Finals Week Day 2

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SWBAT: • Define rate and concentration. • Use a strategy to solve the problem and show their math thinking. • Use 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 second of two lessons.

Notes about Teaching This

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 review the definition of a rate and what it means if a solution is “more concentrated”.  If students struggle I have them look back at their notes about concentration in the previous lesson.  While students work I pass back their “Focusing on One Idea” papers with my comments/questions. 

Students participate in a Think Pair Share with a partner about their answers.  I call on students to share their ideas with the class.  

Revising Work

20 minutes

Students move to work with their partners.  I pass out the show and explain rubric and review it with students.  I remind students that they will have 15 minutes to take my questions and feedback and revise their work.

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? (I print out a copy of the cost picture from the Finals Week website).

My goal is that students have their revised answer on the “My Solution” page.

Gallery Walk

20 minutes

Student puts their revised solution on their desks with a lined sheet of paper.  The paper has 3 columns (+ = strengths, delta = area that can be improved, ? = question).  When I say go, students have to find a different desk to sit at before I count down to 0.  I start the timer and students have a minute and a half to analyze the work and write feedback.  The number of rotations will depend on how efficient students transition from desk to desk.


13 minutes

For Closure each student gives him/herself a score on the “Show” and “Explain” parts of the rubric.  I ask students to share out, “What did you find interesting about your classmates’ work? What did you do well?  What can you improve on?”

I ask students by a show of hands which drink hast the highest caffeine concentration.  If students say that the 5 Hour Energy has the highest concentration of caffeine, I ask how that can be if it has fewer milligrams of caffeine when you compare it to the Double Gulp, the Monster, and the Starbucks Grande Coffee.  I want students to be able to explain what it means for a drink to have a higher concentration of caffeine.  I call on students who used different strategies to come up to the document camera and show their work.  I ask students to share their comments about the student work.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

If I have time, I ask the sequel question from the website, “Which drink gets you the biggest “bang” for your buck? Or, which drink has the best value?”  Students should realize that they would need the cost of each drink in order to determine this.  I show students the cost picture.  Students participate in a Think Pair Share.  I call on students to share out their ideas.   Students will not have time to calculate the answer, but I want students to use their estimation skills to make an educated guess.  I ask students what they would need to do in order to see if their guess is correct.  Through this conversation I can see if students can apply what they worked on with the concentration problem to a slightly different scenario.

Instead of a ticket to go, I collect student work so I can evaluate it.