Product Sample
For questions or more information, contact: Cambium Learning Voyager
17855 Dallas Parkway, Ste. 400 │ Dallas, TX 75287 1‐888‐399‐1995 www.voyagerlearning.com Objective 1
Concept Development
Activities
CD 1
Finding Sets of Factors of Numbers
Use with 5-Day or 3-Day Instructional Plan. In this
activity, students review the definition of a factor and
find the greatest common factor of each pair of integers.
DIRECTIONS
4.Repeat this process for several number pairs. Ask
individual students to list the factors and name the
GCF for each pair.
Sample problems:
8 and 12
8 1, 2, 4, 8
1.Discuss the following terms with students:
12 1, 2, 3, 4, 6, 12
factor A monomial that evenly divides a value
Common factors: 1, 2, 4
g reatest common factor (GCF) The largest
factor that a set of monomials has in common
GCF: 4
2.Have students name the factors of two different
numbers. List the factors on the board as students
name them.
Examples:
10 1, 2, 5, 10
14 1, 2, 7, 14
3.Use the same numbers, and ask students to identify
the common factors of those numbers. Tell students
to identify the largest common factor. Remind
students that the largest common factor is called
the greatest common factor.
Example:
10 and 14
Common factors: 1, 2
GCF: 2
6 and 9
6 1, 2, 3, 6
9 1, 3, 9
Common factors: 1, 3
GCF: 3
18 and 27
18 1, 2, 3, 6, 9, 18
27 1, 3, 9, 27
Common factors: 1, 3, 9
GCF: 9
20 and 30
20 1, 2, 4, 5, 10, 20
30 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2, 5, 10
GCF: 10
16 and 36
16 1, 2, 4, 8, 16
36 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 4
GCF: 4
772
Chapter 9 • Objective 1
5.Review with students how to find the prime factors
of the number 10, which are the prime numbers that
when multiplied together yield 10. Remind students
that they do not need to use 1 because any number
multiplied by 1 yields the same number. 2 • 5
10
Examples:
6 and 9
6=2•3
9=3•3
Common prime factors: 3
2
GCF: 3
5
18 and 27
Repeat with 14. 2 • 7
18 = 2 • 3 • 3
14
27 = 3 • 3 • 3
2
Common prime factors: 3 • 3
7
Point out that the prime factors of 10 and the prime
factors of 14 have the number 2 in common. Point
out that this is the GCF of 10 and 14.
6.Have students look at a number pair they worked
with in Step 4. Tell them to use the common prime
factors of the numbers to find the GCF of the
number pair. Have students compare this answer
to their answers in Step 4.
Example:
20 and 30
20 = 2 • 2 • 5
30 = 2 • 3 • 5
Common prime factors: 2 • 5
GCF: 10
16 and 36
16 = 2 • 2 • 2 • 2
8 and 12
36 = 2 • 2 • 3 • 3
8
2
GCF: 9
Common prime factors: 2 • 2
12
4
2
2 2
6
GCF: 4
2 3
8=2•2•2
12 = 2 • 2 • 3
Common factors: 2 • 2
GCF: 4
7.Repeat this process with the other problems used
in Step 4. Have students compare the GCFs to the
ones they found originally.
NEXT STEPS • Differentiate
5-Day Instructional Plan:
PA 1, page 776—All students, for additional
practice and problem solving
3-Day Instructional Plan:
CD 2, page 774—Students who demonstrate
understanding of the concept, for additional
concept development
PA 2, page 777—Students who need additional
practice
Chapter 9 • Objective 1
773
Objective 1
Concept Development
Activities
Finding the Greatest Common
Factor of Variables
CD 2
Use with 5-Day or 3-Day Instructional Plan. In this
activity, students find the GCF of expressions with
multiple variables.
DIRECTIONS
5. Repeat the process using more pairs of expressions.
Sample problems:
abc and a 2b ab
ab 2c 3 and a 2bc 2 abc 2
x 2y and xy 3 xy
x 2y 2z 2 and x 2yz 3 x 2yz 2
1.Review the following terms with students:
factor A monomial that evenly divides a value
g reatest common factor (GCF) The largest
factor that a set of monomials has in common
2.Review with students how to find the GCF of number
pairs. Answer any questions about this process.
