9.1.1 Comparing Rates

9.1.1 How Can I Compare Rates?

Comparing Rates

First Investigation!
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Open Ended

Recycling for 3/5 week earns $85

Yardwork for 2 weeks earns $320

How can we determine which will earn more money overall?

9-1:

The sixth graders at Shasta Middle School are planning a class trip to Washington, D.C.  They need to raise enough money for all 140 sixth graders to travel, so they have a lot of work to do!  The class officers have collected the data below about different kinds of fundraisers.  They want your help with choosing a fundraising activity.

Math Response

How much will the class members earn if they spend six weeks doing yardwork?

Type answer here

Correct Answer: 960

Deg^°

Rad

Math Response

How much will the class members earn if they spend six weeks having car washes?

Type answer here

Correct Answer: 1050

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Rad

Math Response

How much will the class members earn if they spend three weeks recycling?

Hint: 3/5 of a week is 3 school days. We will say there are 5 days in a week for this problem.

Type answer here

Correct Answer: 425

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Rad

Math Response

Compare the money made from selling cookies and from doing car washes.

How many weeks would the class need to sell cookies in order to earn $5000?

Type answer here

Correct Answer: 30

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Multiple Choice

Compare the money made from selling cookies and from doing car washes.

How many weeks would the class need to have car washes in order to earn $5000?

• 15 weeks
• 20 weeks
• 35 weeks
• 29 weeks

Multiple Choice

Compare the money made from selling cookies and from doing car washes.

Could the class earn $175 each week by washing cars?

• Yes, the class could earn $175 each week by washing cars.
• No, the class could not earn $175 each week by washing cars.
• The class could earn $100 each week by washing cars.
• The class could earn $250 each week by washing cars.

Multiple Choice

Compare the money made from selling cookies and from doing car washes.

How much could the class earn during one week of cookie sales?

• $300.50
• $250.00
• $100.00
• $166.67

Math Response

Nicolette decided to see how much the students could earn in 12 weeks.

How much could the students earn after 12 weeks of cookies sales?

Type answer here

Correct Answer: 2000

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Math Response

Nicolette decided to see how much the students could earn in 12 weeks.

How much could the students earn after 12 weeks of washing cars?

Type answer here

Correct Answer: 2100

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Open Ended

Which fundraising activity raises money the fastest: selling cookies or washing cars? Write a note to the class officers recommending the fastest fundraising activities. Explain your reasoning.

New Investigation!
You can still use a calculator! Go to our Canvas Page, Quick Links, Desmos Calculator

9-14:

The local news station is selecting this week’s student for “Athlete of the Week.”  Wendy and Yoshie, sprinters on the track team, are both finalists.  They are trying to decide who is fastest based on recent race data. 

Math Response

This table shows Wendy's times. How far can Wendy run in 25 seconds?

Type answer here

Correct Answer: 90

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Rad

Multiple Choice

What is Wendy's running rate in meters per second?

• 30 meters per 5 seconds

• 10 meters per 30 seconds

• 5 meters per 30 seconds

• 200 meters per 25 seconds

Open Ended

Wendy can run 30 meters in 5 seconds.

Yoshi can run 70 meters in 11 seconds.

Who is faster?

Open Ended

Based on the graph, who is running faster? How do you know?

Open Ended

Wendy can run 30 meters in 5 seconds.

Yoshi can run 70 meters in 11 seconds.

Vanessa was Athlete of the Week last week. If she raced Yoshi and Wendy, who would win?

Last Investigation!
You can still use a calculator! Go to our Canvas Page, Quick Links, Desmos Calculator

9-16:

triathlon is a race in which participants swim, bike, and run specific distances.  Participants start by swimming.  After swimming, they jump out of the water, get dressed as fast as they can, and ride a bicycle.  After they complete the biking section, the participants finish the race by running several miles.

Multiple Choice

During which segment of the race (a, b, or c) did Diane go the fastest?

• a
• b
• d
• c

Multiple Choice

What was Diane's distance during Segment B?

Hint: What is the difference between 0.5 and 12.5?

• 2 miles
• 6 miles
• 1 mile

• 12 miles

Multiple Choice

What was Diane's time during Segment B?

Hint: What is the difference between 18 and 60?

• 36 minutes

• 42 minutes

• 48 minutes
• 60 minutes

Multiple Choice

Diane traveled 12 miles in 42 minutes during Segment A of the race. What is her rate?

• 12 miles per 42 minutes

• 24 miles per 81 minutes

• 42 miles per 12 minutes

• 6 minutes per 21 miles

YOU DID IT! Congratulations!