.
The student is expected to:
3.4C
Use models to solve division problems and use number sentences to record the solutions.
Readiness Standard
3.6
Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems. The student is expected to:
3.6C
Identify patterns in related multiplication and division sentences (fact families) such as 2 x 3 = 6, 3 x 2 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2. Supporting Standard
3.10
Geometry and spatial reasoning. The student recognizes that a line can be used to represent numbers and fractions and their
page 1 of 37 Enhanced Instructional Transition Guide
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
properties and relationships. The student is expected to:
3.10
Locate and name points on a number line using whole numbers and fractions, including halves and fourths.
Readiness Standard
Underlying Processes and Mathematical Tools TEKS:
3.14
Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
3.14A
Identify the mathematics in everyday situations.
3.14B
Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution
for reasonableness.
3.14C
Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic
guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
3.14D
Use tools such as real objects, manipulatives, and technology to solve problems.
3.15
Underlying processes and mathematical tools. The student communicates about Grade 3 mathematics using informal language. The
student is expected to:
3.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
3.15B
Relate informal language to mathematical language and symbols.
3.16
Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to:
3.16B
Justify why an answer is reasonable and explain the solution process.
Performance Indicator(s):
page 2 of 37 Enhanced Instructional Transition Guide
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Grade 03 Mathematics Unit 04 PI 03
Solve two real-life division problems such as the following:
Karen had 36 stickers arranged on a sheet shown below.
She decorated 4 cups with an equal number of stickers. How many stickers were on each cup?
Frida has a collection of 27 glass eggs she wants to display on 3 shelves. She put the same number of glass eggs on each shelf.
How many glass eggs did she place on each shelf?
Use a graphic organizer for each problem to record: (1) the fact and solution represented by the situation, (2) a sketch of a division model to include the related multiplication
number sentence, (3) the remaining related facts, and (4) a justification of the reasonableness of the solution.
Standard(s): 3.4C , 3.6C , 3.10 , 3.14A , 3.14B , 3.14C , 3.14D , 3.15A , 3.15B , 3.16B
ELPS ELPS.c.1H , ELPS.c.4J , ELPS.c.5G
Key Understanding(s):
Division facts can be recalled using a variety of concrete models (e.g., base-ten blocks, counters, etc.) which can be connected to various pictorial representations
and/or strategies such as arrays, area models, number lines, patterns in fact families, problems in context, and other known facts.
page 3 of 37 Enhanced Instructional Transition Guide
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
The relationship between multiplication and division can be used to develop an efficient procedure to find the quotient and justify the solution for a whole number
division problem.
Fact families and area models can be used to demonstrate the special inverse relationship between multiplication and division, where the product in a
multiplication problem is the dividend in a division problem and the two factors in a multiplication problem are the divisor and quotient in a division problem.
Real-life division problems involving whole numbers can be solved using a variety of models and strategies including problems in context, patterns in fact families,
area models, partitioning, and other known facts.
Problem solving with division of whole numbers involves analyzing the given information, the missing information, and the question(s); developing a plan with
strategies; observing and communicating the mathematical ideas through verbal/written descriptions or statements, and/or equations; and evaluating the solution
for reasonableness.
Misconception(s):
Some students may have difficulty continuing repeated subtraction on a number line all the way to zero.
Some students may think that a division problem represented using traditional division is read from left-to-right. They may incorrectly write a division number
sentence by not placing the dividend first. See below:
Some students may think that when given “24 balloons shared by 3 people results in 8 balloons per person” or 24 ÷ 3 = 8, they should record Vocabulary of Instruction:
dividend
division
divisor
quotient
page 4 of 37 .
Enhanced Instructional Transition Guide
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Materials List:
Bag of Counters (1 set per 4 students, 1 set per teacher) (previously created in Unit 04, Lesson 01 Engage 1)
dry erase marker (1 per student)
math journal (1 per student)
paper plates (5 per 4 students)
sticky note (optional) (3 per 2 students)
whiteboard (student-sized) (1 per student)
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
Apple Time
Apple Time Division Model KEY
Apple Time Division Model
Modeling Division with Counters KEY
Modeling Division with Counters
Donna’s Donuts
Donna’s Donuts Repeated Subtraction Division Modeling KEY
Donna’s Donuts Repeated Subtraction Division Modeling
Repeated Subtraction Number Lines
page 5 of 37 Enhanced Instructional Transition Guide
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Related Division and Subtraction Practice KEY
Related Division and Subtraction Practice
Model Division with Arrays Practice KEY
Model Division with Arrays Practice
Modeling Division Evaluation KEY
Modeling Division Evaluation PI
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Division as sharing
Engage 1
MATERIALS
Students use logic and reasoning skills to separate counters into equal groups for sharing as a
Bag of Counters (1 set per 4 students, 1 set per
model for division.