18 and 24
18 = 2 • 3 • 3; or 2 • 3 2
24 = 2 • 2 • 2 • 3; or 2 3 • 3
Common prime factors: 2 • 3
GCF: 6
3.Introduce variables by letting 2 be a and 3 be b.
Demonstrate how to substitute the variables for
the numbers with the prime factors of 18 and 24.
18 and 24
18 = a • b • b; or a • b 2
24 = a • a • a • b; or a 3 • b
Common prime factors: a • b
GCF: ab
4.Write ab 2c 2 and a 2b 3c on the board. Tell students
to find the GCF. Students may need to write each
expression in the complete factored form.
ab 2c 2 and a 2b 3c
ab 2c 2 = a • b • b • c • c
a 2b 3c = a • a • b • b • b • c
Common prime factors: a • b • b • c
GCF: ab 2c
774
Chapter 9 • Objective 1
NEXT STEPS • Differentiate
5-Day Instructional Plan:
PA 3, page 778—All students, for additional
practice
3-Day Instructional Plan:
PM 3, page 782—Students who are on the
accelerated path, to assess progress
PA 3, page 778—Students who are on the
differentiated path, for additional practice
Objective 1
Concept Development
Activities
Working With Numbers and
Variables
CD 3
6.Have students find the GCF for more pairs of
expressions on their own.
Sample problems:
Use with 5-Day Instructional Plan. In this activity, students
find the GCF of expressions containing numbers and
multiple variables.
6x 2y 3 and 15xy 2
DIRECTIONS
Common Prime Factors = 3 • x • y • y
1.Review the following term with students:
factor A monomial that evenly divides a value
2.Review with students how to find the GCF of number
pairs. Answer any questions about this process.
8 and 12
8 = 2 • 2 • 2; 2 3
12 = 2 • 2 • 3; 2 2 • 3
Common prime factors: 2 • 2
GCF: 4
3.Review the process for finding the GCF of a 2b and
ab 2. ab
4.Tell students to find the GCF for 8a 2b and 12ab 2. If
students have difficulty, remind them that the GCF
for 8 and 12 is 4 and the GCF for a 2b and ab 2 is ab.
8a 2b and 12ab 2
8a 2b = 2 • 2 • 2 • a • a • b
12ab 2 = 2 • 2 • 3 • a • b • b
Common prime factors: 2 • 2 • a • b
GCF: 4ab
6x 2y 3 = 2 • 3 • x • x • y • y • y
15xy 2 = 3 • 5 • x • y • y
GCF: 3xy 2
18ab 2c and 24a 2b 3
18ab 2c = 2 • 3 • 3 • a • b • b • c
24a 2b 3 = 2 • 2 • 2 • 3 • a • a • b • b • b
Common Prime Factors = 2 • 3 • a • b • b
GCF: 6ab 2
NEXT STEPS • Differentiate
5-Day Instructional Plan:
PM 3, page 782—All students, to assess progress
5.Write 16a 2b 3 and 36a 2b 2 on the board. Tell
students to find the GCF for these expressions.
Review the complete factored forms of each.
16a 2b 3 and 36a 2b 2
16a 2b 3 = 2 • 2 • 2 • 2 • a • a • b • b • b
36a 2b 2 = 2 • 2 • 3 • 3 • a • a • b • b
Common prime factors: 2 • 2 • a • a • b • b
GCF: 4a 2b 2
Chapter 9 • Objective 1
775
Objective 1
Practice
Activities
★ PA
1
Factoring 12
Use with 5-Day Instructional Plan. In this activity,
students memorize the factors of 12.
MATERIALS
• Blank cards, 48 per group
Directions
1. Review the following term with students:
factor A monomial that evenly divides a value
2.Organize students into groups of four, and distribute
48 blank cards to each group.
3.Have groups split the cards into four groups of 12
cards each. Tell students to number each set of
their blank cards from 1 to 12 (one number per card).
In their deck of 48 cards, they should have four sets
of cards numbered from 1 to 12. Have a member of
each group shuffle the deck.
4.Explain the game rules to students.
•Each group chooses one student to deal five
cards to each student in the group facedown,
as if playing rummy. Each student holds his
or her hand of five cards.
•The remaining cards are placed in a stack, facedown, and the top card is turned over and
placed next to the deck as a discard pile.
