3rd Grade – Unit 7 – Application of Multiplication and Division
5E Lesson Plan Math
Grade Level: 3
Subject Area: Math
Lesson Title: Application of Multiplication and Unit Number: 7
Division
Lesson Overview:
Lesson Length: 10
Days
This unit bundles student expectations that address solving one- and two-step multiplication
and division problem situations using a variety of strategies, including the standard algorithm.
According to the Texas Education Agency, mathematical process standards including
application, a problem-solving model, tools and techniques, communication, representations,
relationships, and justifications should be integrated (when applicable) with content knowledge
and skills so that students are prepared to use mathematics in everyday life, society, and the
workplace.
Prior to this unit, in Unit 05, students used their understandings of multiplication to form the
framework for developing an understanding of division and the inverse relationship between
these operations.
During this unit, students extend their understanding of multiplication and division and the
mathematical relationships between these operations as they represent multiplication and
division of a two-digit number by a one-digit number using arrays, area models, strip diagrams,
and equations. Students use the commutative (if the order of the factors are changed, the
product remains the same), associative (if three or more factors are multiplied, they can be
grouped in any order, and the product will remain the same), and distributive (if multiplying a
number by a sum of numbers, the product will be the same as multiplying the number by each
addend and then adding the products together) properties of multiplication, mental math,
partial products, and the standard multiplication algorithm to represent and solve one- and
two-step multiplication and division problem situations within 100. Multiplication problems
include determining area of rectangles. Students explore both partitive and quotative
(measurement) division problems and use divisibility generalizations to determine if a number
is odd or even.
Unit Objectives:
The students will…extend their understanding of multiplication and division and the
mathematical relationships between these operations as they represent multiplication and
division of a two-digit number by a one-digit number using arrays, area models, strip diagrams,
and equations.
The students will… use the commutative (if the order of the factors are changed, the product
remains the same), associative (if three or more factors are multiplied, they can be grouped in
any order, and the product will remain the same), and distributive (if multiplying a number by a
sum of numbers, the product will be the same as multiplying the number by each addend and
then adding the products together) properties of multiplication, mental math, partial products,
and the standard multiplication algorithm to represent and solve one- and two-step
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3rd Grade – Unit 7 – Application of Multiplication and Division
multiplication and division problem situations within 100. Multiplication problems include
determining area of rectangles.
The students will…explore both partitive and quotative (measurement) division problems and
use divisibility generalizations to determine if a number is odd or even.
Standards addressed:
TEKS:
3.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
3.1B Use a problem-solving model that incorporates analyzing given information, formulating a
plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
3.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
3.1D Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
3.1E Create and use representations to organize, record, and communicate mathematical
ideas.
3.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
3.1G Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
3.4G Use strategies and algorithms, including the standard algorithm, to multiply a two-digit
number by a one-digit number. Strategies may include mental math, partial products, and the
commutative, associative, and distributive properties
*Supporting Standard
3.4I Determine if a number is even or odd using divisibility rules.
*Supporting Standard
3.4J Determine a quotient using the relationship between multiplication and division.
*Supporting Standard
3.4K Solve one-step and two-step problems involving multiplication and division within 100
using strategies based on objects; pictorial models, including arrays, area models, and equal
groups; properties of operations; or recall of facts.
*Readiness Standard
3.5B Represent and solve one- and two-step multiplication and division problems within 100
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3rd Grade – Unit 7 – Application of Multiplication and Division
using arrays, strip diagrams, and equations.
*Readiness Standard
3.6C Determine the area of rectangles with whole number side lengths in problems using
multiplication related to the number of rows times the number of unit squares in each row.
*Readiness Standard
ELPS:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.2D monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence types,
and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new
English words and build academic language proficiency
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail as more
English is acquired
ELPS.c.4D use prereading supports such as graphic organizers, illustrations, and pretaught
topic-related vocabulary and other prereading activities to enhance comprehension of written
text
ELPS.c.4H read silently with increasing ease and comprehension for longer periods
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level
vocabulary
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and
connecting words to combine phrases, clauses, and sentences in increasingly accurate ways
as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content
area writing needs as more English is acquired.