teacher) (previously created in Unit 04, Lesson
01 Engage 1)
Instructional Procedures:
math journal (1 per student)
page 6 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
1. Place students into groups of 4 and distribute a Bag of Counters to each group. Instruct
student groups to count out 28 of the counters from their bag.
2. Instruct student groups to distribute the “counted­out” counters so that each student in the
group has the same amount of counters. Allow time for students to distribute the counters to
TEACHER NOTE
It may be necessary to join a group to ensure all
groups have 4 students.
everyone in their group. Monitor and assess students to check for understanding.
Ask:
How did you share or distribute your counters evenly among the members of your
group? Answers may vary. Each person took a particular number of counters and
continued until no counters were left. Some may have counted out 1 at a time until none
were left; others may have started giving each student in the group more than 1 color tile,
and then giving more or taking away from each person as they found necessary to do so;
etc.
Did everyone get the same amount? Explain. (Yes; each person received 7
counters.)
What is the process of separating into equal groups called? (division)
When have you used division in real life? Answers may vary. Splitting food or candy
into equal parts for each person; making teams for a game; etc.
What division sentence could be written for this situation? (28 ÷ 4 = 7)
3. Display the following word and definition for division for the class to see:
Division –one of the four basic operations of arithmetic where in the division statement a
÷ b = c, a is the dividend, b is the divisor, and c is the quotient
4. Instruct students to record this definition and a model of the division of counters situation in
page 7 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
their math journal.
Topics:
Fact families for multiplication and division
ATTACHMENTS
Teacher Resource: Apple Time (1 per teacher)
Teacher Resource: Apple Time Division
Explore/Explain 1
Model KEY (1 per teacher)
Students separate counters into equal groups for sharing as a model for division. Students
Handout: Apple Time Division Model (1 per
connect this model to multiplication fact families.
student)
Teacher Resource: Modeling Division with
Instructional Procedures:
1. Remind students that when they combined equal groups, they multiplied. Explain to students
that they will learn that when they share equally, they divide.
Ask:
Counters KEY (1 per teacher)
Handout: Modeling Division with Counters (1
per student)
MATERIALS
How is multiplication similar to division? Answers may vary. They both use equal
paper plates (5 per 4 students)
groups; etc.
Bag of Counters (1 set per 4 students)
How is multiplication different from division? Answers may vary. In multiplication I
(previously created)
start with 1 group and increase by equal groups to find the total; in division, I start with
math journal (1 per student)
the total and separate it into equal groups or take equal groups away 1 at a time; etc.
sticky note (optional) (3 per 2 students)
What are the related family facts for 28 ÷ 4 = 7? (28 ÷ 7 = 4; 4 x 7 = 28; 7 x 4 = 28)
How did the counters help you divide? Answers may vary. You can see how many
items are in each group and/or how many groups there are; etc.
TEACHER NOTE
If students are unsure about the term “fact families,”
2. Place students into groups of 4. Distribute 5 paper plates and a Bag of Counters to each
place students in pairs and distribute 3 sticky notes to
page 8 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
group. Instruct students to count out 20 of the counters from their bag.
3. Display teacher resource: Apple Time. Explain to students that the counters will represent
the apples that are being shared in the problem. Instruct student groups to use their plates to
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Notes for Teacher
each pair. Instruct each pair to record 18 total cookies,
3 cookies, and 6 bags and then rearrange the notes
and read the “note” sentence aloud.
make equal groups of the apples. Allow time for students to distribute the counters. Monitor
and assess students to check for understanding.
Ask:
How many groups did you make using the paper plates? Explain. (5 groups;
because there are 5 friends.)
How many counters (apples) were in each group? (4)
4. Explain to students that they can draw a picture to show a division problem. Instruct
students to draw a rectangle and divide it into 5 equal parts in their math journal.
