Numerical Expressions
Writing & Evaluating Expressions
Equivalent Expressions
Finding Solutions
Equations (Variables, Graphs, Tables)
100

Part A - write 3 to the sixth power in expanded form

Part B - Write 6 x 6 x 6 in exponential form

Part A - 3 x 3 x 3 x 3 x 3 x 3

Part B - 6³

100

Part A:

The sum of 12 and an unknown number

Part B:

25 less than z

Part A:

12 + x

Part B:

z-25

100

Write an equivalent expression with as few factors as possible (simplest form):

Part A: 2x ⋅ 3 ÷ 6y(4)

Part B: ⅓ ⋅ ⅗ ⋅ 4y

ANSWERS

Part A: 6x/24y

Part B: 12y/15

100

Evaluate when x = 3 and y = 5

2x + 6y

 x = 3 and y = 5

2x + 6y

2(3) + 6(5)

6 + 30

ANSWER = 36

100

Luna cuts out paper rectangles. The width of each rectangle is 4 inches more than the length.

Part A: Define the two variables

Part B: Write an equation to represent the relationship between width and length

Part A: let w represent width, let represent length

Part B: w = 4 + l

200

find the value of:

(2/3)³

8/27

200
Part A: One half of the sum of 6 and x

Part B: 10 less than the quotient of 3 and x


Part A: 1/2(6 + x)

Part B: (3 ÷ x) - 10

200

Use the distributive property to find an equivalent expression:

Part A: 2(3x - 6)

Part B: x(4 + 7)

ANSWERS

Part A: 2(3x - 6) = 6x - 12

Part B: x(4 + 7) = 4x + 7x

200

Evaluate & SHOW WORK!:

x - 6 = 32            43 + y = 66

x - 6 = 32            43 + y = 66

   +6     +6          -43         -43

-------------           ------------

     x =38                      y=23

200

Identify the independent and dependent variables

x = 56y

x = dependent

y = independent 

300

Part A: Write an equivalent expression to show the relationship between multiplication and addition:

2 + 2 +2 + 2 +2 + 2 +2 + 2 + 5 + 5 + 5


Part B: Evaluate

Part A:

(8 x 2) + (5 x 3)

Part B:

31

300

Jenna has $20. She spends some of that at the store.

Part A: Define the variable

Part B: Write an algabraic expression to represent the situation

Part A: Let m represent the $ she spends

Part B: 20 - m

300

Use the distributive property and GCF to factor the following expressions:

Part A: 30 + 18

Part B: 8x - 40


ANSWERS

Part A: 30 + 18  = 6(5+3)

Part B: 8x - 40 = 8(x - 5)

300

Evaluate and show work!

3x = 45                x/4 = 14


3x = 45                x/4 = 14

/3      /3               4(x/4 = 14)4 

--------                 ----------------

x = 15                   x= 56

300

A recipe says to roast the chicken for 18 minutes per pound. 

Let m represent minutes

Let p represent the number of pounds of chicken

Part A: Write an equation to represent the relationship between the two variables

Part B: Label the independent & dependent variable

A recipe says to roast the chicken for 18 minutes per pound. Let m represent minutes. Let p represent the number of pounds of chicken.

Part A:  m = 18p

Part B:  m is the DEP and p is the IND

400

Evaluate:

5+ 12 ÷ 3 ⋅ 9 - 7

5+ 12 ÷ 3 ⋅ 9 - 7

5 + 4 ⋅ 9 - 7

5 + 36 - 7

41 - 7

ANSWER =34

400

Timmy earns $15 per hour he babysits. 

Part A: Define the variable

Part B: Write an algebraic expression to represent the situation

Part A: Let h represent the hours he babysat

Part B: 15h

400

Combine like terms:

15g + 5 + 4x + 3g + 2g + 3 + x

15g + 5 + 4x + 3g + 2g + 3 +

ANSWER = 20g + 5x + 8

400

Write an equation to represent the description. Then solve the equation:

The product of 3 and 4 has the same value as the quotient of x and 2.

3 ⋅ 4 = x/2

12 = x/2

ANSWER x = 24

400

Using the equation from the previous problem, complete the table that represents the relationship

m = 18p

pounds | minutes

     1     |

     2     |

     5     |

    10     |

pounds | minutes

     1     |    18

     2     |    36

     5     |    90

    10     |    180

500

Evaluate:

2(50-3 ⋅ 2²)

2(50-3 ⋅ )

2(50-3 ⋅ 4)

2(50 - 12)

2(38)

ANSWER = 76

500

Six friends split the total cost of some pizza and a pitcher of soda. The pizza costs $27.

Part A: Define the variable

Part B: Write an algabraic expression to represent the situation

Part A: Let p represent the pitcher of soda

Part B: (27 + p) ÷ 6

500

Distribute & combine like terms:

4(x+2) + 5(3x +1)

4(x+2) + 5(3x +1)

4x + 8 + 15x + 5

ANSWER = 19x + 13

500

Miss Perez has less than 4 candy bars

Part A: Write an inequality to represent the situation using the variable c

Part B: Graph the inequality on a number line

Part C: Check if the following numbers are solutions: 0, 2, 4, 6

Miss Perez has less than 4 candy bars

Part A:  c < 4

Part B: See Board!

Part C: 

0 <4 YES

2 < 4 YES

4 < 4 NO

6 < 4 NO

500

Maggie is having a bake sale. She starts with $5 in her cash register. She sells each item for $2. 

Part A: Fill out the table

 #  of  Items Sold  (I) | Total Cash in the Register (T)

________0_________|______________________

________1  ________|_______________________

________3_________|_______________________

________5_________|_______________________

Part B: Create an equation using the variables I provided

Part C: Identify the IND and DEP variables


Part A: Fill out the table

$5, $7, $11, $15

Part B: Create an equation using the variables I provided:

(I ⋅  2) + 5 = T

Part C: Identify the IND and DEP variables:

IND = I

DEP = T

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