West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
Week 1 - 3
Learning Standards
Nov 5 – 9
4) Number, operation, and quantitative reasoning.
The student recognizes and solves problems in
multiplication and division situations. The student is
expected to
(A) learn and apply multiplication facts through 12 by
12 using [concrete] models [and objects];
(B) solve and record multiplication problems (up to two
digits times one digit); and
(C) use models to solve division problems and use
number sentences to record the solutions.
Nov 12 – 16
Nov 26 – 30
Major Concepts
Multiplication
Problem Solving
Instruction
Resources
Key Vocabulary – multiplication, division, equal groups, array,
product, factor, horizontal, vertical, multiply, divide, divided by, input,
output, fact family
enVision Math –Topics 6, 7, 8, and 9
The third six weeks is focused on multiplication and division. The
first three weeks will be learning multiplication and the last three
weeks, division. Students are expected to recognize and solve
problems in multiplication and division situations.
Math background for teachers:





Multiplication may be thought of as repeated addition and involves
joining equal groups.
An array involves joining equal groups and is another way to think
of multiplication.
Two numbers can be multiplied in any order.
Help students make connections to multiplication through skip
counting using number lines and hundreds charts.
The ability to break numbers apart in flexible ways is very
important as they use invented strategies to solve multiplication.
2012 - 2013
Processes:
 Problem Solving Model
 Thinking about learning and making
connections
 Use accountable talk by using the language of
mathematics
Math Stations
Interventions/Extensions
Assessment
enVision Math
multiplication games
enVision Math
Assessments
enVision Math Tools
Multiplication games using
dice or cards
Technology: Pearson enVision link
for animated introduction, journal
writing, and review – copy and paste
this link:
https://www.pearsonsuccessnet.com
http://express.smarttech.com/?url=htt
p://exchangedownloads.smarttech.co
m/public/content/77/77c5bbc7-ecd14162-88ddecc7e8816a75/mutiplication.notebook
#
Problem Solving – word
problems involving mixed
operations including
multiplication.
Journal writing – explain
how multiplication is
related to addition
Number of the week
Measurement Station
http://express.smarttech.com/?url=htt
p://exchangedownloads.smarttech.co
m/public/content/95/95a29a91-88454f0a-a1ce8b25d4558c7c/Multiplication%20Ma
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 1
West-Orange Cove ISD


