Finals Week Day 1

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SWBAT: • Define rate and give examples of how they can use rates. • Describe the problem posed in “Finals Week” and identify the needed information. • Brainstorm ideas of how to solve the problem. • Use a strategy to solve the problem and show their math thinking. • Use peer feedback to revise their solution and work.

Big Idea

Which drink has the strongest caffeine concentration? How will you figure out this problem? What information do you need to figure this out? Students work on this problem for the first of two lessons.

Notes about this 2 Day Investigation

This problem was created by Dan Meyer.  The videos can be found at

For this two-day investigation, I Create Homogeneous Groups.  Students will be in groups of 2-3.  Students will complete their work on this problem in the next lesson.

At the end of each page there is a self-evaluation.  I want my students to reflect on the same questions that they think about when reflecting during the Ticket to Go:

  • Did I come to class prepared?
  • Did I follow classroom expectations?
  • Did I try my best?
  • Did I support the learning of other students?

Do Now

7 minutes

See the Do Now video in my Strategy Folder for more information on 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 define rates in their own way and to think about different strategies they have to use with rate problems.  Students may mention tables, graphs, unit rates, double number lines, and equivalent rates. 

Students participate in a Think Pair Share with a partner about their answers.  I call on students to share their ideas with the class.  I write the strategies on the board so students can reference them during their class work.  


8 minutes

I read this sentence out loud, “She wanted to know which drink was more concentrated.”  I ask students what concentrated or concentration means.  Students study this in science and may connect the words to a lab they work on.  I want students to know that if a solution is more concentrated, then it has a higher proportion of the substance compared to other substances.  I have a volunteer read the problem. Students participate in a Think Write Pair Share. Some students may create equivalent fractions such as 4/12 and 3/12 to compare the amount of fruit punch mix.  Other students may be able to compare the two fractions and determine that 1/3 cup of mix for 3 cups of water is more concentrated.  If students struggle, I ask them to look at the strategies we brainstormed and think of one that they could use. 

I call on students to share out their ideas.  I want them to recognize that Gwen’s fruit punch is more concentrated because she has more fruit punch mix than Aida, and they both have the same amount of water.  I ask students, “If you had some of Aida’s and Gwen’s fruit punch, would they taste differently?”  Some students may make a connection to a time where they made lemonade or Kool-Aid.  If you use the same amount of water, the drink with more mix in it will taste sweeter or stronger.  Although with Aida and Gwen’s drinks they may be too close to tell.

Introduction to the Problem

10 minutes


I ask students what they know about caffeine.  I give a disclaimer that students should not try what happens in the video at home J.

We watch the video and students take notes on what happened.  After the video, I read over the questions.   We watch the video again and students add anything they missed to their notes.  I have students share out about what they notice and what they wrote down.  I want students to generate questions about the problem.  These questions will most likely be about the information students need like, “How big is each drink?”  or “How much caffeine is in each drink?”.

After students have shared the questions, I present the information about the name of the drinks, the size of the drinks, and the amount of caffeine in each drink.  Students record this information in their packet.

Brainstorming in Partners

7 minutes

Students move into their partner pairs.  I explain to students that they are going to spend five minutes brainstorming with their partner how they can solve the problem and why they think this idea will work.  These ideas need to be written on the brainstorming page.  When partners find an idea that they agree on, they will raise their hands.  I will check in quickly with each pair to scan their idea.  If they are on track I will tell them to move on to the “Focusing on one idea” page to work on solving the problem.  For students whose idea is off-topic or not specific enough, I ask them questions about the problem and what they need to find out.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Focusing on One Idea

23 minutes

As students work I walk around and monitor student progress and behavior.  Students are engaging with MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, MP4: Model with mathematics, and MP6: Attend to precision

If students are struggling, I may intervene in one of the following ways:

  • Ask them to compare and contrast the finals week problem with the fruit punch problem.  What is similar? What is different? Can we compare caffeine concentration just by looking at the amount of caffeine?  Why or why not?
  • Ask them to make a guess about which drink has the highest caffeine concentration.  How can you prove whether or not your guess is correct?
  • Ask students how they have solved problems comparing rates before.  Can you apply any of those strategies to this problem? 
  • Allow students to use a calculator to help them check their calculations. 

If partner pairs need an extra challenge, I may ask them:

  • What is another way you can solve the problem to confirm your answer?
  • Which drink gets you the biggest “bang” for your buck? Or, which drink is the best value for the amount of money spent?

My goal is that students have part of the question answered by the end of the work time.  I want each student to record and show his or her work on the “Focusing on one idea” page.


5 minutes

For Closure I ask students these questions:

  • What is a rate?
  • What is the finals week problem about?
  • What is one strategy you and your partner used today?

Students participate in a Think Pair Share.  I call on students to share out their ideas.  Instead of giving a ticket to go, I collect students’ work.  Before the next lesson I quickly look over students’ work.  I write at least 1-2 questions on each partner pairs’ work. 

Example questions:

  • What units/labels belong with this data?
  • How can you organize your work so others can easily understand it?
  • Why do you think this drink has the highest caffeine concentration?  Prove it.

What is another way you can solve this problem to support your answer?