Misconceptions:
Although some students may know how to multiply or divide numbers in isolation, when the
operation is presented within context, they have difficulty connecting multiplication or division
to the actions within the problem.
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Although some students may recognize the relationship between multiplication and
division when using basic facts, they do not apply this knowledge beyond the basic
facts.
Some students may be able to perform a symbolic procedure for division with limited
understanding of the division concepts or problem types involved (e.g., 12 ÷ 3 = 4 could
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3rd Grade – Unit 7 – Application of Multiplication and Division
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represent 12 separated into 3 groups with 4 in each group or 12 separated into groups
of 3 creating 4 groups).
Some students may have limited or no experience with strip diagrams and their
relationship to equations that represent problem situations.
Vocabulary:
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Area – the measurement attribute that describes the number of unit squares (or square
units) a figure or region co
Counting (natural) numbers – the set of positive numbers that begins at one and
increases by increments of one each time {1, 2, 3, ..., n}
Dividend – the number that is being divided
Divisor – the number the dividend is being divided by
Equation – a mathematical statement composed of equivalent expressions separated
by an equal sign
Even number – a number divisible by 2
Expression – a mathematical phrase, with no equal sign, that may contain a
number(s), an unknown(s), and/or an operator(s)
Fact families – related number sentences using the same set of numbers
Factor – a number multiplied by another number to find a product
Odd number – a number not divisible by 2
Product – the total when two or more factors are multiplied
Quotient – the size or measure of each group or the number of groups when the
dividend is divided by the divisor
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Related Vocabulary:
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Algorithm
Area model
Array
Column
Divisible
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Mental math
Multiple
Partial products
Partitive division
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Quotative
(Measurement) division
Row
Square unit
Strip digrams
List of Materials:
Properties of Multiplication Anchor Chart Example (Answer Key - completed)
Properties of Multiplication Anchor Chart Example (students will fill in themselves)
Properties of Multiplication and Properties of Addition Charts for the student’s Math Journals
Properties of Multiplication Examples Worksheet and Answer Key
Frame the Equation Worksheet and Answer Key
Dry-erase boards, erasers, and markers for students to use individually
Giant Dice (optional)
Partial Product Worksheet and Answer Key
Math Journal
Missing Number Multiplication Worksheet and Answer Key
Fact Family Worksheet and Answer Key
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3rd Grade – Unit 7 – Application of Multiplication and Division
Construction paper house (template included)
Divisibility by Two Worksheet and Answer Key
Envision Math 2.0 Book or Texas Go Math!
http://teacherweb.com/NY/Quogue/MrsLevy/photo9.aspx (link for key word charts)
http://www.k5learning.com/free-math-worksheets/third-grade-3/word-problems (Multiplication
and Division Word Problems site for word problems) **Free trial is only good for 14 days!
Multiplication and Division Clue Word Match Worksheet and Answer Key
Two-Step Word Problem (Multiplication and Division) and Answer Key
Grid paper
http://www.math-aids.com/Graph_Paper/Graph_Paper.html (grid paper)
Area Compare activity
http://www.k-5mathteachingresources.com/support-files/area-compare.pdf (Area compare
activity)
Extra websites for practicing area.
http://www.shodor.org/interactivate/activities/AreaExplorer/ (Area game)
http://interactivesites.weebly.com/areaperimeter.html (Area game)
http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html
(Area game)
INSTRUCTIONAL SEQUENCE
Phase - Engage
Day 1:
The students will explore the commutative, associative, and distributive property of
multiplication.
Phase: Engage
Materials:
Properties of Multiplication Anchor Chart Example
Properties of Multiplication and Properties of Addition Charts for the student’s Math Journals
Properties of Multiplication Examples Worksheet
Frame the Equation Worksheet
Dry-erase boards, erasers, and markers for students to use individually
Dice
Activity:
 The teacher will review the Properties of Addition with the class by writing different
problems on the whiteboard (one at a time), and having students volunteer to come up
and write the commutative, associative, and identity property of the example. (This has
been previously taught in the last six weeks.)
