Factors
Objectives To provide a review of the meanings of factor and
product;
and to provide opportunities to factor numbers and
p
apply multiplication facts.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Find all factors of a number. Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Beat the Calculator
(Extended-Facts Version)
• Write number models for rectangular
arrays. [Operations and Computation Goal 7]
Student Reference Book, p. 299
per partnership: 4 each of number
cards 1–10 (from the Everything Math
Deck, if available), calculator
Students practice and apply extended
multiplication facts.
Key Activities
Math Boxes 1 3
[Number and Numeration Goal 3]
• Solve and apply multiplication facts. [Operations and Computation Goal 2]
Students are introduced to a multiplication
facts routine. Students form rectangular
arrays, write number models for the arrays,
and list factor pairs for whole numbers.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 10. [Number and Numeration Goal 3]
Math Journal 1, p. 11
Students practice and maintain skills
through Math Box problems.
Study Link 1 3
Math Masters, p. 12
Students practice and maintain skills
through Study Link activities.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Factoring Numbers with Cube Arrays
Student Reference Book, p. 10
Math Masters, p. 13
centimeter cubes
Students build arrays for numbers with
centimeter cubes and record the factor pairs.
EXTRA PRACTICE
5-Minute Math
5-Minute Math™, pp. 13 and 90
Students factor whole numbers.
EXTRA PRACTICE
Practicing Multiplication Facts
Math Journal 1, p. 9
Math Masters, p. 11
Students use a multiplication facts routine.
Key Vocabulary
factor product factor pair
Materials
Math Journal 1, pp. 9 and 10
Study Link 12
Math Masters, p. 11
Class Data Pad 18 counters
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 143
Students add the terms factor, product, and
multiplication to their Math Word Banks.
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 79–83, 107–111, 267–271
Lesson 1 3
27
Mathematical Practices
SMP1, SMP2, SMP4, SMP5, SMP6
Content Standards
Getting Started
5.OA.2
Bold SMP = Guiding Questions at everydaymathonline.com
Mental Math and Reflexes
Math Message
Pose the following problems, and have students write
an expression for each. Students are not expected to
calculate the answers. Answers may vary.
Solve Problem 1 at the top of journal page 10.
Bold = Focus of lesson
Study Link 1 2 Follow-Up
The sum of 5 and 4 5 + 4
The product of 5 and 6 5 ∗ 6
Double 4 2 ∗ 4
Ask a volunteer to explain his or her solution
to Problem 2. Emphasize the use of
appropriate vocabulary.
Five times the sum of 2 and 3 5 ∗ (2 + 3)
Six times the sum of 5 and 2 6 ∗ (5 + 2)
Eight times the product of 3 and 2 8 ∗ (3 ∗ 2)
Double the sum of 5 and 4 2(5 + 4)
Triple the sum of 6 and 2 3 ∗ (6 + 2)
Add 4 and 3, and multiply the sum by 9 9(4 + 3)
Discuss the sample arrays and solicit possible grouping
categories for the Arrays Museum. Encourage students to provide
more examples.
1 Teaching the Lesson
NOTE Some students may benefit from
doing the Readiness activity before you begin
Part 1 of each lesson. See the Readiness
activity in Part 3 for details.
▶ Math Message Follow-Up
(Math Journal 1, p. 10)
WHOLE-CLASS
DISCUSSION
ELL
Have volunteers write their number models for 14 on the board.
Remind students that in a number model such as 3 ∗ 5 = 15 or
5 ∗ 3 = 15, the 3 and the 5 are called factors; and 15, the result
of multiplying, is called the product of 3 and 5. The factors 3 and
5 are a factor pair for the number 15. To support English
language learners, write a number model labeled with the terms
factor and product on the Class Data Pad. Also, discuss the
everyday and mathematical meanings of the words factor and
product.
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
Student Page
Date
LESSON
13
Time
Ask: What is another factor pair for 15? 1 and 15 The factors 1
and 15 are another factor pair for 15. For all numbers, 1 and n
are always factors of n. Are there other whole-number factor pairs
for 15? no
Multiplication Facts Master Lists
Make a check mark next to each fact you missed and need to study.
When you have learned a fact, write “OK” next to the check mark.