•The dealer is the first player.
•On each player’s turn, he or she can either take
the faceup card or draw one card from the top
of the facedown deck. After drawing a card, the
player must discard one card from his or her hand
and place it faceup on the discard pile.
•The object is to end up with a hand of five cards
that are all factors of 12.
•The process continues until a player can discard
one card and have left in his or her hand five
cards, all with numbers that are factors of 12.
That student is the winner.
★ = Includes Problem Solving
776
Chapter 9 • Objective 1
5.Repeat the game using 18 or 24 as the factor
number. Discuss which number makes the game
better, and why.
NEXT STEPS • Differentiate
5-Day Instructional Plan:
PM 1, page 780—All students, to assess progress
Objective 1
Practice
Activities
PA 2
Using Prime Factors
Use with 5-Day or 3-Day Instructional Plan. In this
activity, students find the GCF of a set of numbers.
MATERIALS
• Blackline Master 100
Name _______________________________________________________ Date __________________
100
NUMBER CHART
12 24 18 52 36 30
10 40 9 22 15 30
48 20 38 51 21 26
• Game markers to cover squares
32 14 27 4 55 8
Directions
56 54 6 34 45 42
1. Review the following term with students:
factor A monomial that evenly divides a value
2.Organize students into groups of four. Give one
copy of Blackline Master 100, Number Chart, to
each group.
3.Have each student in the group write a number from
the Number Chart on his or her own paper and put
a marker on that number on Blackline Master 100
so it can’t be used again.
4.Discuss the following term with students:
p rime factorization The prime numbers and/or
variables whose product is the desired expression,
or the process of obtaining those values
5.Instruct students to complete the prime
factorization for the number they selected.
6.Have students in each group write all their
completed prime factorizations on one piece
of paper so they may look at them all at once
to make comparisons.
7.Have each group decide which numbers appear
in all the lists. Instruct groups to write the new
combination of numbers that all the lists have in
common. Remind students that if a number appears
more than once in all their lists, it should be
included in their new list more than once also (one
time for each time it appears in all their lists).
8.Explain that the new list of numbers will be the
factors of the GCF from all their original lists. Have
students in each group multiply the numbers in their
new list. Remind them that the product is the GCF of
the original four numbers they selected.
44 60 16 58 28 50
Copyright 2011 Cambium Learning Sopris West®. All rights reserved. Permission
is granted to reproduce this page for student use.
Inside Algebra • Blackline Master
100
9.Instruct each student to check to see if the group’s
GCF is correct by dividing his or her original
number by the group’s GCF. If the GCF divides into
all the group members’ original numbers evenly
and if no factors were missed, then the group
has successfully found the GCF of all the original
numbers. If they missed factors, they have a
common factor, but not the GCF.
10.Have the groups repeat this activity with four new
numbers from the Number Chart as often as time
allows.
NEXT STEPS • Differentiate
5-Day Instructional Plan:
CD 2, page 774—All students, for additional
concept development
3-Day Instructional Plan:
PM 1, page 780—All students, to assess progress
Chapter 9 • Objective 1
777
Objective 1
Practice
Activities
PA 3
Factoring With Variables
Use with 5-Day or 3-Day Instructional Plan. In this
activity, students find the GCF of each pair of monomials.
MATERIALS
• Blackline Master 101
• Dice (different colors may be helpful)
Directions
1.Organize students into groups of three. Give a
pair of dice and one copy of Blackline Master 101,
Monomial Table, to each group.
2. Explain the game rules to students.
•The monomial table is read like a graph. The first
component is read on the horizontal axis and the
second component is read on the vertical axis. If
dice of two different colors are used, the different
colors can be used for the labels of the axes.
•One student in each group rolls the dice and
forms two ordered pairs from the numbers rolled.
Example:
If the roll is a 2 and a 4,
the ordered pairs are (2, 4) and (4, 2).
If the roll is a 3 and a 3,
the ordered pairs are (3, 3) and (3, 3).
•The student writes the monomials that are in the
squares on Blackline Master 99 that correspond
to the roll. He or she then finds the GCF.
Example:
The monomial for (2, 4) is 3a 3bc 3 ;
the monomial for (4, 2) is 6a 3b 2.