3rd Grade Mathematics – 3rd Six Weeks
Teach the distributive property is an important concept. Teach
students that they can solve 43 x 5 by breaking it into 40 x 5 + 3 x
5 then adding the results. Provide numerous opportunities for
students to manipulate and apply strategies for solving.
 Use number lines to solve multiplication problems.
 Students will not learn multiplication facts through “drill and kill”
 Students must learn to select ways to think about multiplication
that makes sense and are meaningful to them.
 Students tend to use three categories when solving multiplication:
(Van de Walle)
o Complete-Number Strategies – These students are usually
not comfortable breaking numbers into tens and ones. For
example 58 x 5. Students will do repeated addition and
add 58 five times. When they could have multiplied 50 x
5 and 8 x 5 then added them together.
o Partitioning Strategies – (several examples of partitioning)
 27 x 4 - 4 x 20 =80 4x7 = 28
 46 x 3 double 46 = 92 + 46 = 138
 27 x 4 = 10 x 4, 10 x 4, 7 x 4 then add the totals of
each to get 108
 27 x 8 = 25 x 4, 25 x 8, 2 x 8 add the totals to get
216
o Compensation Strategies –numbers are manipulated in a
manner the student is comfortable using. For example 27
x 4 may be seen as 27 + 3 = 30 x 4 = 120, 3 x 4 = 12, 120
– 12 = 108
 Multiples of 10 and 100 – follows the familiar pattern of base 10
students are familiar with. Students will use 4 x 12 = 48 to solve
400 x 12 = 4,800. Students should not be taught to add zeros
without understanding the concept of multiplying by 10 or 100.
Arrays are excellent models for concrete learning of multiplication.
2012 - 2013
nia.notebook#
http://express.smarttech.com/?url=htt
p://exchangedownloads.smarttech.co
m/public/content/cf/cf95375e-cdee4ef4-a2b16013fa870c97/Quick%20Recall%20
Multiplication.notebook#
Foam Tiles
Counters
Dice
Playing Cards
Interventions/Extensions
Products/project
Often students “shutdown”
when they hear the term
multiplication. To help
overcome this use egg
cartons and counters to
make the connection of
multiplication being
repeated addition. Pose
fact problems to students
such as 3 x 5. Students will
put five counters in each of
3 compartments in the egg
carton. Repeat several
times then let students
challenge each other.
Students will use
newspaper or
construction paper
to make arrays for a
given product
Students will work
in groups to create
and present visual
representations of
the properties of
multiplication
Base 10
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
GT: Students that are more
familiar with multiplication
and or know their facts can
play a multiplication game.
Student rolls two dice to get
their first factor and write it
down. Next they roll one
die and multiply the 2 digit
factor by it. Repeat 10
times, each time keeping a
running total. Students
then trade papers and check
each other’s work. The
student with the greatest
ending total wins.
Page 2
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
(This is a good time to connect arrays to finding area.)
There are four problem structures students should be familiar
with to be efficient problem solvers.
1. Equal groups: Whole unknown.
 Jacob has 4 bags of oranges. There are six oranges in each
bag. How many oranges does Jacob have altogether?
(Repeated addition.)
 If oranges cost .10 each, how much will he pay for 5 oranges?
(rate)
 If He walked for 3 hours at 4 miles per hour, how far did he
walk? (rate)
2. Comparison Problems – Product unknown.
 Susan picked 6 apples. Maria picked 4 times as many apples
as Susan. How many apples did Maria pick?
3. Combinations Problems – Product Unknown.
 Juan bought 4 pairs of jeans and 3 shirts and they can all be
worn together. How many different outfits consisting of a
pair of pants and a jacket does Juan have?
4. Area and other product-of-measures problems – the product is a
different type of unit from the other two factors.
 For example, length x width = area (usually square units.)
(adapted from Van De Walle)
Again, the next five weeks are dedicated to multiplication. Begin with
topic 6 – Multiplication meanings. Next introduce facts and strategies
using patterns using topics 7 – 9.
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 3
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Identify Patterns in Multiplication Facts

Use concrete objects, pictorial models, and technology to
identify patterns in multiplication facts.
Example:
Ms. Martin placed 4 vases on her desk. If there were 2 flowers in each
vase, how many flowers were there all together?
Possible Answer: There are four vases, and each vase has 2 flowers.
The number of flowers can be determined by 2 + 2 + 2 + 2 = 8 or
2  4 = 8.
Example:
Tamara purchased sheets of stickers for her sticker collection. Each
sheet had 7 stickers on it. What are the possible numbers that Tamara
could have said if she counted the stickers in groups of 7?
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 4
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Possible Answers: The answers are multiples of 7. Possible answers
are 7, 14, 21, 28 or 21, 28, 35, 42.
Example:
Ask the students, “What number sentence best represents the
arrangement of the objects?”
Answer: 4 × 7
Example:
Albert placed the pencils from his pencil box in the arrangement
shown below. How could you describe Albert’s pencil arrangement?
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 5
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Possible Answers:
2 groups of 5 pencils, 2 equal groups of pencils with 5 pencils in each
group, 2 rows and 5 columns, or 2 × 5
Example:
The pattern below shows a portion of the arrangement of stars in the
floor tiles in Sharice’s room. Describe the arrangement of stars on
Sharice’s floor tiles.
Possible Answers:
7 rows with 6 stars on each row,
6 columns with 7 stars in each column, 7 × 6, or 7 groups of 6 stars.
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 6
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Learn and Apply Multiplication Facts

Use concrete models to learn and apply multiplication
facts through 12 by 12.
Example:
Prompt the students to use concrete models such as color tiles
to represent the array 3  5. Prompt the students to multiply the
number of rows by the number of columns in order to determine
the value of the array.
Answer: 3 × 5 = 15

