K-8 Mathematics Standards
Content Training
Multiplication and Division
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Valerie Adams, Math Coach, Intervention
Specialist, Virgie Robinson Elementary School,
Pasco School District
 [email protected]
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Develop understanding of multiplication and
division concepts for your grade band.
Develop understanding of different problem
types for multiplication and division.
Learn a variety of strategies for solving
multiplication and division problems.
Experience models that support thinking
about Big Ideas in multiplication and division.
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Allow ourselves and others to be seen as
learners.
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Monitor own airtime and sidebar conversations.
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Allow for opportunities for equitable sharing.
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Presume positive intentions.
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Be respectful when giving and receiving
opinions, ideas and approaches.
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For all students to learn significant
mathematics, content should be
taught and assessed in meaningful
situations.
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Conceptual Understanding
◦ Making sense of mathematics
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Procedural Proficiency
◦ Skills, facts, and procedures
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Mathematical Processes
◦ Using mathematics to reason and think
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At each grade level:
◦ 3-4 Core Content areas
◦ Additional Key Content
◦ Core Processes (reasoning, problem solving, communication)
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For each of these:
◦ Overview paragraph
◦ Performance Expectation
◦ Comments/Examples
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Use either your Standards Document or Strands
Document to find all K-8 references to multiplication
and division of whole numbers.
Go back and carefully read the Performance
Expectations and Explanatory Comments and Examples
for your grade level.
Note the expectations for the grade level above and
below yours.
What should your students already know?
What do you need to teach this year?
What do they need to know for next year?
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Big Ideas
Strategies
Models
On your Double Entry Journal record:
Your thought and notes from the activities and
discussion
Implications and ideas for your work with
students.
The understanding of multiplication and division with
whole numbers requires students to think about three
quantities:
 The whole (or total)
 The number of groups
 The amount in each group
If the whole is unknown multiplication is required.
If the whole is known and one of the other quantities is
unknown, division is required.
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Partitioning equal quantities and partitioning a
quantity into equal parts helps us relate
multiplication and division and understand
their properties.
2.4.C,
2.4.D
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Joe counts all of the windows
 Jessica adds 5+5+5=15
 Juan says there are three
fives or 15
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All have answered how many.
But only Juan has thought of it as multiplication. He has
unitized the groups of 5. The others have thought
additively rather than multiplicatively.
3.2.A,
3.2.F
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3.2.A,
3.2.B
REPEAT EQUAL QUANTITIES
There are 5 tables and 6 children can sit at each table.
How many children can we seat?
USE RATES
Apples cost 1.65 a pound. How much would it cost for 3
pounds?
MAKE RATIO COMPARISONS OR CHANGES
Tanya has 5 times as many marbles as Jill. If Jill has 13
marbles, how many does Tanya have?
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MAKE ARRAYS and COMBINATIONS
How many different outfits can we make from 3
pairs of pants and 5 shirts?
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NEED PRODUCTS OF MEASURE
What is the area of a rectangle 15 cm. x 5cm.?
Your group will prepare a poster showing WHY your
problem type is multiplication.
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There are corresponding Division problems for each
type of Multiplication problem. For example:
REAT EQUAL QUANTITIES
We need to seat 30 children in our class. Each table will
seat 6 children. How many tables will we need?
We need to seat 30 children in our classroom. If we have
5 tables how many children will need to sit at each
table?
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Grouping (quotition) Division
The quantity is known
The size of the group is known
Want to find the number of groups to be formed from it.
Sharing (partition) Division
The quantity is known
The number of groups is known
Want to find how many or how much will be in each portion.
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3.2.B,
3.2.C
30 minutes
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ARRAY An arrangement of objects in a rectangle
3 in each row or 3 columns
3.2.A,
3.2.B,
3.2.G,
4.1.C
4 rows
At your table work as a group to make all the arrays
possible for each of the following numbers:
3, 4, 5, 8, 9, 12, 15, 16, 18, 24, 25
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What do you notice?
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How many ways can you split a 24 x 4 array?