GCF: 3a 3b
•The other two students in the group check the
work. If it is correct, the student gets a point.
Name _______________________________________________________ Date __________________
101
M O N O MI A L TA BL E
6
12a 4b 2c 2
30a 3bc 4
4a 2b 3c 4
8a 2b 2
6a 4bc 2
29ab 3c
5
6ab 2c 2
20a 2b 2c
14a 2b 2c 2
12a 3b 5c 2
2a 3b 5c 7
9a 2b 3c 2
4
18a 2b 4c 2
3a 3bc 3
9a 2b 4
27
32a 2b 8c 3
3abc
3
12a 4b 3c 2
9a 2b 4c 2
5a 2
12ab 3c 2
4a 3bc 4
10a 3b 2c 2
2
15a 2b 2c 2
11a 2b 2c 2
6ab 2c 2
6a 3b 2
8a 3bc 3
24a 4b 5c 9
1
7a 3bc
18a 2b 5c3
20a 3b 2c 3
24ab 3c 3
8a 3bc3
2a 2bc3
1
2
3
4
5
6
Copyright 2011 Cambium Learning Sopris West®. All rights reserved. Permission
is granted to reproduce this page for student use.
Example:
Inside Algebra • Blackline Master
101
If 3 and 3 are rolled, then (3, 3) and (3, 3)
are the ordered pairs.
The monomials are 5a 2 and 5a 2 .
GCF: 5a 2
3.Have students play until time expires or a certain
score is reached, such as 20 points.
4.At the end of the activity, have students turn in their
papers with the monomials and the GCFs.
NEXT STEPS • Differentiate
5-Day Instructional Plan:
PM 2, page 781—Students who are on the
accelerated path, to assess progress
C
D 3, page 775—Students who are on the
differentiated path, for additional concept
development
•The three students take turns rolling the dice
and naming the GCF for the pair of monomials.
3-Day Instructional Plan:
PS 1, page 783—Students who are on the
accelerated path, to develop problem-solving skills
•If a double is rolled, the ordered pairs are
identical, and the monomials are identical.
P
M 2, page 781—Students who are on the
differentiated path, to assess progress
778
Chapter 9 • Objective 1
Objective 1
Practice
Activities
PA 4
Using Candy to Find the GCF
Use with 5-Day Instructional Plan. In this activity,
students factor the GCF from a set of different terms.
MATERIALS
• A large bag of candies of different colors
Directions
1. Review the following term with students:
factor A monomial that evenly divides a value
2.Randomly divide students into groups of five. Give
each group an equal amount of candies of different
colors (at least 20 per group).
3.Have students group their candies by color, and
have them determine how many of each color they
have; for example, 5 red, 3 orange, 4 green, 4 yellow,
and 5 blue.
4.Tell students to assign each color with a letter and
write their data as an expression; for example,
5r3o4g4y5b.
5.Have one member of each group write the group’s
expression on the board, one next to another. Place
a plus symbol between each combination. Explain
that the total will represent the total number of
candies in the class.
6.Tell groups to determine the GCF for the
expressions on the board.
7.Walk around the room to observe the groups. When
a group appears to have an answer, ask the group to
select a member to write the answer on the board.
8.Have students discuss whether they agree with the
GCF that group found. If students do not agree, have
the class discuss what the correct GCF is. Students
should be able to prove their answers to the class.
9.When the class agrees on the GCF, ask the groups
to remove that combination of colored candies
from their pile of candies and to write a term that
represents their group of leftover candies.
10.Place an open parenthesis just to the right of the
agreed-upon GCF on the board. Once the groups
have determined their leftover combinations, ask
another member of each group to write the group’s
new expression, one next to another, to the right of
the parenthesis on the board. Have students leave
enough room to write a plus symbol between each
expression. Explain to the class that again the plus
symbols are needed so the total represents the total
number of candies.
11.Close the parentheses when all the groups’
new combinations are written in the expression
on the board.
12.Explain to the class that what they just did was
factor out a GCF based on color for the entire set of
candies. Reaffirm with students that this is really
just the Distributive Property performed backward
and that this process is called factoring out the GCF
from a set of different given terms.
13.Let students in each group divide their candies evenly
among the members of the group and consume.
14.As an extension of this activity, have the class
graph the data according to colors. You may also
review the probability of drawing one particular
color from the bag.