Can anyone tell me a property of addition? (Associative Property, Commutative
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3rd Grade – Unit 7 – Application of Multiplication and Division
Property, Identity Property)
Would anyone like to volunteer to show the class an example of each property on
the whiteboard? (Answers may vary. 4 + 6 = 6 + 4 Commutative Property)
Do you think the same properties would work for multiplication? (Answers may
vary. 4 x 6 = 6 x 4 Commutative Property
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The teacher will generate an anchor chart with the students of the properties of
multiplication.
Property
What it Means
Example
Change place of
parenthesis
( ), and answer stays
the same.
Change the order of
the factors and still
get the same answer.
Multiplication is
“spread out” or
distributed over
addition.
Multiply 1 to any
number, and it stays
the same.
Multiply 0 to any
number, and the
answer will be 0.
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The teacher will give each student a blank anchor chart that they will fill in as they go
over the properties together, and discuss. The teacher will have the students use their
Addition Properties anchor chart in their Math Journal as a reference.
Can anyone tell me what multiplication property fits this definition? (Associative
Property – “(grouping)”
What would be an equation I could write in the example box to show this
property? ( (2 x 4) x 5 = 2 x (4 x 5) )
Continue to fill out the chart, and ask the same questions to the students.
The students will cut out the Multiplication Properties Anchor Chart, and glue it into their
Math Journals, for reference.
The teacher will pass out a colored paper, titled Properties of Multiplication
Examples. The students will need to cut the example strips out. The students will
draw a four-square in their Math Journals, and write one property (Zero Property,
Distributive Property, Associative Property, and Commutative Property) in each square.
The students will classify the different properties, by gluing them down on the four6
3rd Grade – Unit 7 – Application of Multiplication and Division
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square in their Math Journals.
The class will practice writing Addition and Multiplication Property Equations on dryerase boards using examples from Frame the Equation worksheet.
How would you show an example of the Commutative Property of Multiplication
using the numbers 11 and 3? (11 x 3 = 3 x 11)
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Orally ask the class several examples from Frame the Equation worksheet, to check
for understanding. The class can write their equations on dry-erase boards at their
desks.
 The class will complete the Frame the Equation worksheet together by using two or
three numbers, and making an Associative Property of Multiplication and Addition
equation or a Commutative Property of Multiplication and Addition equation together. (If
the teacher does not want the class to do the Frame the Equation worksheet, they can
also roll a dice to get two or three numbers to form the different equations.)
 The teacher will continue to monitor the student’s progress.
What’s the teacher doing?
What are the students doing?
 The teacher facilitates discussion
 The students are actively engaged by using
about previously taught
prior knowledge to orally explain properties
properties of addition.
of addition, as well as volunteering to write
 The teacher helps the students
properties on the whiteboard.
recognize similarities and
 The students are completing their own
differences with the properties of
anchor chart in their Math Journals, to later
multiplication.
use for reference.
 The teacher monitors and guides
 The students are showing understanding of
the class through the lesson.
the concepts by matching up the property
 The teacher checks for
examples with the property names on their
understanding by testing the
four-square chart in their journals.
student’s knowledge of the
 The students are showing understanding of
different properties of
the concepts, by completing the “Frame the
multiplication through a
Equation” worksheet, for a grade.
worksheet.
Phase: Explore
Day 2:
Introduce two-digit times one-digit multiplication using partial products.
Materials:
Dry-erase boards, markers, and erasers
Partial Product Worksheet
Math Journal
Activity:
 Teacher will introduce and model steps to use partial products as a way to solve two
digit times one digit multiplication problems. Students will use marker boards to solve
two digit times one digit multiplication problems using the partial product strategy
 Write a 2 digit plus a one digit adding problem on the board. Have the students write
the steps they would follow to solve the problem.
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3rd Grade – Unit 7 – Application of Multiplication and Division
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(28 + 5) Write in words (in student Math Journals) how you would solve this
problem.
What would be your first step in solving this problem? (Add the 8 + 5, or add the
ones place)
What would be the second step? (Add the 2 plus the one you carried)
If we were going to multiply 28 X 5, what do you think the first step would be?
(multiply the 5 X 8 or the ones place)
What do you think the next step would be? (Multiply the 5 X 2) Is the 2 in this
problem really 2, or is it something else? (The 2 is really 20)
The teacher will model the steps described above and explain how to get a final
product to the problem.