Ask:
What does the whole rectangle represent? (20; the total number of apples to be
shared)
Why did you divide the rectangle into 5 sections? (There are 5 friends sharing the
apples.)
How many apples will go into each section? How do you know? (4) Answers may
vary. It is the number of counters (apples) in each group; etc.
5. Instruct students to illustrate the equal groups of apples in their rectangle drawing.
page 9 of 37 Enhanced Instructional Transition Guide
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Suggested Instructional Procedures
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Notes for Teacher
Ask:
What division sentence is represented by this model? (20 ÷ 5 = 4)
6. Explain to students that there are 2 ways to write a division problem. Record the following
division representations for the class to see. Instruct students to record each representation
in their math journal.
7. Distribute handout: Apple Time Division Model to each student. Instruct student groups to
use their Bag of Counters to model each situation and record their solutions on their handout.
Allow time for students to complete the activity. Facilitate a class discussion to debrief and
discuss solutions.
8. Distribute handout: Modeling Division with Counters to each student. Instruct students to
complete the handout as independent practice or homework.
2
Topics:
Spiraling Review
page 10 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
Division as repeated subtraction
Explore/Explain 2
Students use a repeated subtraction model to assist in solving division problems.
ATTACHMENTS
Teacher Resource: Donna’s Donuts (1 per
teacher)
Instructional Procedures:
1. Facilitate a class discussion to debrief and discuss the previously assigned handout:
Modeling Division with Counters.
2. Place students into groups of 4. Distribute a whiteboard and dry erase marker to each
Teacher Resource: Donna’s Donuts Repeated
Subtraction Division Modeling KEY (1 per
teacher)
Handout: Donna’s Donuts Repeated
Subtraction Division Modeling (1 per student)
student and a Bag of Counters to each group. Instruct students to count out 12 of the
Handout: Repeated Subtraction Number
counters from their bag.
Lines (1 per student)
3. Display teacher resource: Donna’s Donuts. Instruct students to use counters and a
whiteboard to solve the problem. Remind students to start with 12 counters to represent the
total number of donuts. Allow time for students to complete their model. Monitor and assess
students to check for understanding.
4. Demonstrate the solution process using a Bag of Counters for the class to see.
Ask:
Teacher Resource: Related Division and
Subtraction Practice KEY (1 per teacher)
Handout: Related Division and Subtraction
Practice (1 per student)
MATERIALS
whiteboard (student-sized) (1 per student)
How many donuts did Donna make in all? (12)
dry erase marker (1 per student)
How many donuts did Donna give to her first friend? (2)
Bag of Counters (1 set per 4 students, 1 set per
teacher) (previously created)
5. Demonstrate taking away 2 counters. Instruct students to replicate the model.
Ask:
TEACHER NOTE
page 11 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Suggested Instructional Procedures
What subtraction sentence could I use to show what I just did? (12 – 2 = 10)
Notes for Teacher
Repeated subtraction is another way to think about
division. Students are given a total number of items
Continue removing counters in groups of 2 until there are no counters left. Record each
and the number in each group. They model division by
subtraction sentence as each group is removed for the class to see. Instruct students to
repeatedly subtracting a group of objects, then
replicate the model with their counters and whiteboards.
counting to find the number of groups.
RESEARCH
According to Children’s Mathematics Cognitively
Guided Instruction, children naturally will use skip
counting, addition or subtraction until they reach the
given number. With the problem 28 color tiles ÷ 4
students a student might count “4, 8, 12, 16, 20, 24,
Ask:
and 28.” With each count, the student would extend 1
finger. When the student has completed the counting,
How many times did you subtract 2? (6 times)
How many groups of 2 did you separate your counters into? (6 groups)
How does the number of times you subtracted 2 from each group compare to the
number of groups of 2 you made? (They are the same.)
How could you write this as a division sentence? (12 ÷ 2 = 6)
the student would look at the 7 extended fingers and
say, “7, meaning each student has 7 color tiles.” This
natural counting strategy will come before the derived
facts.
What does the 12 stand for in this problem? (the number of donuts)
What does the 2 stand for in this problem? (the number of donuts each friend gets)
What does the 6 stand for in this problem? (the number of friends that get 2 donuts)
Were any donuts left over for Donna? (no) Explain. Answers may vary. There were no
donuts left for Donna because 12 donuts can be divided equally among 6 friends; there
were no donuts left for Donna because 12 donuts can be divided into 6 equal groups of 2;
page 12 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Notes for Teacher
etc.