NEXT STEPS • Differentiate
5-Day Instructional Plan:
PM 3, page 782—All students, to assess progress
Chapter 9 • Objective 1
779
Progress-Monitoring
Activities
A p p ly S k i l l S 1
Find both the common factors and the greatest common factor (GCF) using
prime factorization.
1.
Numbers
Prime Factorization
Common Factors
PM 1
2.
3.
DIRECTIONS
PA 2, page 777—Students who need additional
practice
3-Day Instructional Plan:
CD 2, page 774—All students, for additional
concept development
780
Chapter 9 • Objective 1
Numbers
Prime Factorization
Numbers
Prime Factorization
Common Factors
2 • 3 • 3 = 2 • 32
20
2 • 2 • 5 = 22 • 5
45
3•3•5
GCF
1.Have students turn to Interactive Text, page 337,
Apply Skills 1.
5-Day Instructional Plan:
CD 2, page 774—Students who demonstrate
understanding of the concept, for additional
concept development
18
GCF
4.
NEXT STEPS • Differentiate
Prime Factorization
Common Factors
• Interactive Text, page 337
•Do students correctly find the prime factorization?
2•3•4
GCF
MATERIALS
5.
Numbers
Prime Factorization
Common Factors
GCF
Copyright 2011 Cambium Learning Sopris West.® All rights reserved.
Watch for:
•Do students understand why the number 1
is not a prime number?
Numbers
Common Factors
Use with 5-Day or 3-Day Instructional Plan.
3.Monitor student work, and provide feedback as
necessary.
24
GCF
Apply Skills 1
2.Remind students of the key terms: prime
factorization and greatest common factor (GCF).
progress moNitoriNg
Name __________________________________________ Date __________________________
Objective 1
6.
Numbers
Prime Factorization
Common Factors
60
Expressions
Common Factors
GCF
Inside Algebra
2•3
6
44
2 • 2 • 11 = 22 • 11
2
2
36
2 • 2 • 3 • 3 = 22 • 32
2
4
2
30
2•3•5
3•5
15
90
2 • 2 • 3 • 5 = 22 • 3 • 5 2 • 3 • 3 • 5 =
2•3•5
30
16
2 • 2 • 2 • 2 = 24
GCF
7.
30
2•3•5
a 2b
15
3•5
none
1
abc
ab
ab
Chapter 9 • Objective 1 • PM 1
337
progress moNitoriNg
Objective 1
Progress-Monitoring
Activities
PM 2
Apply Skills 2
Use with 5-Day or 3-Day Instructional Plan.
MATERIALS
• Interactive Text, pages 338–339
DIRECTIONS
1.Have students turn to Interactive Text, pages
338–339, Apply Skills 2.
A p p ly S k i l l S 2
Find the greatest common factor (GCF) of each pair of numbers.
Example:
3x 2y
12x 2y 3 and 9x 3y
2•2
GCF: 3 • x • x • y
6
42: 2 • 3 • 7
36: 2 • 2 • 3 • 3
GCF: 2 • 3
12
12: 2 • 2 • 3
60: 2 • 2 • 3 • 5
GCF: 2 • 2 • 3
1. 42 and 36
3. 9 and 30
9: 3 • 3
30: 2 • 3 • 5
GCF: 3
2. 12 and 60
3
4. 45 and 75
45: 3 • 3 • 5
75: 3 • 5 • 5
GCF: 3 • 5
27
27: 3 • 3 • 3
54: 2 • 3 • 3 • 3
GCF: 3 • 3 • 3
6. a 3b 2 and a 4b 5
xy 4
xy 4: x • y • y • y • y
x 2y 5: x • x • y • y • y • y • y
GCF: x • y • y • y • y
338
Chapter 9
•
15
a 3b 2
a 3b 2: a • a • a • b • b
a 4b 5: a • a • a • a • b • b •