Describe a pictorial representation of a multiplication fact
with a number sentence.
Example:
Ask the students, “How can this representation of a
multiplication fact be described with a number sentence?”
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 7
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Answer: There are 3 equal groups of 4 butterflies for a total of
12 butterflies. 3  4 = 12.
Example:
While walking in the park, Jeremy saw 12 ladybugs. If each
ladybug has 6 legs, how many ladybug legs did Jeremy see?
Prompt the students to use concrete models such as counters to
solve the problem.
Answer: The product is 72.
6  12 = 72.
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 8
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Multiplication

Solve and record multiplication problems.
Example:
There are 8 spiders in a jar. If each spider has 8 legs, how many spider
legs are there all together?
Possible Solution Strategies:
Draw a picture, use concrete models, use repeated addition, or use
multiplication.
Answer: The product is 64. 8+8+8+8+8+8+8+8=64 or 8  8 = 64.
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 9
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Example:
James loads boxes on trucks for a shipping company. On Tuesday,
James loaded 5 trucks with 52 boxes in each truck. How many boxes
did James load on trucks on Tuesday?
Possible Solution Strategy:
Use base ten blocks in an area model.
Using partial products:
52
 5
10
+ 250
260
5  2 = 10
5  50 = 250
Answer: The product is 260.
52  5 = 260.

Solve multiplication problems.
Example:
Jacquelyn’s choir had 95 members. Each member sang 3 solos for
individual competitions during last month’s regional performance.
How many solos did Jacquelyn’s choir sing all together?
Understanding the Problem:

Ask the students, “What are you trying to find out?”
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 10
West-Orange Cove ISD

3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Ask the students to restate the problem.
Possible Answer: “We need to find out how many total solos were
sung by the 95 choir members.”
Making a Plan:
 Ask the students, “Are you joining equal sets or separating sets
of objects into equal groups?”
 Ask the students, “What is the important information in the
problem?”
Possible Answer: “We are joining equal sets, so we will multiply.
The important information in the question is the number of choir
members and the number of solos.”
Carrying out the Plan:
 Ask the students, “How did you solve the problem?”
Possible Answer: “We multiplied
95 by 3.”
Evaluating for Reasonableness:
 Ask the students, “How do you know your answer is
reasonable?”
Possible Answer: “We knew that each choir member sang 3 solos, and
there were 95 choir members. We estimated 95 as 100. So,
100 × 3 = 300 and 300 is close to 285. We multiplied 95 by 3 to get
our answer.”
Answer: 285 solos
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 11
3rd Grade Mathematics – 3rd Six Weeks
West-Orange Cove ISD
Week 4 - 6
Learning Standards
Major Concepts
4) Number, operation, and quantitative reasoning. The student
Dec 3 – 7
Dec 10 – 14
Dec 17 - 21
recognizes and solves problems in multiplication and division
situations. The student is expected to
(A) learn and apply multiplication facts through 12 by 12 using
[concrete] models [and objects];
(B) solve and record multiplication problems (up to two digits times
one digit); and
(C) use models to solve division problems and use number sentences
to record the solutions.
Division
Problem Solving
2012 - 2013
Processes:
 Problem Solving Model
 Thinking about learning and making
connections
 Use accountable talk by using the language of
mathematics
Instruction
Resources
Math Stations
Interventions/Extensions
Assessment
Key Vocabulary – division, dividend, division, quotient, array,
difference, fact family, factor, product
enVision Math -Topic 10
enVision Math
multiplication and division
games
enVision Math
Assessments
enVision Math Tools
Math background for the teacher:
 Multiplication and division have an inverse relationship.
 Every division fact has a related multiplication fact.
 Students can use near facts to solve problems.
 There are two concepts of division:
o The partition or fair sharing – Tom has 360 Pokeman
cards and he wants to share them equally with three
friends. How many cards will Tom and each of his three
friends have?
o The measurement or repeated subtraction – Spot’s master
has a bag of 125 dog treats. Spot loves his dog treats and
will do tricks to earn them. If spot’s master gives him 5
treats a day, how long will the bag of treats last?
 Students must learn to solve both types of problems but you should
start with the fair sharing because it is an easier concept for
students to grasp and have success.
 Fact families can be used to make connections to multiplication
and division.
Technology: Pearson enVision link
for animated introduction, journal
writing, and review – copy and paste
this link:
https://www.pearsonsuccessnet.com
http://express.smarttech.com/?url=http
://exchangedownloads.smarttech.com/p
ublic/content/e7/e70adfb2-a7b4-4ce2b83049a8103fa3db/Division%20Lesson.note
book#
Multiplication games using
dice or cards
Problem Solving – word
problems involving mixed
operations including
multiplication and division.
Journal writing – explain
how division is related to
multiplication
Number of the week
http://express.smarttech.com/?url=http
://exchangedownloads.smarttech.com/p
ublic/content/c1/c14097a3-4d76-4dc2a36c3ecb946abc66/Fact%20Family(41).note
book#
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Measurement Station
Page 12
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Interventions/Extensions
Products/project
Students will use
manipulatives to
demonstrate fair sharing
and repeated subtraction to
solve problems.
Students will work
in groups to create
and present visual
representations of
division problems
GT: Students will write a
letter to their grandmother
explaining how to multiply
and divide using their
favorite strategy.