Multiplication Facts
3s
5s
7s
9s
3∗3
5∗3
7∗3
9∗3
3∗4
5∗4
7∗4
9∗4
3∗5
5∗5
7∗5
9∗5
3∗6
5∗6
7∗6
9∗6
3∗7
5∗7
7∗7
9∗7
3∗8
5∗8
7∗8
9∗8
3∗9
5∗9
7∗9
9∗9
7 ∗ 10
9 ∗ 10
▶ Introducing the Multiplication
Facts Routine
(Math Journal 1, p. 9; Math Masters, p. 11)
Multiplication Facts
4s
6s
8s
10s
4∗3
6∗3
8∗3
10 ∗ 3
4∗4
6∗4
8∗4
10 ∗ 4
4∗5
6∗5
8∗5
10 ∗ 5
4∗6
6∗6
8∗6
10 ∗ 6
4∗7
6∗7
8∗7
10 ∗ 7
4∗8
6∗8
8∗8
10 ∗ 8
4∗9
6∗9
8∗9
10 ∗ 9
6 ∗ 10
8 ∗ 10
10 ∗ 10
Math Journal 1, p. 9
EM3cuG5MJ1_U01_001-028.indd 9
28
1/11/11 11:30 AM
Unit 1
Number Theory
WHOLE-CLASS
ACTIVITY
The authors of Everyday Mathematics expect that most fifth-grade
students will have automaticity of the multiplication facts and are
building toward automatic recall of the extended facts. Facility
with extended facts is important because it provides powerful
mental arithmetic strategies that can be used when working
with large numbers. Mastery of the basic facts helps students
make quick estimates and compute with larger numbers. Use
the following facts routine to screen the class to determine which
students have automaticity with the basic multiplication facts.
Although multiplication facts will not be addressed in Part 1 of the
Teaching Master
remaining lessons, this routine may be used in Part 3 to continue
practice with multiplication facts. Achieving automatic recall of the
basic facts helps students to develop automaticity of the extended
multiplication facts. Use the following steps:
Name
13
A List
3. Students write their answers on their papers.
As students work with their facts, emphasize the turn-around rule
for multiplication to help them recognize the facts they already
know. Circle the problems on Math Masters, page 11 that are
missed most frequently so that you use them again for continued
practice.
B List
3 ∗ 6 = 18
6 ∗ 3 = 18
3 ∗ 7 = 21
7 ∗ 3 = 21
3 ∗ 8 = 24
8 ∗ 3 = 24
3 ∗ 9 = 27
9 ∗ 3 = 27
4 ∗ 6 = 24
6 ∗ 4 = 24
4 ∗ 7 = 28
7 ∗ 4 = 28
4 ∗ 8 = 32
8 ∗ 4 = 32
4 ∗ 9 = 36
9 ∗ 4 = 36
5 ∗ 7 = 35
7 ∗ 5 = 35
5 ∗ 9 = 45
9 ∗ 5 = 45
6 ∗ 6 = 36
6 ∗ 7 = 42
7 ∗ 6 = 42
6 ∗ 8 = 48
8 ∗ 6 = 48
6 ∗ 9 = 54
9 ∗ 6 = 54
7 ∗ 7 = 49
7 ∗ 8 = 56
8 ∗ 7 = 56
7 ∗ 9 = 63
9 ∗ 7 = 63
8 ∗ 8 = 64
8 ∗ 9 = 72
9 ∗ 8 = 72
9 ∗ 9 = 81
2. Dictate 10 problems from list A on Math Masters, page 11;
five problems from list B; and one problem from the bonus
problems. Repeat each problem only once. Proceed fairly
rapidly.
Time
Multiplication Facts
1. Have each student number a sheet of paper from 1 to 16.
4. Go over the problems, reading the answers. Students correct
any mistakes and record them by making check marks next
to the problems on the Master List on journal page 9. These
are the problems they will target to study in order to reach
automaticity. As students improve, they write “OK” next to
their check marks on journal page 9. Students who have not
reached automaticity for all of the facts should be encouraged
to use this list as a guide for continued study.
