Area & Volume (6.GM.3, 6.GM.4)
A small jewelry box is shaped like a right rectangular prism. Its dimensions are as follows:
length: 4 1/4 cm
width: 2 cm
height: 3 1/2 cm
What is the volume of the jewelry box?
V = lwh
Volume = 4 1/4 x 2 x 3 1/2 = 29 3/4 cm3
A delivery driver starts at the Warehouse located at (-3,4). They make two stops:
1. Stop A: (5,4)
2. Stop B: (5, -2.5)
How far is the drive from the Warehouse to Stop A? How far is the drive from Stop A to Stop B?
Warehouse to Stop A is 8 units.
Stop A to Stop B is 6.5 units.
A baker is preparing a large order of sourdough bread. Each loaf requires 2.25 pounds of flour. If the baker needs to make 15 loaves, but only has a 50-pound bag of flour, how much flour will be left in the bag after the order is finished?
16.25 pounds
2.25 x 15 = 33.75 pounds of flour needed
50 - 33.75 = 16.25 pounds of flour left in the bag
Determine which value(s) from the set {4, 6, 8} make the following equation true:
3x + 5 = 23
{6}
3(4) + 5 = 17
3(6) + 5 = 23
3(8) + 5 = 29
In a science experiment, the number of bacteria in a dish triples every hour. If the experiment starts with 1 bacterium, the number of bacteria after 4 hours can be represented as 34. How many bacteria are in the dish after 4 hours?
3 x 3 x 3 x 3 = 81 bacteria
A shed's side wall looks like a house: a rectangle with a triangle on top.
* The rectangular base is 8 feet wide and 7 feet high.
* The peak of the triangular roof is 3 feet higher than the top of the rectangle.
Calculate the total area of the wall by combining the area of the rectangle (A = l x w) and the area of the triangle (A = 1/2 bh).
rectangle = 8 x 7 = 56 ft2
triangle = 8 x 3 x 1/2 = 12 ft2
total area = 56 + 12 = 68 ft2
A rectangular playground is plotted on a map. Three of its corners are at (-4.5, -2), (2, -2), and (2,3). What are the coordinates for the 4th corner?
(-4.5, 3)
Javier is hiking a trail that is 8 3/4 miles long. He hiked 3 1/2 miles before stopping for lunch. After lunch, he hiked another 2 1/4 miles. How many miles does Javier have left to reach the end of the trail?
3 miles left
3 1/2 + 2 1/4 = 5 3/4 miles hiked
8 3/4 - 5 3/4 = 3 miles left
A group of friends has a set of possible budgets: {$12, $18, $25}. They want to buy snacks, and the total cost must follow the inequality: s - 4.50 is less than or equal to 13.50 (where s is the total money they spend on snacks). Which budget allows them to stay within this limit?
{$12, $18}
12 - 4.50 = 7.50 yes
18 - 4.50 = 13.50 yes
25 - 4.50 = 20.50 no
A gardener is designing a triangular flower bed. She measures two of the corners (interior angles) and finds they are 45 degrees and 55 degrees. What is the measure of the third angle?
45 + 55 + x = 180
x = 80 degrees
A school stage is shaped like a large rectangle with two identical triangles added to the sides (a trapezoid).
* The middle rectangular section is 20 feet wide.
* The total width of the stage along the bottom is 30 feet.
* The depth (height) of the stage is 15 feet.
Find the total area of the stage. Use A = l x w and A = 1/2 b x h.
middle rectangle: 20 x 15 = 300 ft2
triangles: 1/2 x 15 x (30-20) = 37.5 ft2
total area: 300 + 37.5 + 37.5 = 375 ft2
To make a specific fruit punch, the ratio of cups of orange juice to cups of pineapple juice is 3:2.
Create a table of equivalent ratios for 2, 4, and 6 batches. Then list the pairs as (x,y) coordinates, where x is orange juice and y is pineapple juice.
Batches orange juice (x) pineapple juice (y) ordered pair (x,y)
1 3 2 (3,2)
2 6 4 (6,4)
4 12 8 (12,8)
6 18 12 (18,12)
A student has $45.50 to spend on school supplies. They buy a backpack for $28.90. They want to spend the remaining money on notebooks that cost $2.10 each. How many notebooks can the student buy?
The student can buy 7 notebooks.
45.50 - 28.90 = 16.60 money left after buying the backpack
16.60 / 2.10 = 7.9... (not enough for 8)
Mrs. Stump's classroom library started the month with a certain number of books (x). After students borrowed 12 books, 38 books remained on the shelf.
1. Write an equation of the form x - p = q to represent the situation.
2. Solve the equation to find how many books were in the library originally.
1.
x = number of books in Mrs. Stump's library
x - 12 = 38
2.
Add 12 to both sides.
x = 50 books
A student is making a kite shaped like a quadrilateral. The interior angles are as follows:
* Two opposite angles are 110 degrees each.
* One of the other angles is 50 degrees.
What is the measure of the fourth angle?
110 + 110 + 50 + x = 360
x = 90 degrees
A rectangular planter box has a base area (B) of 10 1/2 feet2. The height (h) of the planter is 1 1/3 feet. How much soil (volume) can the planter hold?
V = Bh
V = Bh = 10 1/2 x 1 1/3 = 14 feet3
time distance
2 10
3 ?
? 25
6 ?
Find the missing information. Write each answer as an ordered pair.
(2,10)
(3,15)
(5, 25)
(6, 30)
Manolo is looking at three different scores from his math quizzes. He wants to know which score is the highest, but the scores are written in different formats:
* quiz A: 4/5
* quiz B: 0.82
* quiz C: 78%
Change all three scores into percentages and list them from least to greatest.
78% (quiz C is 78%)
4/5 (quiz A is 80%)
0.82 (quiz B is 82%)
A group of friends bought several pizzas for a total of $54. If each pizza costs $13.50, how many pizzas (x) did they buy?
1. Write an equation of the form px = q to represent this situation.
2. Solve the equation.
1.
x = pizzas the friends bought
13.50x = 54
2.
Divide both sides by 13.50.
x = 4 pizzas
Someone posted this question on Facebook and said the answer was 15. Are they right? If not, what is the correct answer?
32 + (1.2 + 0.8)x5 - 12/3
A pool is 9 feet deep and 6 1/2 feet wide. If the volume of water in the pool is 409 1/2 feet3, what is the length of the pool?
7 feet long
Maya saves money every week at a constant rate. She saves $15 every two weeks.
Complete a table showing her total savings over 8 weeks. Write your answers as ordered pairs.
weeks (x) total savings (y) ordered pair
2 $15 (2,15)
4 $30 (4,30)
6 $45 (6,45)
8 $60 (8,60)
A water bottle is 0.65 full. What fraction of the bottle is full? What percent of the bottle is empty?
Full: 65/100 = 13/20
Empty: 100% - 65% = 35%
A gas tank is 1/4 full. The amount of gas currently in the tank is 3.5 gallons. How many gallons (x) does the tank hold when it is completely full?
1. Write an equation of the form x/p = q to represent the situation.
2. Solve the equation.
1.
x = gallons in the full tank
1/4 x = 3.5 or x/4 = 3.5
2.
Multiply both sides by 4.
x = 14 gallons
Evaluate the expression below without using a calculator:
(12.5 + 0)x(2/3 x 3/2)
12.5