28
X5
20 + 8
X5
40
+ 100
140
Students will start an anchor chart showing strategies and algorithms used to solve
multiplication problems
 Students will practice several problems using the partial product strategy.
 The students will complete the Partial Product Worksheet.
What’s the teacher doing?
What are the student’s doing?
 The teacher is guiding a
 The students are answering questions about
discussion on the steps of partial
the steps to solving multiplication using
products.
partial products.
 The teacher is modeling partial
 The students are using marker boards to
products with the students.
practice finding products using the partial
products algorithm.
Phase - Explore
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3rd Grade – Unit 7 – Application of Multiplication and Division
Day 3:
Introduce two-digit times one-digit using standard algorithm.
Materials:
Dry-erase boards, markers, and erasers
Three dice
Activity:
 The teacher will model the difference between partial product and standard algorithm
multiplication on the Smartboard or whiteboard by writing the problem 24 X 6 on the
board. The teacher will first work the problem using the partial product algorithm. The
teacher will work the problem a second time using the standard algorithm.
What are some of the differences you see between the two types of multiplication
problems? (Answers will vary. The partial product problem has more steps and the
standard problem looks more like adding.)
Which type of problem would you choose to use to solve two-digit times onedigit multiplication? (The standard problem.)
 The teacher will roll three dice and use the numbers to make a two-digit times one-digit
multiplication problem on the whiteboard.
What are the steps I need to take to solve this problem using the standard
algorithm? 24 x 6 = (Multiply 6 x 4, write the 4 in the ones place and carry the 2 to the
tens place. Then multiply 6 x 2, and get 12. Then add in the 2 that you carried to the
tens place. The answer is 146.)
 The students will add the standard algorithm their anchor chart of ways to solve
multiplication problems.
 The teacher will model several problems using the standard algorithm method.
 The teacher will allow a student to roll the dice, and model the problem a second time
on the whiteboard.
 The teacher will give each student a dry-erase board to solve multiplication problems
using the standard algorithm method.
 The students will take turns rolling the three dice, and calling out the numbers for the
class to complete problem at their desk for practice. (The students could also do this in
small groups.)
What’s the teacher doing?
What are the students doing?
 The teacher is guiding a
 The students are answering questions about
discussion on the steps of
the steps to solving multiplication using
standard algorithm.
standard algorithm.
 The teacher is modeling standard
 The students are using marker boards to
algorithm with the students.
practice finding products using the standard
algorithm.
 The teacher is monitoring student
progress on the dry-erase
boards.
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3rd Grade – Unit 7 – Application of Multiplication and Division
Phase - Explore
Day 4:
Materials:
Missing Number Multiplication Worksheet
Division Vocabulary Illustration
Fact Family Worksheet
Activity:
 Introduce division vocabulary by illustrating the parts of a division equation in their Math
Journal. Example below.
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The teacher will explain the connection between division and multiplication.
What is the opposite operation of addition? (subtraction)
When operations are opposite, that is called inverse.
What operation do you think is the opposite of multiplication? (division)
Multiplication is putting equal groups together and division is putting something
into equal groups.
The teacher will explain to the students that you can easily solve division problems if
you know your multiplication facts because they are relate, or inverse operations.
The teacher will introduce missing number multiplication by writing the following on the
whiteboard. 30 ÷ 6 = ___
How could you solve this problem by using a multiplication fact you already
know? (6 x ? = 30; 6 X 5 = 30)
The teacher will do several of these on the board for the students to solve out loud.
The students will complete the Missing Number Multiplication Worksheet, to check
for understanding.
After the students complete this worksheet, the teacher will review addition and
subtraction fact families as an introduction to multiplication and division fact families.
How would you make an adding and subtracting fact family with these three
numbers: 3, 8, and 11? (Make two adding and two subtracting facts…3 + 8 = 11, 8 +
3 = 11, 11 – 8 = 3, and 11 – 3 =8) *Remember when you write a subtraction equation,
the big number has to be first!
How do you think you would make a multiplication and division fact family using
the following numbers: 2, 4, and 8? (Make two multiplication and two division
facts…2 x 4 = 8, 4 x 2 =8, 8 ÷ 4 = 2, and 8 ÷ 2 = 4) *Remember when you write a
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3rd Grade – Unit 7 – Application of Multiplication and Division
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division equation, the big number has to be first!