6. Distribute handout: Donna’s Donuts Repeated Subtraction Division Modeling to each
student. Instruct students to complete the handout independently. Allow time for students to
complete the activity. Monitor and assess students to check for understanding. Facilitate a
class discussion to debrief and discuss solutions.
7. Display teacher resource: Repeated Subtraction Number Lines and distribute handout:
Repeated Subtraction Number Lines to each student.
Ask:
How did you use number lines to multiply? Answers may vary. I used skip-counting
or repeated addition to find the multiples of numbers; etc.
Could you use number lines to divide? Explain. (yes) Answers may vary. Using
repeated subtraction and going backwards on the number line to model our process; etc.
How could you use this number line to show 20 ÷ 4? Answers may vary.
8. Display a drawn number line for the class to see. Use the number line to model how to skipcount backwards by 4s from 20 to 0. Explain to students that when they skip count on a
number line to show multiplication or repeated addition, they always start at zero.
Emphasize that when they skip count backwards on a number line to show division or
repeated subtraction, they must end at 0.
Ask:
page 13 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Notes for Teacher
How is skip counting backwards on a number line like skip counting forward?
Answers may vary. You move the same number of times over and over until you get to
the number; etc.
How is skip counting backwards on a number line different from skip counting
forward? Answers may vary. You move to the right and use repeated addition when you
skip-count forward. Skipping forward is related to multiplication. To skip-count
backwards, you move to the left and use repeated subtraction. Skipping backwards is
related to division; etc.
9. Record the following division problems for the class to see.
10. Place students in pairs. Instruct student pairs to solve each problem using a number line on
their handout: Repeated Subtraction Number Lines. Allow time for students to complete
the activity. Monitor and assess student pairs to check for understanding. Facilitate a class
discussion to debrief and discuss each number line solution.
page 14 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
11. Distribute handout: Relate Division and Subtraction Practice to each student. Instruct
students to complete the handout as independent practice or homework.
3
Topics:
Spiraling Review
Arrays and area models for division
Elaborate 1
Students use arrays to assist in solving division problems.
ATTACHMENTS
Teacher Resource: Model Division with
Arrays Practice KEY (1 per teacher)
Instructional Procedures:
1. Facilitate a class discussion to debrief and discuss the previously assigned handout: Relate
Division and Subtraction Practice.
2. Remind students that they have already learned how to model division with counters by
making equal groups, by using repeated subtraction, and by showing repeated subtraction on
a number line.
3. Distribute a whiteboard and dry erase marker to each student and a Bag of Counters to each
Handout: Model Division with Arrays
Practice (1 per student)
MATERIALS
whiteboard (student-sized) (1 per student)
dry erase marker (1 per student)
Bag of Counters (1 set per 4 students, 1 set per
teacher) (previously created)
pair. Instruct students to count out 16 of the counters from their bag.
Ask:
How many counters are in 4 equal groups of 4? (16)
State Resources
How many groups of 4 are in 16? (4)
MTC 3 – 5 Multiplication-Division
4. Instruct students to use their Bag of Counters to create an array of counters that models 4
equal groups of 4 and record the model and related multiplication sentence on their
TEXTEAMS: Rethinking Elementary
Mathematics Part I: The Great Divide; A
page 15 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
whiteboards: (4 x 4 = 16).
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Notes for Teacher
Remainder of One; Leftovers
Ask:
What division problem could be written using this same array? Explain. (16 ÷ 4 =
4) Answers may vary. This division problem is in the same fact family as 4 x 4 = 16; or
that 16 separated into 4 equal groups is 4; etc.
5. Instruct students to circle rows of 4 on their whiteboard.
Ask:
How many groups of 4 are in 16? (4)
How does making an array help you to divide? Answers may vary. It helps by
showing how many rows there are; etc.
What does this model tell us about the relationship between multiplication and
division? Answers may vary. They are inverse operations; multiplication joins equal
groups together and division separates into equal groups; etc.
6. Distribute handout: Model Division with Arrays Practice. Instruct students to complete the
handout independently. Remind students that they may use their counters to model each
problem first. Monitor and assess students as they work. Allow time for students to complete
page 16 of 37 Enhanced Instructional Transition Guide
Suggested
Day
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
the activity. Monitor and assess student pairs to check for understanding. Facilitate a class
discussion to debrief and discuss student solutions.