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Record your arrays on grid paper.
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A 4 x 3 array
Split into
(2x6) + (2x6)
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3.2.A,
3.2.G
4.1.G
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I have 36 Christmas ornaments from my Grandmother.
I want to make a special box to hold them all. How many
different boxes can I make?
How much cardboard would it take to make each box?
Solve the problem with a partner or in your group
What Big Ideas does this problem support?
3.2.H
Associative property: (6x3)x2 = 6x(3x2)
4.1.J
4.1.D
(ab)c = a(bc)
5.1.B
Volume
What if we changed the problem to make boxes for base
ten blocks?
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Number Talk
◦ Mini-lessons to develop computation strategies
◦ Short lessons around a focused collection of related
facts or strategies
◦ Happens after concept development
◦ Problems done mentally then recorded and discussed
as a group
3.2.A, 3.2.D,
3.2.E, 3.2.G,
4.1.D, 4.1.G
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Keep Doubling
12x6 = (12 x 2) + (1 2 x 2) + (12x2)
 Halving and Doubling
16 x 12 = 8 x 24 = 4 x 48 = 2 x 96
 Using Distributive property
12 x 16 = (12 x 10) + (12 x 6)
 Using Friendly 10s
12x19 = (12 x 20) - 12
Commutative Property
3x8 = 8 x 3
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3.2.A,
3.2.D,
4.1.A,
4.1.C
5.1.A
2.4.D
3.2.C
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Division is defined mathematically as the inverse of
multiplication.
When solving division situations children will often begin by
counting, trial and error, or adding up to the whole. They are
thinking additively.
When students can consider the whole and the group
simultaneously. The are beginning to think multiplicatively in
division situations.
Division can be solved by multiplication or Division
2.4.D, 3.2.C,
3.2.F, 4.1.J
The problems we use can help develop the relationship
between multiplication and division and develop
students’ strategies.
There are 72 parents coming to Open House. We can
seat 6 at each table. How many tables do we need?
How many groups of 6 to seat 72?
? x 6 = 72 Represents the semantic structure of
the problem
72 ÷ 6 =
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The only way to solve the problem with
missing factor on the calculator.
I want to serve coffee to the parents at Open House. My
coffee pot makes seven cups of coffee. How many pots will I
need to make to serve all 72 parents?
The problem encourages the use of unitizing
rather than counting because the cups aren’t
easy to visualize.
With experience with many types of division problem
situations and discussion of strategies and recording,
students come to see that the same situation can be
described with multiplication or division.
2.4.D, 3.2.C,
3.2.F, 4.1.J
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Third
grade is taking busses to the museum. There are
192 graders. Each bus holds 60 children. How many busses
will we need?
192 ÷ 60 = 3 R 13 Round up to 4 busses.
Our school ordered 50 pound f clay for 8 classroom to
share equally. How many pounds will each classroom get?
50 ÷ 8 = 6 R 2 6¼ share out remainders
The Really Great Rose Company has 250 roses in stock.
They are running a bouquet special, 8 in a bouquet.
How many bouquet specials can they make?
 31 R 2 Round down 31 Bouquets
3.2.F, 4.1.J
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Solve these problems with a partner and record your
strategies. Try out a strategy that might be new to you.
100 ÷ 6
153 ÷ 3
180 ÷ 15
270 ÷ 6
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3.2.B, 3.2.C,
3.2.E, 3.2.G
4.1.C, 4.1.F
4.1.G, 5.1.B
5.1.C, 5.1.E
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Thinking about the Big Ideas, Strategies and
Models from tonight, record in your Journal:
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Something new I learned
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Something I want to try
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Something I am still wondering about
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Young Mathematicians at Work: Constructing
Multiplication and Division, Catherine Twomey Fosnot
Teaching Student-Centered Mathematics, Grades 3-5
John A. Van de Walle www.ablongman.com
Mini-lessons for Early Multiplication and Division,
Mini-lessons for Extending Multiplication and
Division, Catherine Twomey Fosnot
First Steps in Mathematics, Number