Your friend Sam wants to paint her room. She wants to paint the ceiling white and the four walls purple.
You are helping Sam determine the cost and the amount of time needed to paint her room.
The room is shaped like a rectangular prism with a height of 8 feet, length of 12 feet, and width of 10 feet as shown.
Additional information about Sam's room:
The door has an area of 22 square feet.
The room has 2 square windows.
Each window opening is 2 feet by 2 feet.
What is the area, in square feet, of the ceiling?
Sam needs to figure out how much purple paint to buy. Calculate for her the total area, in square feet, of the four walls. She will not paint the door or windows.
Part way through painting her room, Sam runs out of paint.
She estimates that there are about 125 square feet left to paint.
The purple paint that Sam is using is only available in 1-quart cans. (Assume she must buy whole cans of paint.)
Each can of paint covers 40 square feet.
How many cans of paint does Sam need to buy to finish painting her room? Explain to Sam why she needs this many cans of paint.
You would also like your room painted.
Your room has 300 square feet of wall of space to paint.
Sam says it took her 10 minutes to paint 25 square feet.
At this rate, if Sam painted your room, how many hours would it take?
Sam and you are going to paint your room together.
Sam takes 10 minutes to paint 25 square feet.
It takes you 5 minutes to paint 25 square feet.
Sam says, "If we paint together, then it will take 15 minutes for us to cover 50 square feet."
Give an explanation to convince Sam that she is incorrect.
Your class is doing a class project on conserving water. One way to conserve water is by shortening the time you shower. Another way is by using low-flow shower heads that have a lower rate of water flow than regular shower heads. Your task is to determine which of these two is the better option.
To figure out which option would save more water and money, the 20 students in the class recorded how long they took showers yesterday.
The data is shown in Figure 1.
Figure 1. Shower Times of the Class Yesterday
The class calculated that they spent a total of 180 minutes showering
yesterday.
The water flow rate of a regular shower head is 3.5 gallons per minute. All 20 students currently have regular shower heads.
The class will choose one of the two options to save water.
Option 1
Set a maximum time limit of 10 minutes for showering.
Option 2
Purchase low-flow shower heads for every student in the class. The water flow rate of low-flow shower heads is 1.5 gallons per minute less than the water flow rate of regular shower heads.
In this task, you will:
Analyze the class data.
Decide which option is better for the class to choose.
How many students used less than 30 gallons of water showering yesterday?
English glossary :
showering : taking a shower
The water flow rate of a regular shower head is 3.5 gallons per minute. At this rate, it would cost $1.90 for the water used for a 10-
minute shower.
What is the cost, rounded to the nearest cent, of 1 gallon of water?
English glossary :
water flow : movement of water
shower head : devices that spray water in a shower
Now, you will consider Option 1, setting a maximum shower time of 10 minutes.
Assume all students who showered longer than 10 minutes will now shower for exactly 10 minutes. Assume the rest of the students will shower for the same amount of time as they did yesterday.
Blake claims Option 1 would result in the class mean going below 8 minutes, but the class median would not change.
Explain whether you agree or disagree with Blake’s claim. Include the class mean and median that would result from Option 1 in your explanation.
English glossary :
consider: think about
showered: took a shower
claims: says
claim: sentence
You will now consider Option 2—using low-flow shower heads instead
of regular shower heads.
Courtney claims that Option 2 would result in the class using 270 gallons of water during 180 minutes of showering because:
(180 minutes)× (1.5 gallons per minute)= 270 gallons.
Courtney is incorrect.
Identify her error.
Explain how to find the correct amount of water used if the class chooses Option 2.
Include how much water would be used.
You will now decide whether Option 1 or Option 2 is better for the class. The goal is to save both water and money.
Option 1
Set a maximum shower time of 10 minutes. Assume all students who showered longer than 10 minutes will now shower for exactly 10 minutes. Assume the rest of the students will shower for the same
amount of time as they did yesterday.
Option 2
Purchase low-flow shower heads at $15 each for every student. Assume the shower time lengths are the same as yesterday for all students.
How much water will the class use each day for each option?
Find the total cost for the first 25 days for each option (include the cost of the new shower heads in Option 2). Assume every
student showers every day and water now costs $0.07 per gallon.
Is Option 1 or Option 2 better for the class? Justify your response.
A local skate park is being planned by the Community Recreation
Committee.
In this task, you will make recommendations for a skate park design that most of the local skateboarders like. You will use your recommended design to create a safety code for the park.
The area of the planned skate park is 10,000 square feet.
The committee asks you to gather data about skate ramps. You survey 8 local skateboarders on their preferences for the number of single ramps and number of double ramps for the skate park. The survey results are shown in the line plots.
The single and double ramps are shown. Each ramp has a rectangular base.
Single Ramp
Double Ramp
Based on the survey data, what percent of skateboarders requested 2 or more single ramps?
The skate park will be in the shape of a square. It will have an area of 10,000 square feet. A scale drawing of the skate park is shown.
Choose the correct scale for the scale drawing.
The base of the single ramp is a rectangle 30 feet by 30 feet.
The base of the double ramp is a rectangle 30 feet by 60 feet.
Enter the area, in square feet, of the base of a single ramp.
Enter the area, in square feet, of the base of a double ramp.
Based on the survey data, you will recommend a number of single ramps and double ramps the park should have.
Use the information from the Preferences of 8 Local Skateboarders line plots.
At least 50% of the skateboarders must have requested the number of ramps you recommend.
What is the number of single ramps you recommend?
What is the number of double ramps you recommend?
English glossary :
Preferences: what people prefer (like better)
Local: that live nearby
ramps: equipment with a slope
skateboarders: people who ride a skateboard
The town safety code requires 10 square feet of empty floor space per person. Empty floor space is defined as space where no ramps will be built.
Based on the number of ramps you’ve chosen, what is the maximum number of people that can be in the skate park at any given time?
Use information from previous questions to fully explain your answer.
English glossary :
skate park: place specifically made for skateboarding
ramps: equipment with a slope