The teacher will give each student a Fact Family Worksheet to complete with a partner.
The teacher will give the class some time to complete the worksheet, and then call one
group up at a time to show their work on the whiteboard.
What is the teacher doing?
What are the students doing?
 The teacher is guiding a
 The students are answering questions about
discussion on the connection
the connections between division and
between division and
multiplication facts and division and
multiplication facts, as well as
multiplication fact families.
division and multiplication fact
 The students are illustrating the vocabulary
families.
for division in their Math Journals.
 The teacher is modeling
 The students will generate multiplication and
multiplication and division fact
division fact families.
families.
 The students will demonstrate how to
 The teacher is monitoring student
connect division to multiplication by using the
progress and understanding of
inverse operation.
multiplication and division fact
families.
Phase - Elaborate
Day 5:
The students will show an understanding of fact families by completing a fact family
neighborhood bulletin board.
The students will determine if a number is even or odd using divisibility rules.
Materials:
Construction paper house (template included)
Divisibility by Two Worksheet
Envision Math 2.0 Book or Texas Go Math!
3 Dice
Activity:
 The class will review multiplication and division fact family on the whiteboard from our
previous lesson the day before.
 The teacher will explain the Fact Family Neighborhood project.
*The students will each be given a House Template to make their project with.
*The teacher will model an example of the Fact Family House project on the
whiteboard. Ex. 5x6=30, 6x5=30, 30÷6=5 and 30÷5=6
*The students will generate their own fact family of their choosing to complete the Fact
Family Neighborhood Project.
*The 3 fact family numbers will go on the roof, and the four fact family equations each
be written on a window the students will draw.
 The students will complete the project on their own.
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3rd Grade – Unit 7 – Application of Multiplication and Division
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After completing the neighborhood project, the teacher will introduce the odd or even
divisibility rules.
The teacher will review the divisibilty by 2 rule, previously taught in Unit 5.
How can someone tell if a number is odd or even? (Even numbers end with 0, 2, 4,
6, 8 and odd numbers end with 1, 3, 5, 7, 9)
Is the number 0 odd or even? (0 by itself is not odd or even.)
How can someone tell if a number is divisible by two? If the number is even it is
divisible by two.
The students will take notes in their Math Journals, defining divisibility rules for 2.
Divisibility Rules for 2 – If a number has a 0, 2, 4, 6, or 8 in the ones place, it is divisible
by 2.
The number 0 (by itself) is NOT considered odd or even.
To illustrate this rule, the teacher will roll three dice to make a three-digit number. The
students will copy the number down into their Math Journals, and then write odd or
even next to the number. The students will then circle the numbers that are divisible by
two.
The teacher will assign Lesson 7-5 from the Envision 2.0 math textbook, pg. 411-413.
(Also available in the Texas Go Math! Volume 1 math textbook…Lesson 11.3 pg. 351352.) (Divisibility Worksheet by Two included, if you don’t have a textbook to use.)
What’s the teacher doing?
 The teacher is reviewing
multiplication and division fact
families with the students.
 The teacher explains the
neighborhood project.
 The teacher introduces the
divisibility rules by 2’s.
 The teacher will generate threedigit numbers by rolling dice for
the students to determine
odd/even and when they are
What are the students doing?
 The students are reviewing multiplication and
division fact families.
 The students are completing the
neighborhood fact family projects.
 The students taking notes on divisibility rules
by 2’s.
 The students are completing a worksheet on
divisibility by 2’s.
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3rd Grade – Unit 7 – Application of Multiplication and Division
divisible by 2.
 The teacher will assign book
pages for the students to
complete to check for
understanding.
Phase - Elaborate
Day 6 and 7
The students will brainstorm “clue words” related to multiplication and division word problems.
The students will use these words to solve a mixture of multiplication and division word
problems.
Materials:
http://teacherweb.com/NY/Quogue/MrsLevy/photo9.aspx (link for key word charts)
Multiplication and Division Key Word Charts
http://www.k5learning.com/free-math-worksheets/third-grade-3/word-problems (and Division
Word Problems site for word problems)Multiplication
Multiplication and Division clue word match worksheet
Activity:
Day 6
The teacher will guide students in a review of multiplication and division clue words. The
students will brainstorm clue words and the teacher will write the words on the board. After
the class has generated the words, group multiplying and division words together and add to
Math notebook.
