The State Fair

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SWBAT: • Use multiplication and division to solve problems involving equivalent rates. • Use tables to represent and describe relationships. • Apply different strategies for explaining comparisons between quantities.

Big Idea

Which store offers the best deal for tickets to the state fair? How do you know? Students apply what they know about equivalent rates to answers questions.

Do Now

10 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to review what they know about comparing rates.  I want to make sure that students understand that they can compare rates that have a common measurement.  For instance, some students may calculate the amount of time it takes each runner to run a mile and then compare to see who runs the mile in the lowest time.  Other students may create equivalent rates showing how long it takes each runner to run 6 miles.  The runner who runs 6 miles in the lowest time is the fastest. 

As students are working on the do now, I walk around and see what strategies students are using.  I use this time to identify students who are using different strategies.  When we come together, I call these students up to the front to show and explain their reasoning.  I ask the class if they agree or disagree with the student’s work.  Students are engaging with MP3: Construct viable arguments and critique the reasoning of others.



5 minutes

Before students work with their groups, I want to review these questions together.  Students participate in a Think Write Pair ShareI want students to write down their ideas so they can use this as a resource if they struggle with the next set of questions.

The State Fair

23 minutes


  • Before this lesson, I use data from the previous lesson’s ticket to go to Create Homogeneous GroupsStudents work in groups of 2-3.
  • I give each group a Group Work RubricThis way I can silently give them feedback on their cooperation throughout the work time.  This will be their citizenship grade for the day.
  • I have calculators ready if there are students who are still struggling with multiplying and dividing.  Even if they use the calculator, they must first set up and label the rates.

Students move into their groups.  I call on a student to read the situation.  I call on a different student to read question 1.  I re-emphasize that there are different ways to solve this problem.  It is important that students show their work.

As students work, I walk around and monitor student progress and behavior.  I take note of different strategies that students are using.  I will use this information to help me during the closure. Different groups will work at different paces and that is fine.  My goal is for all groups to complete question 1 and show their work.  Students are engaging in MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, MP4: Model with mathematics, and MP5: Use tools strategically.

If students are struggling, I may ask one or more of the following questions:

  • What is the problem asking?
  • What do you know?
  • What specifically is your question?
  • What notes did you write down for the questions at the beginning of the packet?
  • How much do the ticket booklets cost at each store?
  • Which store charges the most for a booklet of tickets?
  • Does this mean that the tickets are most expensive at City-Mart?
  • What makes it hard to determine which store has the best deal?
  • What strategies have you used in problems similar to this?
  • How could you make it easier to see which store has the best deal on tickets?

If students need extension, I may ask them one or more of the following questions:

  • How are these problems related to finding equivalent rates?
  • Suppose you own a store and decide to sell tickets to the State Fair as well.  You decided to keep the ticket booklet price competitive with the other stores in town.  How many tickets would you include in one booklet?  What price would you charge for a ticket booklet? 
  • Karen’s school collected exactly 300 tickets from these stores as a donation for the students.  List the number of booklets each store could have donated if all the stores donated at least one booklet.

Closure and Ticket to Go

12 minutes

I use what I noticed during the group work time and I call students up to show and explain their strategy for finding the best deal.  As students present, we create a list in their packet of the different strategies.  These strategies could include:

  • Find unit rates
  • Find same amount of tickets, then compare cost
  • Find the same dollar amount and then compare number of tickets (This was more complicated with the prices in this problem)
  • Think about them as fractions and find common denominators
  • Make a table

I have students star the strategy they used.  I want them to circle a strategy they did not use, but that makes sense to them.  I ask them to use this strategy to answer the question in the do now.

I pass out the Ticket to Go and the HW The State Fair.