Date
LESSON
3 ∗ 3= 9
3 ∗ 4 = 12
4 ∗ 3 = 12
3 ∗ 5 = 15
5 ∗ 3 = 15
4 ∗ 4 = 16
4 ∗ 5 = 20
5 ∗ 4 = 20
5 ∗ 5 = 25
5 ∗ 6 = 30
6 ∗ 5 = 30
5 ∗ 8 = 40
8 ∗ 5 = 40
6 ∗ 10 = 60
10 ∗ 6 = 60
7 ∗ 10 = 70
10 ∗ 7 = 70
8 ∗ 10 = 80
10 ∗ 8 = 80
9 ∗ 10 = 90
10 ∗ 9 = 90
10 ∗ 10 = 100
Bonus Problems
11 ∗ 11 = 121
11 ∗ 12 = 132
5 ∗ 12 = 60
12 ∗ 6 = 72
7 ∗ 12 = 84
12 ∗ 8 = 96
9 ∗ 12 = 108
10 ∗ 12 = 120
5 ∗ 13 = 65
15 ∗ 7 = 105
12 ∗ 12 = 144
6 ∗ 14 = 84
Math Masters, p. 11
002-032_EMCS_B_MM_G5_U01_576973.indd 11
8/16/11 3:44 PM
NOTE Although a factor may be a whole
number, decimal, or fraction, Unit 1 deals with
whole-number factors only. The work with
factors in this unit involves basic multiplication
and division facts.
NOTE This facts routine will appear in Part 3 of Lessons 1-3, 1-5, and 1-9.
Adjusting the Activity
Prepare a written quiz or a transparency of the problems as an
alternative. With the transparency, you can use a sheet of paper to cover the
problems, uncovering them one at a time as you read.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Student Page
Date
Time
LESSON
Factor Pairs
13
▶ Finding Factor Pairs
(Math Journal 1, p. 10)
WHOLE-CLASS
ACTIVITY
Math Message
A 2-row-by-5-column array
2 ∗ 5 = 10
PROBLEM
PRO
PR
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
L
LV
VIN
V
IIN
NG
Factors
With the class, list all the whole-number factor pairs for the
number 18. Record the list on the board or on a transparency.
1 and 18, 2 and 9, 3 and 6 Remind students that each of the
turn-around facts uses only 2 factors. 1 ∗ 18 and 18 ∗ 1 use the
factors 1 and 18. If students have trouble finding factor pairs,
ask them to use counters to make all possible arrays for 18. Then
write a number model for each array. 1 ∗ 18 = 18, 18 ∗ 1 = 18,
2 ∗ 9 = 18, 9 ∗ 2 = 18, 3 ∗ 6 = 18, 6 ∗ 3 = 18
1. a.
b.
2 ∗ 5 = 10 is a number model for the 2-by-5 array.
10 is the product of 2 and 5.
2 and 5 are whole-number factors of 10.
2 and 5 are a factor pair for 10.
1 and 10 are also factors of 10 because 1 ∗ 10 = 10.
1 and 10 are another factor pair for 10.
Product
Use counters to make all possible arrays
for the number 14.
1 ∗ 14 = 14
Write a number model for each array
you make.
2 ∗ 7 = 14
1 ∗ 14 = 14, 14 ∗ 1 = 14,
2 ∗ 7 = 14, 7 ∗ 2 = 14
c.
7 ∗ 2 = 14
List all the whole-number factors of 14.
1, 2, 7, 14
14 ∗ 1 = 14
Write number models to help you find all the factors of each number below.
2.
Number
20
16
13
27
32
Number Models with 2 Factors
All Possible Factors
1 ∗ 20 = 20, 20 ∗ 1 = 20, 2 ∗ 10 = 20
1, 2, 4, 5, 10, 20
10 ∗ 2 = 20, 5 ∗ 4 = 20, 4 ∗ 5 = 20
1 ∗ 16 = 16, 16 ∗ 1 = 16, 4 ∗ 4 = 16
1, 2, 4, 8, 16
2 ∗ 8 = 16, 8 ∗ 2 = 16
1 ∗ 13 = 13, 13 ∗ 1 = 13
1, 13
1 ∗ 27 = 27, 27 ∗ 1 = 27
1, 3, 9, 27
3 ∗ 9 = 27, 9 ∗ 3 = 27
1 ∗ 32 = 32, 32 ∗ 1 = 32, 16 ∗ 2 = 32
1, 2, 4, 8, 16, 32
2 ∗ 16 = 32, 8 ∗ 4 = 32, 4 ∗ 8 = 32
10
Math Journal 1, p. 10
EM3cuG5MJ1_U01_001-028.indd 10
1/11/11 11:30 AM
Lesson 1 3
29
Student Page
Date
Time
LESSON
13
1.