The teacher will review strategies that will be used when solving word problems. When you
are solving a word problem, what is the first step? (Read the problem carefully.)
Remember you may need to read the question more than once. After you read the
question, what would be the next step? (Underline or circle the clue words). The clue
words will help you decide what kind of problem you need to set up. Once you decide
how you are going to solve the problem, what is the next step? (Write a number sentence
and work it out.) What should you do after you solve your problem? (Check your work and
think if your answer makes sense.)
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3rd Grade – Unit 7 – Application of Multiplication and Division
These strategies have been taught for addition and subtraction.
The teacher will write the following problem on the board to use as an example:
Jim placed 4 stacks of pennies on the table. There are 15 pennies in each stack. How many
pennies did Jim place in the table?
Allow the student’s to work out the problem using any type of strategy they wish. After the
students have completed their work, ask if anyone would like to come and share their work on
the board. Choose students that used different strategies (standard alogrithm, partial product,
drawing a picture, making an array). Talk about how you can get the same answer by using
different strategies. Work out the above example a variety of ways: pictorial models, arrays,
equal groups and standard algorithms. Tell students that they can choose different ways to
solve the same problem. Students will need to practice a variety of multiplication and division
problems. You may use your math book or the online resources provided above as a
source of word problems.
Day 7
The teacher will quickly review multiplication and division clue words with the Multiplication
and Division clue word match worksheet. (This is strictly to help students be able to identify
clue words in word problems.) After reviewing clue words, go over the problem solving steps
and strategies for solving word problems. The teacher will assign one and two step
multiplication and division word problems for the students to work independently. The teacher
will monitor for understanding as the students are working with Two-Step Word Problems
(Multiplication and Division) Worksheet.
What’s the teacher doing?
 The teacher is reviewing
multiplication and division clue
words.
 The teacher is reviewing problem
solving strategies.
 The teacher is modeling a variety
of ways to solve multiplication
and division word problems.
Phase - Elaborate
What are the student’s doing?
 The students are brainstorming clue words.
 The students are reviewing the steps in
problem solving.
 The students are working on a variety of one
and two step multiplication and division word
problems.
Day 8
The students will use strip diagrams as a strategy for solving multiplication and division word
problems.
Materials:
Dry erase boards and markers
Teacher generated word problems (similar to the examples written below, located in Activity
Day 8)
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3rd Grade – Unit 7 – Application of Multiplication and Division
Activity Day 8
The teacher will guide the students in a review of the strip diagram strategy for problem
solving that they learned in Unit 2.
Students have used strip diagrams as a strategy for solving addition and subtraction problems.
The teacher will show the students how strip diagrams can also be used for solving
multiplication problems. The teacher will start by solving an addition problem using a strip
diagram as a review of how to use strip diagrams.
Sam has 23 pennies and 57 nickels. How many coins does Sam have in all? Remember
when you are looking for the total of how many in all you will be adding. You will write in the
parts and add them together to find the whole or total.
Whole or total
part
part
Whole or total
23
57
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3rd Grade – Unit 7 – Application of Multiplication and Division
80
23
57
Review the steps when using strip diagrams. This was taught for addition and subtraction.
Write the following multiplication problem on the board.
Sandy’s mother baked 5 batches of cookies. There were 15 cookies in each batch. How
many cookies did Sandy’s mother bake in all? Draw a blank strip diagram on the board. Have
the students use dry erase markers of pencils to work the problems along with the teacher.
Are we looking for the parts or the total in the problem? (The total or how many in all.
We know there are 5 batches and 15 cookies in each batch. We do not know how many
cookies in all.)
Have the students write the word total in the top box. This is what we are trying to find.
Total ?
How can we show 5 equal batches? (Make 5 boxes in the bottom row because there are 5
batches.)
Total ?
What numbers are we going to put into the 5 boxes? (15, because there are 15 cookies in
each batch and there are 5 batches.)
Total ?
