CC Course 1
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  • Introduction
  • Chapter 1
  • Chapter 2
  • Chapter 3
  • Chapter 4
  • Chapter 5
  • Chapter 6
  • Chapter 7
  • 7 Opening
  • 7.1.1
  • 7.1.2
  • 7.1.3
  • 7.2.1
  • 7.2.2
  • 7.2.3
  • 7.2.4
  • 7.3.1
  • 7.3.2
  • 7.3.3
  • 7.3.4
  • 7 Closure
  • Chapter 8
  • Chapter 9
  • Reference
  • Teacher
  • Lesson (ENG)
  • Lección (ESP)
  • Answers
  • Teacher Notes
  • My Notes
  • Sharing

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Whenever you are trying to describe how quickly or slowly something occurs, you are describing a rate. To describe a rate, you need to provide two pieces of information. If two people each walk 10 miles, for example, it may seem like they are doing the same thing. But if you find out that one person walked the whole distance in 3hours while the other person took 8hours, then it becomes clear that they were traveling at different speeds. In this lesson, you will be describing how things change in comparison to each other.

  • 7-1. 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. Theywant your help with choosing afundraising activity.

Type of
Fundraiser / Time / Expected Profit
Cookie sales / 3 weeks / $500
Car washes / 4 weeks / $700
Recycling / week / $85
Yardwork / 2 weeks / $320
  1. How much will the class members earn if they spend six weeks doing yardwork? How much will they earn if they spend six weeks having car washes? Be prepared to explain your reasoning.
  2. How much money would the class earn if it recycled bottles and cans during the next three weeks of school?
  • 7-2. MAKING MONEY
  • The class president has decided that the students will either sell cookies or hold car washes. The rest of the officers need your help to compare the profit from cookie sales tothe profit from car washes.
  • Your task:With your team, discuss ways of comparing the two fundraising strategies to recommend which one to use. Use the data in problem 7-1 and the questions below to start your discussion. Thenwrite a note to the class officers recommending which fundraising activity theyshould do. Be sure to justify your recommendation with details about rates.
  • What can we compare?
  • Which fundraising activity raises money faster?
  • Which raises money slower?
  • 7-3. Isabelle decided to see how long it would take to earn $5000 with each kind offundraiser.
  • For how many weeks would the class need to sell cookies in order to earn$5000?
  • For how many weeks would the class need to have car washes to earn $5000?
  • How can this help Isabelle decide which way will earn more money?
  • 7-4.Liam thinks that the class could earn $175 each week by washing cars.
  • Is this reasonable? How could he have figured out this amount? Discuss his claim with your team and record your ideas.
  • How much could the class earn during one week of cookie sales? Show your work.
  • How can this help Liam decide which fundraiser will earn more money?
  • 7-5. Nicolette decided to see what the class could earn from each activity in the same number of weeks. She decided to see how much they could earn in weeks.
  • Why do you think Nicolette chose 12 weeks?
  • How much could they earn from each activity in 12 weeks?
  • Write a pair of equivalent ratios (as fractions) for each of the relationships in parts (a) and (b) above.
  • How can this help Nicolette decide which way will earn more money?
  • 7-6.Which fundraising activity raises money the fastest: selling cookies or washing cars? Write a note to the class officers recommending the fastest fundraising activity. Be sure to justify your recommendation with how you know it will raise money the fastest.
  • 7-7. The seventh-grade class was also looking at the data from problem 7-1. They had information about another fundraiser: selling lemonade. They could earn $65 every two days selling lemonade. Assume all of the fundraising activities happen only on school days, and that there are 5 days in a school week.
  • Which activity will raise money faster: selling lemonade or selling cookies? Remember that the rate for selling cookies was $500 every 3 weeks. Be sure to justify your answer.
  • Trinh described the profit from lemonade sales as earning at a rate of “$325 in two weeks.” A rate is ameasure of how one quantity changes in comparison to another. It can be expressed as a ratio or a single number.

Is Trinh’s rate of the same as earning money at a rate of ? Why or why not?

  • 7-8.Additional Challenge:Eliza is saving her allowance to buy a new computer so she can email her pen pals around the world. She currently saves $45 every 4 weeks.
  • If her brother saves $39 every 3 weeks, who saves at a faster rate? Explain yourreasoning.
  • Instead of using dollars and cents, money in Armenia is called “drams.” One American dollar is worth the same as 360 drams. Eliza’s pen pal in Armenia saves 2880 drams from her allowance every week. Work with your team to determine who is saving money faster, Eliza or her pen pal. Explain your reasoning.
  • Eliza’s pen pal in Laos is also saving money. Money in Laos is called “kips.” Her Laotian pen pal is saving 17,000 kips per week. Can you determine who is saving at a faster rate? Determine the rate or write a question that you would need answered in order todetermine it.
  • 7-9.Adam earns $36 for every four hours of work. If he continues to be paid at the samerate:Homework Help ✎
  • How long will it take him to earn $144? Show and explain your reasoning.
  • How long will it take him to earn $222? Show and explain your reasoning.
  • How could you describe his rate for a 40-hour work week? For a 7-hour day? Show and explain your reasoning.
  • 7-10. A college has a 2:3 ratio of men to women in its student body. Homework Help ✎
  • What is the ratio of women to men?
  • What is the ratio of women to total students?
  • What percent of the college is men?
  • What fraction of the college is women?
  • 7-11. For each of the following multiplication problems, first estimate the product. Then check your estimation by multiplying. Homework Help ✎
  • 7-12. Kip and Jordan are brothers. Their dad measures them once a year by drawing a line on a doorframe in their house. Homework Help ✎
  • Kip grew from 42inches to 48inches. How much did he grow last year?
  • Jordan was 40inches and grew 5inches. How tall is he now?
  • Which boy grew more last year?
  • 7-13. Draw a rectangle with an area of 22 square units. Find the perimeter of the rectangle. Label the length and width of the rectangle. 7-13 HW eTool (Desmos) Homework Help ✎

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