4
Evaluate 1
ATTACHMENTS
Instructional Procedures:
Teacher Resource (optional): Modeling
1. Assess student understanding of related concepts and processes by using the Performance
Indicator(s) aligned to this lesson.
Division Evaluation KEY (1 per teacher)
Handout (optional): Modeling Division
Evaluation PI (1 per student)
Performance Indicator(s):
MATERIALS
Grade 03 Mathematics Unit 04 PI 03
Solve two real-life division problems such as the following:
Bag of Counters (1 set per student) (previously
created)
Karen had 36 stickers arranged on a sheet shown below.
TEACHER NOTE
In addition to the Performance Indicator assessment,
as an additional assessment tool, use handout:
Modeling Division Evaluation PI if time permits.
She decorated 4 cups with an equal number of stickers. How many stickers were on each cup?
Frida has a collection of 27 glass eggs she wants to display on 3 shelves. She
put the same number of glass eggs on each shelf.
page 17 of 37 Enhanced Instructional Transition Guide
Suggested
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Suggested Instructional Procedures
Grade 3/Mathematics
Unit 04:
Suggested Duration: 4 days
Notes for Teacher
How many glass eggs did she place on each shelf?
Use a graphic organizer for each problem to record: (1) the fact and solution represented by the
situation, (2) a sketch of a division model to include the related multiplication number sentence, (3)
the remaining related facts, and (4) a justification of the reasonableness of the solution.
Standard(s): 3.4C , 3.6C , 3.10 , 3.14A , 3.14B , 3.14C , 3.14D , 3.15A , 3.15B
, 3.16B
ELPS ELPS.c.1H , ELPS.c.4J , ELPS.c.5G
04/01/13
page 18 of 37 Grade 03
Mathematics
Unit: 04 Lesson: 02
Apple Time
Five friends picked 20
apples. They wanted to
share them equally.
How many apples
should each friend get?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Apple Time Division Model KEY
Use counters to model each problem. Then draw each model in the space provided. The first one has
been done for you.
(1) Five friends shared 20 apples.
5 groups of 4 apples = 20 apples
4
Division Sentence: 20 ÷ 5 = 4 apples each or 5 20
Related Fact Family Sentences: 20 ÷ 4 = 5; 4 x 5 = 20; 5 x 4 = 20
(2) Four friends shared 20 apples. Drawings may vary, but should show 4 groups
with 5 in each group.
4 groups of 5 apples = 20 apples
Division Sentence: 20 ÷ 4 = 5 apples each
Related Fact Family Sentences: 20 ÷ 5 = 4; 4 x 5 = 20; 5 x 4 = 20
©2012, TESCCC
08/03/12
page 1 of 2
Grade 03
Mathematics
Unit: 04 Lesson: 02
Apple Time Division Model KEY
(3) Two friends shared 20 apples. Drawings may vary, but should show 2 groups with
10 in each group.
2 groups of 10 apples = 20 apples
Division Sentence: 20 ÷ 2 = 10 apples each
Related Fact Family Sentences: 20 ÷ 10 = 2; 2 x 10 = 20; 10 x 2 = 20
(4) Ten friends shared 20 apples. Drawings may vary, but should show 10 groups
with 2 in each group.
10 groups of 2 apples = 20 apples
Division Sentence: 20 ÷ 10 = 2 apples each
Related Fact Family Sentences: 20 ÷ 2 = 10; 2 x 10 = 20; 10 x 2 = 20
©2012, TESCCC
08/03/12
page 2 of 2
Grade 03
Mathematics
Unit: 04 Lesson: 02
Apple Time Division Model
Use counters to model each problem. Then draw each model in the space provided. The first one has
been done for you.
(1) Five friends shared 20 apples.
5 groups of 4 apples = 20 apples
4
Division Sentence: 20 ÷ 5 = 4 apples each or 5 20
Related Fact Family Sentences: 20 ÷ 4 = 5; 4 x 5 = 20; 5 x 4 = 20
(2) Four friends shared 20 apples.
____________ groups of ____________ = _____________ apples
Division Sentence:
Related Fact Family Sentences:
©2012, TESCCC
08/03/12
page 1 of 2
Grade 03
Mathematics
Unit: 04 Lesson: 02
Apple Time Division Model
(3) Two friends shared 20 apples.
