1.
Name Date
Mrs. Labuski / Mrs. Portsmore Period _____ Mid Module 4 Review
1. Yolanda is planning out her vegetable garden. She decides that her garden will be square.
Below are possible sizes of the garden she will create.
a. Complete the table by continuing the pattern.
Side length foot feet feet feet feet feet
Notation
Formula
ft2
ft2
Representation
b. Yolanda decides the length of her square vegetable garden will be ft. She calculates
that the area of the garden is ft2
. Determine if Yolanda’s calculation is correct.
Explain.
2.
2. Yolanda creates garden cubes to plant flowers. She will fill the cubes with soil and needs to
know the amount of soil that will fill each garden cube. Volume is determined by the
following formula: , where s represents the side length.
a. Represent the volume of the garden cube above using a numerical expression.
b. Evaluate the expression to determine the volume of the garden cube, and the amount of
soil she will need for each cube.
3. Explain why .
inches
3.
4. Yolanda is building a patio in her back yard. She is interested in using both brick and wood
for the flooring of the patio. Below is the plan she has created for the patio. All
measurements are in feet.
a. Create an expression to represent the area of the patio.
b. Yolanda’s husband develops another plan for the patio because he prefers the patio to be
much wider than Yolanda’s plan. Determine the length of the brick section and the
length of the wood section. Then use the dimensions to write an expression that
represent the area of the entire patio.
5. The landscaper hired for Yolanda’s lawn suggests a patio that has the same measure of wood
as it has brick.
a. Express the perimeter of the patio in terms of first using addition, and then using
multiplication.
b. Use substitution to determine if your expressions are equivalent. Explain. Let x = 2
brick wood
4.
6. Elena and Jorge have similar problems and find the same answer. Each determines that the
solution to their problem is .
a. Evaluate each expression to determine if both Elena and Jorge are correct.
Elena: Jorge:
b. Why would each find the solution of ? What mistakes were made, if any?
7. Jackson gave Lena this expression to evaluate: . Lena said that to evaluate the
expression was simple; just multiply the factors and . Jackson told Lena she was
wrong. He solved it by finding the product of and , then adding that to the product of
and .
a. Evaluate the expression using each student’s method.
Lena’s Method Jackson’s Method
b. Who was right in this discussion? Why?
5.
8. Rewrite the expression using the fewest number of symbols and characters possible.
6g 8h_________________ 3 5 2 s p_________________
9. Find the product
7d 8c __________________ 4f 9gh _________________
10. Use the GCF and the distributive property to write equivalent expressions
25x + 40y__________________ 16a + 20b__________________
9g + 30h__________________ 16f + 4__________________
5st + 7st__________________
11. Apply the distributive property to write equivalent expressions.
5(3x + 9y) __________________ a(3b + 4f) __________________
12. Create a model to show that 2(2x + 3y) = 4x + 6y
13. Write an expression using variables and number for each statement below.
18 less than a number x ___________________________
the quotient of a number and 21 ______________________
8 times the sum of x and 15 ___________________________
7 less than the product of a number n and 5 __________________
The country fair charges and admission of $6 and then charges $2 for each ride. Write an
algebraic expression to represent the total cost after r rides at the fair.
6.
Name Date
Mrs. Labuski / Mrs. Portsmore Period _____ Mid Module 4 Review
1. Yolanda is planning out her vegetable garden. She decides that her garden will be square. Below are possible sizes
of the garden she will create.
a. Complete the table by continuing the pattern.
b. Yolanda decides the length of her square vegetable garden will be ft. She calculates that the area of the
garden is ft2
. Determine if Yolanda’s calculation is correct. Explain.
Side length 1 foot 2 feet 3 feet 4 feet 5 feet feet
Notation
Formula = 1 1
= 1 ft2
Representation
7.
2. Yolanda creates garden cubes to plant flowers. She will fill the cubes with soil and needs to know the amount of soil
that will fill each garden cube. Volume is determined by the following formula: , where equals the side
length.
a. Represent the volume of the garden cube above using a numerical expression.
b. Evaluate the expression to determine the volume of the garden cube, and the amount of soil she will need for
each cube.
3. Explain why .
inches
8.
4. Yolanda is building a patio in her back yard. She is interested in using both brick and wood for the flooring of the
patio. Below is the plan she has created for the patio. All measurements are in feet.
a. Create an expression to represent the area of the patio.
b. Yolanda’s husband develops another plan for the patio because he prefers the patio to be much wider than
Yolanda’s plan. Determine the length of the brick section and the length of the wood section. Then use the
dimensions to write an expression that represents the area of the entire patio.
5. The landscaper hired for Yolanda’s lawn suggests a patio that has the same measure of wood as it has brick.
a. Express the perimeter of the patio in terms of first using addition, and then using multiplication.
b. Use substitution to determine if your expressions are equivalent. Explain.
c.
brick wood
9.
6. Elena and Jorge have similar problems and find the same answer. Each determines that the solution to their
problem is .
a. Evaluate each expression to determine if both Elena and Jorge are correct.
Elena: Jorge:
b. Why would each find the solution of ? What mistakes were made, if any?
7. Jackson gave Lena this expression to evaluate: . Lena said that to evaluate the expression was simple;
just multiply the factors and . Jackson told Lena she was wrong. He solved it by finding the product of and
, then adding that to the product of and .
a. Evaluate the expression using each student’s method.
Lena’s Method Jackson’s Method
b. Who was right in this discussion? Why?
10.
8. Rewrite the expression using the fewest number of symbols and characters possible.
6g 8h 48gh 3 5 2 s p 30ps
9. Find the product
7d 8c 56cd 4f 9gh 36fgh
10. Use the GCF and the distributive property to write equivalent expressions
25x + 40y 5(5x+8y) 16a + 20b 4(4+5b)
9g + 30h 3(3g + 10h) 16f + 4 4(4f + 1)
5st + 7st st(5 + 7)
11. Apply the distributive property to write equivalent expressions.
5(3x + 9y) 15x+ 45y a(3b + 4f) 3ab + 12af
12. Create a model to show that 2(2x + 3y) = 4x + 6y
13. Write an expression using variables and number for each statement below.
18 less than a number x x – 18 the quotient of a number and 21
8 times the sum of x and 15 8(x + 15)
7 less than the product of a number n and 5 5n - 7
The country fair charges and admission of $6 and then charges $2 for each ride. Write an
algebraic expression to represent the total cost after r rides at the fair.
6 + 2r
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