Grade 8 Mathematics
Quarter 1 CCPM
Student Name: ______________________________
General Directions: Follow the directions for each problem below.
1.
Identify all the expressions that have a value between 0 and 1.
65 ∙ 6−8
A.
True
False
True
False
1 2 1 6
C. ( ) ∙ ( )
2
2
True
False
(−4)3
(−4)8
True
False
54
B.
5−3
D.
Standard(s) 8.EE.1
2.
Mathematical Practices: 1,5,7
Scoring: 4 points
Some students made this conjecture and found two examples to support their conjecture.
-If a rational number is not an integer, then the square root of the rational
number is irrational. For example, √4.6 is irrational and √
1
3
is irrational.
Provide two examples of non-integer rational numbers that show that the conjecture is false.
Example 1 :
√. 49
Standard(s) 8.NS.1
Palmdale School District, ©2013
Example 2:
Mathematical Practices: 1, 5, 7, 8
√
1
4
Scoring: 2 points (Multiple Answers, 1
point per correct example).
Page 1
Grade 8 Mathematics
Quarter 1 CCPM
3.
Student Name: ______________________________
Three students solved the equation 2(4x – 12) = 24 in different ways, but each student arrived at the
correct answer. Determine if each problem shows the correct steps for finding a solution.
a.
2(4x – 12) = 24
6x – 12 + 12= 24 + 12
Yes
No
Yes
No
Yes
No
6x = 36
6
36
6
6
x =
x=6
b.
1
2
∙2(4x – 12) = 24 ∙
1
2
4x - 12 = 12
4x - 12 + 12 = 12 + 12
4x = 24
4x
4
=
24
4
x=6
c.
2(4x – 12) = 24
8x – 24 = 24
8𝑥
8
8𝑥
8
–
–
24
8
24
=
8
+
24
8
24
8
24
=
x=
8
+
24
8
48
8
x=6
Standard(s) 8.EE.7,
4.
Mathematical Practices: 1, 3, 7, 8
Scoring: 3 points
The average distance from Jupiter to the Sun is about 5 x 108 miles. The average distance from
Venus to the Sun is about 7 x 107 miles.
The average distance from Jupiter to the Sun is about how many times as great as the average
distance from Venus to the Sun?
Any answer between and including 7 and 7.14
______________ Miles
Standard(s) 8.EE.3
Palmdale School District, ©2013
Mathematical Practices: 1, 5
Scoring: 1 point
Page 2
Grade 8 Mathematics
Quarter 1 CCPM
5.
Student Name: ______________________________
Consider the equation 2(4x + 7) = ax + b
Part A. Find one value for a and one value for b so that there is exactly one value of x that makes
the equation true.
a=
b=
Explain your reasoning.
Sample Score Response:
Part A
A = 6; b = 16
When you put these numbers in for a and b you get a single solution of x = 1.
Part B. Find one value for a and one value for b so that there are infinitely many values of x that
make the equation true.
a=
b=
Explain your reasoning.
Part B
a=8; b = 14; When you put these numbers in for a and b you get a solution of 0 = 0 so there are infinitely
many solutions, not just one.
Standard(s) 8.EE.7
Palmdale School District, ©2013
Mathematical Practices: 1, 3, 7
Scoring: Part A is 2 points and Part B is
2 points. (1 point if the student gives
acceptable values for a and b in both
parts and 1 point if the student provides
complete and correct explanations).
Page 3
Grade 8 Mathematics
Quarter 1 CCPM
6.
Student Name: ______________________________
Classify the numbers given in the box below as perfect squares and perfect cubes. Write the
number in the appropriate column in the chart. Numbers that are neither perfect squares nor
perfect cubes should NOT be placed in the chart.
64
121
32
Perfect Squares but NOT
Perfect Cubes
1
49
225
Standard(s) 7.AF.1.1, 8.EE.2
125
BOTH Perfect Squares and
Perfect Cubes
64
1
121
49
225
16
7.
8
72
16
27
Perfect Cubes but NOT Perfect
Squares
8
125
27
Mathematical Practices: 6
Scoring: 3 points (1 point for each
correct column)
Equations sometimes don’t have a single solution.
Part A. For each linear equation in this table: indicate whether the equation has no solution, one
solution, or infinitely many solutions. Place an x in the appropriate column to indicate the solution
type.
Equation
1.
2.
3.
4.
-5x + 7 = 7
2x + 11 = -8x + 35
3(x – 8) = 3x – 24
8 + 13x = 13x + 9
Palmdale School District, ©2013
No Solution
One Solution
Infinitely Many
Solutions
x
x
x
x
Page 4
Grade 8 Mathematics
Quarter 1 CCPM
Student Name: ______________________________
Part B. Solve any equation that was identified to have one solution from Part A
1. -5x + 7 = 7
-5x = 0
X=0
2. 2x + 11 = -8x + 35
10x + 11 = 35
10x = 24
X = 2.4
Part C. For the given equations in Part A, complete the chart by identifying the component(s) of
each equation that is the given term.
Equation
1. -5x + 7 = 7
2. 2x + 11 = -8x + 35
Standard(s) 7.AF.1.1 – 1.3, 8.EE.7.a and b
Number of Terms
3
Coefficients
-5
Constants
7
4
2, -8
11, 35
Mathematical Practices: 1, 5, 6
Scoring: Part A is 4 points, Part B is 2
points, Part C is 6 points (1 point for
each correct column for each equation)
Total Points: 29
Palmdale School District, ©2013
Page 5