____________ groups of ____________ = _____________ apples
Division Sentence:
Related Fact Family Sentences:
(4) Ten friends shared 20 apples.
____________ groups of ____________ = _____________ apples
Division Sentence:
Related Fact Family Sentences:
©2012, TESCCC
08/03/12
page 2 of 2
Grade 03
Mathematics
Unit: 04 Lesson: 02
Modeling Division with Counters KEY
Draw counters in each box. Then complete the table.
Counters
Number of Equal Groups
24
Number in
Each Group
4
Division Sentence: 24 ÷ 6 = 4
35
7
Division Sentence: 35 ÷ 5 = 7
18
3
Division Sentence: 18 ÷ 6 = 3
16
4
Division Sentence: 16 ÷ 4 = 4
25
5
Division Sentence: 25 ÷ 5 = 5
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Modeling Division with Counters
Draw counters in each box. Then complete the table.
Counters
Number of Equal Groups
Number in
Each Group
24
Division Sentence:
35
Division Sentence:
18
Division Sentence:
16
Division Sentence:
25
Division Sentence:
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Donna’s Donuts
Donna made 12 donuts. She
wants to give some of her
friends 2 donuts each. How
many friends can get donuts?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Donna’s Donuts Repeated Subtraction
Division Modeling KEY
Use counters to model each problem as repeated subtraction. Then draw each model in the space
provided. Write each subtraction sentence as counters are removed.
(1) There are 12 donuts. Each person gets 3 donuts. How many people are sharing
donuts?
12 – 3 = 9
9–3=6
6–3=3
3–3=0
How many groups of 3 are in 12? 4 groups
Division Sentence: 12 ÷ 3 = 4 people
(2) There are 12 donuts. Each person gets 4 donuts. How many people are sharing
donuts?
12 – 4 = 8
8–4=4
4–4=0
How many groups of 4 are in 12? 3 groups
Division Sentence: 12 ÷ 4 = 3 people
As the number of donuts given to each person changes, how does the number of
people who shared donuts change? Answers may vary, but should include that as
the number of donuts shared increases, the number of people who get the donuts
decreases.
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Donna’s Donuts Repeated Subtraction
Division Modeling
Use counters to model each problem as repeated subtraction. Then draw each model in the space
provided. Write each subtraction sentence as counters are removed.
(1) There are 12 donuts. Each person gets 3 donuts. How many people are sharing
donuts?
How many groups of 3 are in 12?
Division Sentence:
(2) There are 12 donuts. Each person gets 4 donuts. How many people are
sharing donuts?
How many groups of 4 are in 12?
Division Sentence:
As the number of donuts given to each person changes, how does the number of
people who shared donuts change?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Repeated Subtraction Number Lines
©2012, TESCCC
0
10
20
30
40
0
10
20
30
40
0
10
20
30
40
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Relate Division and Subtraction Practice KEY
Use the number line below to model each problem.
(1) Sharon bought 40 newspapers. Each bundle contained 10 newspapers. How many
bundles of newspapers did she buy?
0
10
30
20
40
Repeated Subtraction Sentence: 40 – 10 = 30; 30 – 10 = 20; 20 – 10 = 10; 10 – 10 = 0
How many times did you subtract? 4
Division Sentence: 40 ÷ 10 = 4
How many bundles of newspaper did Sharon buy? 4 bundles
(2) Daniel has 24 flowers in a bunch. He put 6 flowers in each of his vases. How many
vases does he use?
0
10
20
30
Repeated Subtraction Sentence: 24 – 6 = 18; 18 – 6 = 12; 12 – 6 = 6; 6 – 6 = 0
How many times did you subtract? 4
Division Sentence: 24 ÷ 6 = 4
How many vases did Daniel use? 4 vases
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Relate Division and Subtraction Practice
Use the number line below to model each problem.
(1) Sharon bought 40 newspapers. Each bundle contained 10 newspapers. How many
bundles of newspapers did she buy?
0
10
30
20
40
Repeated Subtraction Sentence:
How many times did you subtract?
Division Sentence:
How many bundles of newspaper did Sharon buy?
(2) Daniel has 24 flowers in a bunch. He put 6 flowers in each of his vases. How many
vases does he use?
0
10
20
30
Repeated Subtraction Sentence:
How many times did you subtract?