15 15
15 15
15
How will this help us find the answer to the problem? (There are 5 equal groups of 15,
16
3rd Grade – Unit 7 – Application of Multiplication and Division
then we can multiply 15 x 5 to get 75 cookies in all)
The teacher will have the students use the strip diagram strategy to solve several
multiplication problems. You may do this as a guided practice. After the students have
practiced using the strip diagram strategy for multiplication introduce using strip diagrams for
division.
Multiplication and division are inverse (opposite) operations. How do you think we
could use the strip diagram strategy to solve a division problem? (The missing numbers
would be on the bottom because we know how many in all or the total.)
Write the following division problem on the board.
James has 24 quarters. He wants to put the quarters into 4 stacks. Each stack will have the
same number of quarters. How many quarters will be in each stack?
How could you use a strip diagram to solve this problem? (Put 24 on top because that is
the total.)
24
What will you do on the bottom of the diagram? (Make it into 4 equal parts for the 4 equal
stacks.)
24
What number are you going to put in each box? (6 because if you put 24 into 4 stacks,
there will be 6 in each stack. 4 X ? = 24) )
24
6
6
6
6
How does this help us solve the problem? (If you divide 24 into 4 equal groups, there will
be 6 in each group. 24 ÷ 4 = 6)
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3rd Grade – Unit 7 – Application of Multiplication and Division
Have the students work several division problems using the strip diagram strategy as practice.
Using strip diagrams is just another strategy that students can use when solving word
problems. Students should know that they should choose the strategy that works best for
them. The strategy they choose should make solving the problem easier.
Each child has 5 tickets. If there are 50 children, how many tickets are there in total? 250
There are 3 eggs in each box. How many eggs are in 4 boxes? 12
Each child has 8 peanuts. If there are 8 children, how many peanuts are there in total? 64
What’s the teacher doing?
 Modeling how to use strip
diagrams to solve multiplication
and division problems.
 Asking guiding questions.
What are the students doing?
 Answering questions
 Following steps to use strip diagrams for
multiplication and division.
Phase - Elaborate
Day 9 Activity:
The students will determine the area of a rectangle.
Materials:
Grid paper
Area Compare activity
http://www.shodor.org/interactivate/activities/AreaExplorer/ (Area game)
http://interactivesites.weebly.com/areaperimeter.html (Area game)
http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html
(Area game)
http://www.math-aids.com/Graph_Paper/Graph_Paper.html (grid paper)
http://www.k-5mathteachingresources.com/support-files/area-compare.pdf (Area compare
activity)
Students will determine the area of a rectangle by multiplying the number of rows times the
number in each row. The students will also determine the area of a shaded rectangle on grid
paper.
What is area? (How many square tiles inside?)
What word does area remind you of? (Array) Remember that arrays show objects in equal
rows and columns. You can us an array to help you find the area of a rectangle.
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3rd Grade – Unit 7 – Application of Multiplication and Division
3
5
Look at the rectangle. If I wanted to find the area using an array, how could I do that?
(Count how many rows(3) and how many in each row(5) then multiply those numbers together.
3 X 5 = 15)
To find the area of a rectangle you need to know how many cubes it would take to fill the
rectangle. You can count the number of rows and the number in each row. Multiply those
numbers to determine the area of the rectangle.
3 X 5 = 15
The area of the rectangle would be 15 square units.
If you wanted to determine the area of a shaded rectangle on grid paper, how would this
be like using an array to determine area? (You need to get a number for the sides and
multiply.) Show the students an example of a shaded rectangle on grid paper.
[Type a quote from
the document or the
summary of an
interesting point.
You can position the
text box anywhere in
the document. Use
the Drawing Tools
tab to change the
formatting of the pull
quote text box.]
Have students count the shaded squares in the first column (3), and write than number next to
the first column. Count the shaded squares in the first row (4), and write that number above
the first row. After you have the numbers filled in, how can you use this to determine the
19
3rd Grade – Unit 7 – Application of Multiplication and Division
area of the rectangle? (Multiply the two numbers together 3 X 4 = 12. The area of the
shaded rectangle would 12 square units.) Have the class practice determining the area of
shaded rectangles by creating shaded rectangles on grid paper. This can be done as a whole
class activity. Pass out grid paper.
http://www.math-aids.com/Graph_Paper/Graph_Paper.html This is a link to print your own
grid paper for this activity.