Have students work independently to complete Problem 2 on
journal page 10. Encourage students to use their knowledge of the
multiplication facts to solve the problem.
Math Boxes
Where in the Student Reference Book
would you look to find the definition of
factor pair?
Fill in the circle next to the best answer.
A
Table of Contents
B
Index
C
Glossary
D
Whole Numbers Section
Write a 6-digit numeral with
4 in the hundreds place,
8 in the hundred-thousands place,
3 in the ones place,
and 7s in all other places.
2.
8 7 7,4 7 3
10
3.
28
List all the factors of 20.
Complete the
fact triangle.
4. a.
1, 2, 4, 5, 10, 20
5∗6
6∗5
30 / 5
30 / 6
12
Write a 7-digit numeral with
6.
6 in the ones place,
3 in the thousandths place,
1 in the thousands place,
2 in the tenths place,
and 0s in all other places.
*, /
6
[Number and Numeration Goal 3]
30
30
6
5
=
=
=
=
219 412
Add or subtract.
494
1,816
287
39 + 71 + 177 =
39,754
40,031 − 277 =
a.
67 + 109 + 318 =
b.
2,005 − 189 =
c.
1,0 0 6.2 0 3
5
Journal
Page 10
Problem 2
Use journal page 10, Problem 2 to assess students’ ability to identify factor
pairs. Students are making adequate progress if they have used factor pairs to
write correct multiplication number models for the numbers in this problem.
•
30
Write the fact
family for this
triangle.
b.
5.
Ongoing Assessment
Recognizing Student Achievement
d.
2 Ongoing Learning & Practice
4 27–31
▶ Playing Beat the Calculator
13–17
11
Math Journal 1, p. 11
EM3cuG5MJ1_U01_001-028.indd 11
PARTNER
ACTIVITY
(Extended-Facts Version)
1/11/11 11:30 AM
(Student Reference Book, p. 299)
Students practice multiplication of extended facts by playing Beat
the Calculator (Extended-Facts Version).
NOTE Use a permanent marker to change ordinary decks of playing cards so they
will have the same frequency of each number card as an Everything Math Deck.
• Mark each of the 4 aces with the number 1.
• Mark each of the 4 queens with the number 0.
• Mark the 4 jacks and the 4 kings with the numbers 11–18.
• Mark the 2 jokers with the numbers 19 and 20.
▶ Math Boxes 1 3
Study Link Master
Name
Date
STUDY LINK
13
(Math Journal 1, p. 11)
Time
Number Models for Arrays
Complete the chart. You will need to find each missing part and write it
in the correct space.
Array
INDEPENDENT
ACTIVITY
Number Model
10
Factors
Product
6, 4
24
2, 12
24
3, 8
24
1 ∗ 15 = 15;
15 = 1 ∗ 15
1, 15
15
5
3 ∗ 5 = 15;
5 ∗ 3 = 15
3, 5
15
6
1∗5=5
1, 5
5
24
1
6º4=
2
2 ∗ 12 = 24;
12 ∗ 2 = 24
3
3º8=
4
24
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 1-1. The skill in Problem 6
previews Unit 2 content.
Writing/Reasoning Have students write a response to the
following: Willa wrote the following true statements based
on the fact family she wrote for Problem 4: 30 is 5 times as
great as 6, and 30 is 6 times as great as 5. Write similar
statements for 7 ∗ 6 = 42. Sample answers: 42 is 7 times
as great as 6; 42 is 6 times as great as 7. The number that
is 6 times as great as 7 is 42.
▶ Study Link 1 3
INDEPENDENT
ACTIVITY
(Math Masters, p. 12)
Reminder: Look for examples of arrays and bring them to school.
Practice
7.
12 3 =
9.
307 ∗ 9 =
4
2,763
8.
10.
1,288 + 2,631 =
306 - 147 =
3,919
Home Connection Students match arrays, factor pairs,
and products. Encourage students to bring examples of
arrays to school.
159
Math Masters, p. 12
EM3cuG5MM_U01_002-032.indd 12
30
Unit 1
1/13/11 3:17 PM
Number Theory
3 Differentiation Options
READINESS
▶ Factoring Numbers
PARTNER
ACTIVITY
5–15 Min
with Cube Arrays
(Student Reference Book, p. 10; Math Masters, p. 13)
To provide experience finding factor pairs using concrete models,
have students build arrays with centimeter cubes. This activity
highlights the relationships between arrays, factor pairs, and all
possible factor pairs of a number.