Division with Models
Use models to solve division problems and use number
sentences to record the solutions.
Prompt the students to use concrete models or pictorial models to solve
division problems.
Example:
Andrea has a teddy bear collection with 15 teddy bears. She wants to
put her teddy bears in 3 baskets. If each basket has the same number
of teddy bears, how many will be in each basket?
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 13
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Possible Solution:
Answer: 15  3 = 5

Match a pictorial representation of a division situation
with a number sentence.
Prompt the students to write a division number sentence that represents
a model.
Example:
Possible Answer:
There are 25 stars in all. The 25 stars are divided into 5 equal groups.
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 14
3rd Grade Mathematics – 3rd Six Weeks
West-Orange Cove ISD
2012 - 2013
Answer: 25  5 = 5

Identify how repeated subtraction can be used to solve
division problems.
Prompt the students to discover patterns that show division as repeated
subtraction. (Relate division as repeated subtraction to multiplication
as repeated addition.)
Example:
Riley placed a plate of 12 cookies on his kitchen counter for his family
to share. Each family member took 4 cookies from the plate. There
were no cookies left over. How many family members took cookies
from the plate?
Perso
n1
124=8
Perso
n2
8-4=4
Perso
n3
4-4=0
1 2
- 4
Person 1
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 15
3rd Grade Mathematics – 3rd Six Weeks
West-Orange Cove ISD
2012 - 2013
8
- 4
Person 2
4
- 4
Person 3
0
4 was subtracted from 12 three times.
Answer: 12  4 = 3
Identify Patterns in Multiplication and Division Fact Families

Identify patterns in related multiplication and division number
sentences.
Prompt the students to describe the array in four different ways.
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 16
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Possible Answers:
 3 rows of 4 (3 x 4)
 4 columns of 3 (4 x 3)
 12 divided into 3 rows ( 12  3 )
 12 divided into 4 columns ( 12  4 )
Given the set of numbers, prompt the students to use the 3 digits to
create 2 multiplication number sentences and 2 division number
sentences that represent the fact family.
Answer:
4× 3 = 12
3× 4 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
Prompt the students to identify the number sentences that create a
multiplication and division fact family.
Example:
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 17
West-Orange Cove ISD
3rd Grade Mathematics – 3rd Six Weeks
2012 - 2013
Which set of number sentences identifies a multiplication and division
fact family?
Set A
Set B
Set C
Answer: Set A

Make generalizations from sets of examples and nonexamples
of related multiplication and division sentences.
Example:
What number sentence does NOT belong in the fact family?
Answer: 9  5 = 45
TEKS 3.14, 3.15, and 3.16 are incorporated into all concepts and taught every day
Page 18