b•b•b
GCF: a • a • a • b • b
5. 27 and 54
7. xy 4 and x 2y 5
Objective 1 • PM 2
4
4
m n
8. m 5n 4 and m 4n 6
m 5n 4: m • m • m • m •
n•n•n•n
m 4n 6: m • m • m • m •
n•n•n•n•n
m•
n•
GCF: m • m • m • m • n •
n•n•n
Inside Algebra
Name __________________________________________ Date __________________________
A p p ly S k i l l S 2
(continued )
5-Day Instructional Plan:
PA 4, page 779—All students, for additional
practice
10. m 3np 3 and m 2n 2p 2
a 3b 4c
a 6b 4c 3: a • a • a • a • a • a •
b•b•b•b•c•c•c
a 3b 5c: a • a • a • b • b • b • b •
b•c
GCF: a • a • a • b • b • b • b • c
12. a 3b 4 and a 2b 6
xy 3
x 4y 3: x • x • x • x • y • y • y
x 2y 5: x • x • y • y • y • y • y
xy 5: x • y • y • y • y • y
GCF: x • y • y • y
14. 12, 24, and 30
11. a 6b 4c 3 and a 3b 5c
3-Day Instructional Plan:
PM 3, page 782—All students, to assess progress
m 2np 2
m 3np 3: m • m • m • n • p •
p•p
m 2n 2p 2: m • m • n • n • p • p
GCF:
m•m•n•p•p
a 4b 4
a 6b 4: a • a • a • a • a • a • b •
b•b•b
a 4b 7: a • a • a • a • b • b • b •
b•b•b•b
GCF: a • a • a • a • b • b • b • b
9. a 6b 4 and a 4b 7
NEXT STEPS • Differentiate
13. x 4y 3, x 2y 5, and xy 5
a 2b 4
a 3b 4: a • a • a • b • b • b • b
a 2b 6: a • a • b • b • b • b •
b•b
GCF: a • a • b • b • b • b
12: 2 • 2 • 3
24: 2 • 2 • 2 • 3
30: 2 • 3 • 5
GCF: 2 • 3
6
16
32: 2 • 2 • 2 • 2 • 2
48: 2 • 2 • 2 • 2 • 3
64: 2 • 2 • 2 • 2 • 2 • 2
GCF: 2 • 2 • 2 • 2
Copyright 2011 Cambium Learning Sopris West.® All rights reserved.
15. 32, 48, and 64
Inside Algebra
Chapter 9 • Objective 1 • PM 2
progress moNitoriNg
•Do students realize that one of the numbers
being compared may be the GCF?
3•3•x•x•x•y
3•2•2•x•x•y•y•y
3.Monitor student work, and provide feedback as
necessary.
Watch for:
•Do students use factor trees to find the prime
factors?
9x 3y
12x 2y 3
3•4•x•x•y•y•y
339
Chapter 9 • Objective 1
781
Copyright 2011 Cambium Learning Sopris West.® All rights reserved.
2.Remind students of the key term: greatest common
factor (GCF).
Name __________________________________________ Date __________________________
Progress-Monitoring
Activities
PM 3
Name __________________________________________ Date __________________________
progress moNitoriNg
Objective 1
Apply Skills 3
Use with 5-Day or 3-Day Instructional Plan.
MATERIALS
• Interactive Text, pages 340–341
DIRECTIONS
1.Have students turn to Interactive Text, pages
340–341, Apply Skills 3.
Find the greatest common factor (GCF) of each pair of numbers.
Example:
18a 3b 4 and 24a 2b 5
18a 3b 4
GCF: 2 • 3 • a • a • b • b • b • b = 6a 2b 4
1.
2.
x 2y
x 5y 4: x • x • x • x • x • y • y • y • y
x 2y: x • x • y
x 5y 4 and x 2y
m 2n 4
m 2n 4: m • m • n • n • n • n
m 4n 6: m • m • m • m • n • n • n • n • n • n
4.
c 6d 3 and c 3d 5
5.