EXTRA PRACTICE
▶ 5-Minute Math
SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience factoring whole numbers, see
5-Minute Math, pages 13 and 90.
EXTRA PRACTICE
▶ Practicing Multiplication Facts
SMALL-GROUP
ACTIVITY
5–15 Min
(Math Journal 1, p. 9; Math Masters, p. 11)
To provide additional practice with basic multiplication facts,
have students use the facts routine introduced in Lesson 1-3. See
Teacher’s Lesson Guide, pages 28 and 29 to review the procedure.
ELL SUPPORT
▶ Building a Math Word Bank
SMALL-GROUP
ACTIVITY
5–15 Min
Teaching Master
Name
Time
Factoring Numbers with Cube Arrays
13
䉬
(Differentiation Handbook, p. 143)
To provide language support for multiplication, have students
use the Word Bank Template found on Differentiation Handbook,
page 143. Ask students to write the terms factor, product, and
multiplication, draw pictures relating to each term, and write
other related words. See the Differentiation Handbook for more
information.
Date
LESSON
Use centimeter cubes to build arrays for the following numbers. With each array
write the factor pair. Remember that the number of rows in the array is one
factor and that the number of columns in the array is the other factor.
10
Continue to build every possible array until you have all of the factors for the number.
1.
14
Factors:
3.
5.
4.
20
1, 10, 2, 5
Factors:
1, 8, 2, 4
1, 20, 2, 10, 4, 5
33
Factors:
6.
8
Factors:
10
Factors:
2.
1, 14, 2, 7
1, 33, 3, 11
Can you tell when you have all of the factors for a number before you have built every
possible array?
Yes
Explain.
Answers vary.
Try This
7.
Write three true statements about factors.
Answers vary.
Math Masters, p. 13
Lesson 1 3
31
Name
LESSON
13
Date
Multiplication Facts
Copyright © Wright Group/McGraw-Hill
A List
3 ∗ 6 = 18
6 ∗ 3 = 18
3 ∗ 7 = 21
7 ∗ 3 = 21
3 ∗ 8 = 24
8 ∗ 3 = 24
3 ∗ 9 = 27
9 ∗ 3 = 27
4 ∗ 6 = 24
6 ∗ 4 = 24
4 ∗ 7 = 28
7 ∗ 4 = 28
4 ∗ 8 = 32
8 ∗ 4 = 32
4 ∗ 9 = 36
9 ∗ 4 = 36
5 ∗ 7 = 35
7 ∗ 5 = 35
5 ∗ 9 = 45
9 ∗ 5 = 45
6 ∗ 6 = 36
6 ∗ 7 = 42
7 ∗ 6 = 42
6 ∗ 8 = 48
8 ∗ 6 = 48
6 ∗ 9 = 54
9 ∗ 6 = 54
7 ∗ 7 = 49
7 ∗ 8 = 56
8 ∗ 7 = 56
7 ∗ 9 = 63
9 ∗ 7 = 63
8 ∗ 8 = 64
8 ∗ 9 = 72
9 ∗ 8 = 72
9 ∗ 9 = 81
Time
B List
3 ∗ 3= 9
3 ∗ 4 = 12
4 ∗ 3 = 12
3 ∗ 5 = 15
5 ∗ 3 = 15
4 ∗ 4 = 16
4 ∗ 5 = 20
5 ∗ 4 = 20
5 ∗ 5 = 25
5 ∗ 6 = 30
6 ∗ 5 = 30
5 ∗ 8 = 40
8 ∗ 5 = 40
6 ∗ 10 = 60
10 ∗ 6 = 60
7 ∗ 10 = 70
10 ∗ 7 = 70
8 ∗ 10 = 80
10 ∗ 8 = 80
9 ∗ 10 = 90
10 ∗ 9 = 90
10 ∗ 10 = 100
Bonus Problems
11 ∗ 11 = 121
11 ∗ 12 = 132
5 ∗ 12 = 60
12 ∗ 6 = 72
7 ∗ 12 = 84
12 ∗ 8 = 96
9 ∗ 12 = 108
10 ∗ 12 = 120
5 ∗ 13 = 65
15 ∗ 7 = 105
12 ∗ 12 = 144
6 ∗ 14 = 84
11