# Ratios and Rates Involving Fractions

Fraction review

• Glencoe: P. 680 Lessons 2-3 through 2-6 (by 3’s)

Finding unit rates involving fractions.

Finding unit rates involving fractions.

#### Wrkst – Unit rates involving fractions

Equations and graphs of proportional relationships involving fractions

Essential Question: Can we use equations and graphs to represent proportional relationships arising from ratios and rates involving fractions?

7.RP.2c, 7.RP.2d, 7.RP.3

Warm up

Example 1: Mothers 10K Race

Sam’s mother has entered a 10K race. Sam and his family want to show their support of their mother but they need to figure out where they should go along the race course. They also need to determine how long it will take her to run the race so that they will know when to meet her at the finish line. Previously, his mother ran a 5K race with a time of 1 1⁄2 hours. Assume Sam’s mother ran the same rate as the previous race in order to complete the chart.

Discuss with your partner: Can you find Sam’s mother’s average rate for the entire race based on her
previous race time?

Lesson

Example 1: Continued

Discussion

d. Write the equation that models the data in the chart

Example 2: Organic Cooking (Group Work)

Summary

Exit

Multi-step ratio problems

• Glencoe: 4-3 Get Ready, Ex 1-3

Solving proportions

How much sugar is in each bottle?

Part 1 – Act One

How many sugar packets do you think are inside a 20-oz bottle of soda?

Write down a guess for each of the following:

• Give an answer you know is too high.
• Give an answer you know is too low.
• Guess as close as you can.

Discussion: What information do we need to answer this question?

Hint

Finding the number of packets

Using the information gathered, find the number of packets in a 20 oz. Coke bottle.

Assignment: DM Sugar Proportions

Part 2 – Challenge

Compare sugar content of each beverage

• Find the number of sugar packets in your group’s beverage
• Rank the beverages from least to greatest number of sugar packets

Part 3 – Representing data

• With your group, decide how to best represent the amount of sugar in each beverage and create a graphic.

• Glencoe: 4-3 Get Ready, Key Concept, Ex 1-3
• P. 201 (1-15)

Activity

Highway Robbery (NCTM)

Dear Detective,

Someone has robbed the National Bank of Illuminations in Washington D.C. It is your job to use the clues left by the perpetrators to locate and apprehend the robber. Your tools will be your power of deduction and your mathematical knowledge. Good luck cracking this case! Sincerely, Captain P. Thagoras

CLUES:

• The perpetrator is _____cm tall in the security camera image.
• _____pounds of quarters were stolen.
• The getaway car was a silver 1989 HN Cosine which travels _____miles per gallon of gas.

Highway Robbery Clue Sheet

Formative Assessment:

• IM (180)
• Inside Math. (Mixing Paint, Cereal, Lawn Mowing)
• NCTM (L510)