m 5n 7 and m 4n
c 3d 3
c 6d 3: c • c • c • c • c • c • d • d • d
c 3d 5: c • c • c • d • d • d • d • d
m 4n
m 5n 7: m • m • m • m • m • n • n • n • n • n • n • n
m 4n: m • m • m • m • n
3ab 3
6ab 4: 2 • 3 • a • b • b • b • b
9a 3b 3: 3 • 3 • a • a • a • b • b • b
6ab 4 and 9a 3b 3
5x 2y 6
10x 3y 6: 2 • 5 • x • x • x • y • y • y • y • y • y
25x 2y 8: 5 • 5 • x • x • y • y • y • y • y • y • y • y
10x 3y 6 and 25x 2y 8
Chapter 9
•
Objective 1 • PM 3
Inside Algebra
A p p ly S k i l l S 3
progress moNitoriNg
Name __________________________________________ Date __________________________
NEXT STEPS • Differentiate
(continued )
4a 3b 2
2•2•a•a•a•b•b
20a 4b 5: 2 • 2 • 5 • a • a • a • a • b • b • b • b • b
8. 32a b and 20a b
32a 3b 2: 2 • 2 • 2 •
3
5-Day Instructional Plan:
PS 1, page 783—All students, to develop problemsolving skills
9.
3-Day Instructional Plan:
PA 3, page 778—Students who are on the
accelerated path, for additional practice
2
4
5
9st 2
27s 3t 4: 3 • 3 • 3 • s • s • s • t • t • t • t
18st 2: 2 • 3 • 3 • s • t • t
27s 3t 4 and 18st 2
10. 48m 2n 2p 3 and 60m 4n 5p 2 12m n p
48m 2n 2p 3: 2 • 2 • 2 • 2 • 3 • m • m • n • n • p • p • p
60m 4n 5p 2: 2 • 2 • 3 • 5 • m • m • m • m • n • n • n • n •
2
Objective 1 Posttest, page 785—Students who are
on the differentiated path
11.
12.
Copyright 2011 Cambium Learning Sopris West.® All rights reserved.
13.
Chapter 9 • Objective 1
a 4b 3
a 7b 4: a • a • a • a • a • a • a • b • b • b • b
a 4b 3: a • a • a • a • b • b • b
m 2n 4 and m 4n 6
340
2•3
2•2•2•3•a•a•b•b•b•b•b
a 7b 4 and a 4b 3
3.
7.
Watch for:
•Do students recognize that variables are
treated the same way as prime factors?
782
2•6
3•3•2•a•a•a•b•b•b•b
3.Monitor student work, and provide feedback as
necessary.
2 • 12 • a • a • b • b • b • b • b
3•3
6.
•Do students compare each factor separately?
24a 2b 5
9•2•a•a•a•b•b•b•b
14.
15.
2
2
n•p•p
3ab 2
6ab 2: 3 • 2 • a • b • b
15a 2b 2: 3 • 5 • a • a • b • b
21a 3b 4: 3 • 7 • a • a • a • b • b • b • b
6ab 2, 15a 2b 2, and 21a 3b 4
8xy 3z
16x 3y 6z: 2 • 2 • 2 • 2 • x • x • x • y • y • y • y • y • y • z
2 8 2
24x y z : 2 • 2 • 2 • 3 • x • x • y • y • y • y • y • y • y • y • z • z
32xy 3z: 2 • 2 • 2 • 2 • 2 • x • y • y • y • z
16x 3y 6z, 24x 2y 8z 2, and 32xy 3z
2m 2np 2
26m 2n 2p 3: 2 • 13 • m • m • n • n • p • p • p
12m 2np 2: 2 • 2 • 3 • m • m • n • p • p
18m 3n 2p 3: 2 • 3 • 3 • m • m • m • n • n • p • p • p
26m 2n 2p 3, 12m 2np 2, and 18m 3n 2p 3
2ab 2
8ab 2: 2 • 2 • 2 • a • b • b
2 2
16a b : 2 • 2 • 2 • 2 • a • a • b • b
22a 3b 4: 2 • 11 • a • a • a • b • b • b • b
30a 3b 2: 2 • 3 • 5 • a • a • a • b • b
5xy 3
15x 3y 6z, 45x 2y 8z, 90xy 3z, and 25x 2y 8
15x 3y 6z: 3 • 5 • x • x • x • y • y • y • y • y • y • z
45x 2y 8z: 3 • 3 • 5 • x • x • y • y • y • y • y • y • y • y • z
90xy 3z: 2 • 3 • 3 • 5 • x • y • y • y • z
25x 2y 8: 5 • 5 • x • x • y • y • y • y • y • y • y • y
8ab 2, 16a 2b 2, 22a 3b 4, and 30a 3b 2
Inside Algebra
Chapter 9 • Objective 1 • PM 3
341
Copyright 2011 Cambium Learning Sopris West.® All rights reserved.