Roll two dice. The students will need to make a rectangle whose sides match the number on
the dice. Have the students shade in their rectangles then determine the area by multiplying
the sides together. After the students have had several opportunities to practice, introduce
and go over the activity “Area Compare”.
http://www.k-5mathteachingresources.com/support-files/area-compare.pdf
Have students work in pairs as they complete the activity. Monitor students for understanding
throughout the activity.
Envision Math 2.0 teaches this in Lesson 13-5 p. 725.
Texas Go Math teaches this in Lesson 16. 2 p. 519.
Both books have a variety of examples.
*If you do not have access to these books, included are links to area game websites.
What’s the teacher doing?
What are the students doing?
 The teacher is connecting finding
 The students are answering questions.
area to arrays.
 Students are constructing rectangles on
 The teacher is monitoring student
graph paper.
understanding.
 Students are determining area of a variety of
rectangles.
 Teacher is modeling how to
construct rectangles on graph
paper.
 The teacher is teaching how to
determine area of a rectangle
using the array strategy.
20
3rd Grade – Unit 7 – Application of Multiplication and Division
Phase - Evaluate
Day 10:
Activity:
The students will work on the Performance Indicator from the IFD.
Materials:
Performance Assessment 1 and 2.
Performance Assessment 1:
Analyze the situation(s) described below. Organize and record your work for each of the
following tasks. Using precise mathematical language, justify and explain each mathematical
process.
1) At the local grocery store ice cream cups were on sale for 15 cents each. Mrs. Ellermann
allowed each of her 4 children to select their favorite flavors. They each selected an equal
amount, placing a total of 52 ice cream cups in the shopping cart.
a) Create an array, strip diagram, and equation to determine how many ice cream cups each
child selected.
b) Use the standard multiplication algorithm to determine how much it would have cost Mrs.
Ellermann had she only allowed each child to select 1 ice cream cup.
2) The Ramsey family picked 84 apples on a recent trip to the apple orchard. The 4 boys in the
family each picked 13 apples.
a) Use a pictorial representation and algorithm of your choice to determine how many apples
the 2 girls in the family picked together.
b) If all 6 Ramsey children had picked the same number of apples, how many of the 84 apples
would each child have picked?
3) Allison placed 54 cupcakes evenly into 3 boxes.
a) Use a pictorial representation and algorithm of your choice to determine how many
cupcakes Allison placed in each box.
b) Allison stated she had an even number of cupcakes. Determine if she is correct using
divisibility rule. In writing, explain how the divisibility rule was used to determine if a number is
odd or even.
Standard(s): 3.1A , 3.1B , 3.1C , 3.1D , 3.1E , 3.1F , 3.1G , 3.4G , 3.4I , 3.4J , 3.4K , 3.5B
ELPS.c.1A , ELPS.c.2D , ELPS.c.3C , ELPS.c.3D , ELPS.c.3H , ELPS.c.4D , ELPS.c.4H
, ELPS.c.5B , ELPS.c.5F , ELPS.c.5G
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3rd Grade – Unit 7 – Application of Multiplication and Division
Performance Assessment 2:
Analyze the situation(s) described below. Organize and record your work for each of the
following tasks. Using precise mathematical language, justify and explain each mathematical
process.
1) Clara constructed a flower garden that was 16 feet in length and 5 feet in width. What is the
area of Clara’s flower garden?
a) Use a pictorial representation and an equation to represent and record your solution
process in an equation.
b) In writing, explain the process used to determine the area of the garden.
Standard(s): 3.1A , 3.1C , 3.1D , 3.1E , 3.1F , 3.1G , 3.6C ELPS.c.1A , ELPS.c.2D
, ELPS.c.3C , ELPS.c.3D , ELPS.c.3H , ELPS.c.4D , ELPS.c.4H , ELPS.c.5B , ELPS.c.5F
, ELPS.c.5G
What’s the teacher doing?
What are the student’s doing?
 Monitor students as they work on
 The students are completing the
Performance Indicator to
Performance Indicator.
determine if any re-teaching is
necessary.
22