Evaluating Expressions
Writing expressions
Rectangular Prism Volume
Lots of Layers
More than one prism
100
What is the value of
30 - 3 x 6 ?
In order of operations, multiplication comes before adding, so
30 - 18 =
12
100
Which phrase matches the numeric expression
7 + 15 ÷ 3 ?
a) Seven added to the product of fifteen and three.
b) The difference of 7 and the quotient of fifteen and three.
c) The sum of seven and the quotient of fifteen and three.
d) Seven times as much as the quotient of fifteen and three.
C
100
The dimensions of a rectangular prism are:
Length = 5 feet Width = 8 feet Height = 2 feet
What is the volume of the rectangular prism?
length x width x height = volume
5 x 8 x 2 =
80 cubic feet
100
A rectangular prism has 4 layers. Each layer is made of 10 cubes. What is the volume of the prism?
cubes on bottom layer x height = volume
40 cubic units
100
A two-level bookshelf has two levels. Each level has the following dimensions:
Length = 5 feet Width = 2 feet Height = 3 feet
What is the total volume of the bookshelf?
L x W x H = volume
5 x 2 x 3 = 30 cubic feet for each layer
2 layers x 30 cubic feet in each layer =
60 cubic feet
200
Evaluate the numerical expression:
100 − 10 × 8
multiplication comes before subtraction, so
100 - 80
20
200
Choose the numeric expression that represents the phrase: "four times the difference between twelve and five."
a) 4 + (12 - 5)
b) 4 x 12 - 5
c) (12 - 5) ÷ 4
d) 4 x (12 - 5)
D
200
Each side of a cube is 8 centimeters long. What is the volume of the cube?
it's a cube, so all dimensions are the same:
8 x 8 x 8 =
512 cubic centimeters
200
A box has a volume of 72 cubic inches. The area of the base is 12 square inches. How many inches tall is the rectangular prism?
area of base x height = volume
12 x ___ = 72
6 inches
200
There's a shape made up for two rectangular prisms, not just one.
- one has a length of 2, width of 3, and height of 5
- the other has a length of 6, width of 3, and height of 5
What is the total volume of the shape?
2 x 3 x 5 = 30
6 x 3 x 5 =90
30 + 90 =
120 cubic units
300
Fill in the blanks with operation symbols to make the equation true.
300
Write an expression that matches the phrase "add 12 and 18, then multiply the result by 5."
parentheses are necessary to make addition come before multiplication
(12 + 18) x 5
300
Sam went to the store to pick up a juice box for his little brother. The juice box is 7 cm long, 4 cm wide, and holds 280 cubic cm of juice. How tall is the juice box?
CALCULATOR ALLOWED FOR THIS QUESTION
length x width x height = volume -- so
7 x 4 x ___ = 280
10 cm
300
Terrell uses chicken-flavored seasoning cubes in some recipes. The cubes are in a plastic container that is shaped like a rectangular prism. When full, the bottom of the container is completely covered by 40 cubes. Five layers can be stacked in the container. How many cubes are in a full container?
cubes in bottom layer x number of layers = volume
40 x 5 =
200 cubes
300
What is the volume of this figure?
top prism: 2 x 3 x 2 = 12 cubic cm
bottom prism: 10 x 3 x 5 = 150 cubic cm
12 + 150 =
162 cubic centimeters
400
What is the value of this expression?
addition and subtraction are done from left to right, so subtraction comes first.
400
A farmer picks baskets of apples. He puts 20 apples into each of 6 baskets. He has 24 extra apples but doesn't have a basket to put them in. Which expression shows the number of apples the farmer picked?
a) 24 x 6 + 20
b) 20 x (6 + 24)
c) (24 + 20) x 6
d) 6 x 20 + 24
D
400
Roger has a box in the shape of a rectangular prism that has a volume of 36 cubic inches. The box is 6 inches tall. Select three options that could be the length and width of the box.
a) L=3 in. , W=2 in.
b) L=6 in. , W=1 in.
c) L=10 in. , W=3 in.
d) L=6 in. , W=5 in.
e) L=2 in. , W=3 in.
The area of the base has to be 6 square inches, because area of base x height = volume
a, b, and e
400
A rectangular prism is made of 8 layers. Each layer has 24 cubes. What is the volume of the prism?
cubes in each layer x number of layers = volume
24 x 8 =
192 cubic units
400
What is the volume of this figure?
CALCULATOR ALLOWED FOR THIS PROBLEM
top prism - 3 x 14 x 3 = 84
bottom prism - 3 x 11 x 4 = 132
84 + 132 =
216 cubic yards
500
The expression 10 × 4 + 8 is how many times as large as 4 + 8 ?
If there were parentheses in the first expression,
10 x (4 + 8) --> then it would be 10 times larger than 4+8. Since there are not, the value of the first expression is 48 (40 + 8 = 48). The value of 4 + 8 = 12. Comparing the values, 48 is 4 times 12, so
4 times as large
500
Write an expression to represent the phrase "4 times as much as the sum of 15 and 22"
(15 + 22) x 4
or
4 x (15 + 22)
500
A prism has a volume of 108 cubic feet. The area of the base of the prism is 36 square feet. What is the height?
CALCULATOR ALLOWED FOR THIS PROBLEM
area of base x height = volume
36 x ______ = 108
3 feet
500
You are setting up a new fish tank for your pet fish. The fish tank has the following dimensions:
Length = 30 in. Width = 12 in. Height = 18 in.
You want to fill the tank with water to a depth of 15 inches. What is the volume of water required to fill the tank to that depth?
CALCULATOR ALLOWED FOR THIS PROBLEM
length x width x height = volume
30 x 12 x 15 (not filling to the top) =
5,400 cubic inches
500
Alexandra arranges tower-building blocks to fit inside their case. Each block is 8 cm long, 3 cm wide, and 2 cm tall. The case is shaped like a rectangular prism, and 54 blocks fit in the case with no extra space. What is the volume of the case?
CALCULATOR ALLOWED FOR THIS PROBLEM
8 x 3 x 2 = 48 cubic centimeters for each block
48 cubic cm x 54 blocks =
2,592 cubic centimeters