2.Remind students of the key term: greatest common
factor (GCF).
A p p ly S k i l l S 3
Objective 1
Problem-Solving
Activity
★ PS
1
Using the Machine
Use with 5-Day or 3-Day Instructional Plan. In this
activity, students find the GCF of each pair of monomials
and understand that some monomials have a GCF of 1.
6.Give students pairs of inputs with variables,
and instruct them to find the out values. Discuss
the results.
Sample problems:
in = a 2b and ab 2 out = ab
DIRECTIONS
in = a 3b 3 and ab 2 out = ab 2
1. Review the following term with students:
in = 6ab 2 and 12a 2b 3 out = 6ab 2
factor A monomial that evenly divides a value
2. Draw the machine shown below on the board.
in
in
7.Have students make up some inputs using numbers
and variables. Select some of the inputs to give
to the class. Include at least one example of two
monomials that have a GCF of 1, so students will see
that some numbers or monomials have no common
factors other than 1.
out
3.Write the following values on the board, showing
them on the machine diagram one set at a time:
in = 18 and 30
out = 6
NEXT STEPS • Differentiate
5-Day and 3-Day Instructional Plans:
Objective 1 Posttest, page 785—All students
in = 28 and 14
out = 14
in = 64 and 28
out = 4
4.Ask students what the machine is doing. Then have
them find the out value for several pairs of in values.
Sample problems:
in = 54 and 42 out = 6
in = 51 and 9 out = 3
in = 42 and 30 out = 6
5.Have students make up some inputs of their own and
exchange them with a partner, who should find the
out values. Have them check their partners’ answers.
★ = Includes Problem Solving
Chapter 9 • Objective 1
783
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CHAPTER
9
Objective 1
Ongoing Assessment
Objective 1 Posttest
Discuss with students the key concepts in Objective 1.
Following the discussion, administer the Objective 1
Posttest to all students.
Using the Results
• Score the posttest and update the class record card.
• Provide reinforcement for students who do not
demonstrate mastery of the concepts through individual
or small-group reteaching of key concepts.
1.
3.
5.
Copyright 2011 Cambium Learning Sopris West.® All rights reserved.
7.
9.
48 and 36
2.
x 4y 3 and x 6y
4.
32 and 50
6.
a 2b 5 and a 3b 3
81 and 36
8.
20m 5n 3 and 42m 2n 4
40 and 16
10.
48 = 2 • 2 • 2 • 2 • 3
36 = 2 • 2 • 3 • 3
2•2•3
12
x 4y 3 = x • x • x • x • y • y • y
x 6y = x • x • x • x • x • x • y
x •x •x •x • y
x 4y
32 = 2 • 2 • 2 • 2 • 2
50 = 2 • 5 • 5
2
81 = 3 • 3 • 3 • 3
36 = 2 • 2 • 3 • 3
3•3
9
40 = 2 • 2 • 2 • 5
16 = 2 • 2 • 2 • 2
2•2•2
8
Inside Algebra
90 and 60
90 = 2 • 3 • 3 • 5
60 = 2 • 2 • 3 • 5
2•3•5
30
30m 2n 4 and 45m 6n 3
30m 2n 4 = 2 • 3 • 5 • m • m •
n•n•n•n
45m 6n 3 = 3 • 3 • 5 • m • m •
m •m •m •m • n • n • n
3•5•m•m•n•n•n
15m 2n 3
Chapter 9 • Objective 1
Find the greatest common factor (GCF) of these pairs using prime factorization.
Posttest
Name __________________________________________ Date ____________________________
a 2b 5 = a • a • b • b • b • b • b
a 3b 3 = a • a • a • b • b • b
a •a •b •b • b
a 2b 3
20m 5n 3 = 2 • 2 • 5 • m • m •
m •m •m • n • n • n
42m 2n 4 = 2 • 3 • 7 • m • m • n •
n•n•n
2•m•m•n•n•n
2m 2n 3
28a 2b 5 and 14a 3b
28a 2b 5 = 2 • 2 • 7 • a • a • b •
b•b•b•b
14a 3b = 2 • 7 • a • a • a • b
2 • 7 • a •a •b
14a 2b
Chapter 9 • Objective 1
125
Chapter 9 • Objective 1
785