1 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 3 hours while the other person took 8 hours, 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. Vocabulary – Rate: A ratio comparing two quantities, often a comparison of time. For example, miles per hour. 60 miles 1 hour

2 Type of Fundraiser Time Expected Profit Cookie sales3 weeks$500 Car washes4 weeks$700 Recycling week$85 Yardwork2 weeks$ 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. a)How much will the class members earn if they spend six weeks doing yardwork? b)How much will they earn if they spend six weeks having car washes? Be prepared to explain your reasoning. c)How much money would the class earn if it recycled bottles and cans during the next three weeks of school?

3 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… profit from cookie sales 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. Justify your recommendation to the class officers. Which fundraising activity they should do? Be sure to justify your recommendation with details about rates. Discussion Points What can we compare? Which fundraising activity raises money faster? Which raises money slower?

4 Further Guidance 3. Isabelle decided to see how long it would take to earn $5000 with each kind of fundraiser. a)For how many weeks would the class need to sell cookies in order to earn $5000? b)For how many weeks would the class need to have car washes to earn $5000? c)How can this help Isabelle decide which way will earn more money? 4. Liam thinks that the class could earn $175 each week by washing cars. a)Is this reasonable? How could he have figured out this amount? Discuss his claim with your team and record your ideas. b)How much could the class earn during one week of cookie sales? Show your work. c)How can this help Liam decide which fundraiser will earn more money? 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 12 weeks. a)Why do you think Nicolette chose 12 weeks? b)How much could they earn from each activity in 12 weeks? c)Write a pair of equivalent ratios (as fractions) for each of the relationships in parts (a) and (b) above. d)How can this help Nicolette decide which way will earn more money? 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.

5 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. a)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. b)Trinh described the profit from lemonade sales as earning at a rate of “$325 in two weeks.” A rate is a measure 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?

6 Tonight’s homework is… Review & Preview, problems # 9-13 Show all work and justify your answers for full credit.