Fifth Grade Math Alignment Document
Algebra
Number of Problems: 8
2. Explain and analyze number relationships and functions using algebraic symbols, and demonstrate an understanding of the properties of the basic
operations.
Objective
a. Determine the value of
variables in equations and
inequalities, justifying the
process.
(DOK 2)
Envision or
Investigation
34–36, 74–76, 110–
112, 288–289, 376–
381, 382–388
Unit 1: 115, 122,
126, 127, 134
PLD Level
Proficient: Determine the
value of variables in equations
and inequalities, justifying the
process
Assessment Item
Suggested Teaching Strategy
1. What is the value of n in the
following equation?
9x4=nx6
A. 6 *
B. 36
C. 42
D. 216
Depth of Knowledge Level: 1
Performance Level: Proficient
2. What number is represented by x in
the equation below?
_x = 15
45
A. 205
B. 270
C. 655
D. 675 *
Depth of Knowledge Level: 2
Performance Level: Proficient
Present a relationship (equation). For example,
3b = 18. Model the relationship (equation) using
manipulatives. Students should be modeling as
you do.
b
b
b
b
b
b
The first diagram shows the relationship
expressed in the equation. Because the
relationship indicates that three times some
number is 18, to find that number we think
about the meaning of multiplication (which links
to the inverse relationship to division). Thus in
the second diagram, it shows that each b must
then represent 6 because the quantity of 18 can
be broken apart into three groups of 6.
As students model, they should note that the
actions performed on one side of the scale
mirror the actions performed on the other side
of the scale. These actions can be linked to
equality properties and other real number
properties
b. Devise a rule for an
input/output function table,
describing it in words and
symbols. (DOK 2)
382–384
Unit 8: 45, 50–
51, 57–58, 67–
68, 71–72, 76–
78, 90–92
Proficient: Devise a rule for 1. Carrie made a rule for a function
an input/output table.
table. A friend guessed numbers and
Carrie used the rule to
make the table below.
Friend’s Guess Carrie’s
Play U-Say, I-Say with students. Think of a rule,
like multiply a number by 2 and add 1. Tell
students that you have a rule in mind. They will
give you a number; you will record that number
in the U-Say column. You are then going to use
your rule on that number and record the result
Number
11
24
37
4 10
5 13
Which describes Carrie’s rule?
A. Multiply the friend’s number by 1
B. Multiply the friend’s number by 2
C. Multiply the friend’s number by 2
and add 1
D. Multiply the friend’s number by 3
and subtract 2*
Depth of Knowledge Level: 2
Performance Level: Proficient
in the I-Say column. They are to continue giving
you numbers until they think they know the rule
you are using. When they think they know the
rule, they are to raise their hand but not say the
rule. (If some students raise their hands and
think they know the rule early in the game, you
can ask those students to predict what number
you will write down in the I-Say column when a
number is given.) A typical table might look like
this:
U-Say
2
4
1
0
100
42
I-Say
5
9
3
1
201
85
When several students think they know the rule,
before you ask them for the rule, have them
apply it by giving them the number in the I-Say
column. For example, with this rule and table
above, you might record 43 in the I-Say column.
Ask, what number do you think would be in the
U-Say column? Students, if they know the rule,
will work backwards to find the number. Then,
ask students to describe the rule in words.
Record the rule as they say it. Ask students for
other ways to describe it in words. They may
say
Double the number and add 1
Add the number to itself and then add 1
more
Multiply the number by 2 and add 1
Finally, record a variable, say n, in the U-Say
column to represent any number that might be
given. Ask students to say and write the rule
using the variable. How many different ways
can the rule be written? In the above example,
students might say: 2n + 1, n + n + 1, and so
on.
c. Apply the properties of basic
operations to solve problems:
(DOK 2)
 Zero property of
multiplication
 Commutative
properties of addition
and multiplication
 Associative properties
of addition and
multiplication
 Distributive properties
of multiplication over
addition and
58–59, 223
156–157
Online Activity:
Unit 7 Activity 64
Unit 7: 11, 16–
18
Online Activity:
Unit 7 Activity 40
Proficient: Apply the
properties of basic operations
to solve problems.
Basic: Recognize properties
of basic operations used to
solve problems.
1. If n equals 1, what is the value of
the following expression?
n (0 x 6)
A. 0 *
B. 1
C. 6
D. 7
Depth of Knowledge Level: 2
Performance Level: Proficient
Present a relationship (equation). For example,
3b = 18. Model the relationship (equation) using
manipulatives. Students should be modeling as
you do.
b
b
b
b
b
b

subtraction
Identity properties of
addition and
multiplication
The first diagram shows the relationship
expressed in the equation. Because the
relationship indicates that three times some
number is 18, to find that number we think
about the meaning of multiplication (which links
to the inverse relationship to division). Thus in
the second diagram, it shows that each b must
then represent 6 because the quantity of 18 can
be broken apart into three groups of 6.
As students model, they should note that the
actions performed on one side of the scale
mirror the actions performed on the other side
of the scale. These actions can be linked to
equality properties and other real number
properties
Properties can help students use flexibility of
number ideas. For example, ask students to
simplify this expression: (75 x 4) x 25. Allow
time to work and then have them share their
processes. If students first do the operation in
the parentheses, and then multiply by 25, it
becomes a much more difficult problem than if
they were to use the Associative Property and
change the problem to: 75 x (4 x 25). This is
much easier and accurate than the first way.
You can use other problems, such as (100 +
25) + 75; 18 + (25 – 18); and so on to provide
other explorations for students.
d. Apply inverse operations of a
ddition/subtraction and
376–379, 422–423
Unit 1: 121–125
Advanced: Justify solutions 1. The teachers counted 3 classes of
to problems involving the
5th graders and used the equation
Give students a problem such as the following:
Lani had some money in her wallet. She went
multiplication/division to problemsolving situations. (DOK 2)
Unit 3: 58–60
application of
addition/subtraction and
multiplication/division.
Proficient: Apply inverse
operations of
addition/subtraction and
multiplication/division to
problem-solving situations.
below to represent x, the
total number of 5th graders:
x = 3 × 25
Which equation represents the
number of students in each class?
A. 25 = 3/ x
B. 25 = x /3 *
C. 25 = x – 3
D. 25 = x + 3
Depth of Knowledge Level: 2
Performance Level: Proficient
shopping and spent $14.50 on a shirt. She then
bought a CD for $12.00. She was thirsty and
got a soda for $3.50. She had $2 left. How
much money did she start with? [This problem
allows for working backwards which is an
appropriate context for discussing inverse
operations.] Allow students time to work the
problem and then have them share their
solution strategy(ies). Ask students to relate
their process to inverse operations.
Other problems might be more straightforward.
For example, Josh bought three CDs that
totaled $38.25. He knew that each CD cost the
same but he couldn’t remember the cost for
each CD. Find the cost of one CD. Students
may think of this as an application of the
inverse properties. For example, if c represents
the cost of one CD, then 3c = $38.25. To undo
the multiplication, students would divide $38.25
by 3.