Download Grade-6-Expressions-and-Equations-SOLUTIONS

Name: _______________________
Score: ______/ 34 points
Grade 6 – Algebra
1.
Zack computes the perimeter of a rectangle by adding the length, L, and width, W, and doubling the sum. Rachel
computes the perimeter by doubling the length and doubling the width and adding the doubled amounts. Write
an expression for Zack’s way of calculating the perimeter. Write an expression for Rachel’s way as well.
(_____ / 2 points)
Zack’s way: (L + W) 2

Rachel’s way: (2L) + (2W)
Use both of the expressions to find the perimeter of a rectangle with length 10 and width 5.
(_____ / 2 points)
Zack’s: (10 + 5) 2 = 30

Rachel’s: (2x10) + (2x5) = 20+10 = 30
Explain why Zack and Rachel always get the same answer, no matter what the length and width of
the rectangle are.
(_____ / 2 points) Algebraic distributive property
2.
Is 9 a solution of p-7=2? Explain your answer. (_____ / 2 points) YES because 9‐7=2 is TRUE.
3.
Using a variable, how would you write an equation for the mathematical sentence that “6 more plus a
number equals eighteen” (_____ / 2 points) x +6 = 18
4.
Evaluate the expression when x=4 and y=7. (_____ / 2 points)
2x+5y
5.
This is 2x+5y=2(4)+5(7)=8+35=43
Simplify this expression by combining like terms: (_____ / 2 points)
8b-2b This is just 6b. Putting in all the steps: 8xb‐2xb=bx8‐bx2=bx(8‐2)=bx6=6xb=6b.
6. Simplify this expression by combining like terms: (_____ / 2 points)
5x + 2 - 3x + 1
This is 5x‐3x+2+1= 2x+3
7. David has $15, and Joanna has $6 less than David. How much money does Joanna have? (_____ / 2 points)
Let D be the amount that David has and J the amount that Joanna has. Then J=D‐6. Since D=15 we have that
J=15‐6=9. Thus Joanna has $9.11
8. If David has some money, and Joanna has $6 less than David, then how much money does Joanna have?
(_____ / 2 points)
Use the assignments given above. J=D‐6 or D=J+6 are equally valid ways to express this.
9. True or False? (_____ / 2 points) Show your thinking
9 + 15 = 40 - 16
This is true. The principle here is that a+b=(a+h)+(b‐h). In our calculation we have a=9,b=15, and h=31. Thus
a+h=9+31=40 and b‐h=15‐31=‐16.
6+6+6+6 = 2 x 12
This is true. The principle here is that (a+a)+(a+a)= 2(2a). In our calculation we have a=6. Thus, 2(2x6) = 2x12.
10. Evaluate x3 when x = 2. (_____ / 2 points)
A) 6
B) 8
C) 5
D) 2/3
23 = 2x2x2 = 4x2 = 8 = B
13. Which value is NOT a solution to the inequality 5 + x ≤ 10 (_____ / 2 points)
A) 6
B) 4
C)2
D)0
A, because 5+6 = 11, which is not less than/equal to 10.
14. Select the equation where x = 5 is the solution:
A) 5x = 55
B) 2x + 5 = 15
(_____ / 2 points)
C) 5x + 2 = 15
D) 5x = 10
B, because 2(5) = 10; 10+5 = 15.
1
It is a little silly perhaps to “algebratize” this problem so formally since it makes it seem like such a problem could only be solved by
middle school students. Of course that is not true but we are just showing the mechanism here which is most suitable for more
complicated problems.
15. Match the inequality to the graph at the right.
(_____ / 2 points)
A) x < 2
B) x > 2
–1 0 1 2 3 4
C) x ≤ 2
D) x ≥ 2
A, because an open circle denotes a set that does not include the starting number (2 in this case), and the
arrow points towards numbers less than 2.
16. It cost $3 to rent a movie from Movie Box. Jose has a monthly movie rental budget of $24. How many
movies can he rent each month? (_____ / 2 points)
$24 month / $3 each movie = 8 movies per month
17. Write the variable expression for: “seven less than twice a number” (_____ / 2 points)
A) 14x
B) 2x · 7
C) 2(x - 7)
D) 2x – 7
D, because twice a number is written as 2x, which you must subtract 7 from, leaving 2x – 7.
Scoring Rubrics
2-point problems:
0 points
No Work
1 point
Work arriving at wrong answer
2 points
Work arriving at correct
answer
3-point problems:
0 points
No work
1 point
Work and explanation
or drawing; incorrect
answer
2 points
Work and explanation
or drawing ; error in
calculation or visual
representation
3 points
Work and explanation
or drawing correct