Ratios and Rates Involving Fractions

[expand title=”Fraction review”]

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


[expand title=”Finding unit rates involving fractions.”]

Finding unit rates involving fractions. 


Using unit rates with fractions

Wrkst – Unit rates involving fractions


[expand title=”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

S 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?




 Example 1: Continued


T  Discussion


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



 Example 2: Organic Cooking (Group Work)












[expand title=”Multi-step ratio problems”]

  • Glencoe: 4-3 Get Ready, Ex 1-3


[expand title=”Solving proportions”]

How much sugar is in each bottle?

Sugar Packets Beverages


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?


Finding the number of packets

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

Answer – Act Three

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)


[expand title=”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


  • 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)