Division Sentence:
How many vases did Daniel use?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Model Division with Arrays Practice KEY
Use the diagrams to complete the division problems in the tables.
(1) Six rows of 3 = 18
(4) Five rows of 2 = 10
(2) Multiplication Sentence: 6 x 3 = 18
(5) Multiplication Sentence: 5 x 2 = 10
(3) Division Sentence: 18 ÷ 6 = 3
(6) Division Sentence: 10 ÷ 5 = 2
(7) 2 rows of six = 12
(10) 4 rows of seven = 28
(8) Multiplication Sentence: 2 x 6 = 12
(11) Multiplication Sentence: 4 x 7 = 28
(9) Division Sentence: 12 ÷ 2 = 6
(12) Division Sentence: 28 ÷ 4 = 7
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Model Division with Arrays Practice
Use the diagrams to complete the division problems in the tables.
(1) Six rows of ________ = ________
(4) Five rows of ________ = ________
(2) Multiplication Sentence: _____________
(5) Multiplication Sentence: _____________
(3) Division Sentence: _______________
(6) Division Sentence: _______________
(7) ______ rows of six = ______
(10) ______rows of seven =______
(8) Multiplication Sentence: ____________
(11) Multiplication Sentence: ____________
(9) Division Sentence: _______________
(12) Division Sentence: _______________
©2012, TESCCC
08/03/12
page 1 of 1
Grade 03
Mathematics
Unit: 04 Lesson: 02
Modeling Division Evaluation KEY
Use counters to help you model and solve the following problems.
(1) Helen had 42 pencils. She gave each friend 7 pencils. If Helen gave each friend an equal
number of pencils, how many friends received pencils?
Use the spaces below to model this problem using a grouping model and an array.
Grouping Model
Array
P P
P P P
P P
P P
P PPPP
P P
PPPPP
P P
P P P
P P
P P
PPPPP
P P
PPPPP
Use this number line to find the number of friends who received pencils.
0
10
20
30
40
Write a repeated subtraction sentence for this problem:
42 – 7 = 35; 35 – 7 = 28; 28 – 7 = 21; 21 – 7 = 14; 14 – 7 = 7; 7 – 7 = 0
Write a division sentence for this problem:
42 ÷ 7 = 6
Solution:
6 friends received pencils.
©2012, TESCCC
08/03/12
page 1 of 2
Grade 03
Mathematics
Unit: 04 Lesson: 02
Modeling Division Evaluation KEY
Use counters to help you model and solve the following problems.
(2) A box contains 20 kittens. The kittens are separated into 5 equal groups. How many kittens are
in each group?
Use the spaces below to model this problem using a grouping model and an array.
Grouping Model
K K
K K
KK
KK
K K
K K
K K
K K
Array
K K
K K
Use this number line to find the number of kittens in each group.
0
10
20
Write a repeated subtraction sentence for this problem:
20 – 4 = 16; 16 – 4 = 12; 12 – 4 = 8; 8 – 4 = 4; 4 – 4 = 0
Write a division sentence for this problem:
20 ÷ 5 = 4
Solution:
Each group contained 4 kittens.
©2012, TESCCC
08/03/12
page 2 of 2
Grade 03
Mathematics
Unit: 04 Lesson: 02
Modeling Division Evaluation PI
Use counters to help you model and solve the following problems.
(1) Helen had 42 pencils. She gave each friend 7 pencils. If Helen gave each friend an equal
number of pencils, how many friends received pencils?
Use the spaces below to model this problem using a grouping model and an array.
Grouping Model
Array
Use this number line to find the number of friends who received pencils.
0
10
20
30
40
Write a repeated subtraction sentence for this problem:
Write a division sentence for this problem:
Solution:
©2012, TESCCC
08/03/12
page 1 of 2
Grade 03
Mathematics
Unit: 04 Lesson: 02
Modeling Division Evaluation PI
Use counters to help you model and solve the following problems.
(2) A box contains 20 kittens. The kittens are separated into 5 equal groups. How many kittens are
in each group?
Use the spaces below to model this problem using a grouping model and an array.
Grouping Model
Array
Use this number line to find the number of kittens in each group.
0
10
20
Write a repeated subtraction sentence for this problem:
Write a division sentence for this problem:
Solution:
©2012, TESCCC
08/03/12
page 2 of 2