Nana's Chocolate Milk

This packet is broken down into small chunks and I teach it before students start Unit 5 on ratios and rates.  It helps if students work on the packet over a week or two.  The problem gets students thinking about the relationship between the milk and chocolate and pushes them to come up with a mathematical solution.

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?

Students independently complete page 1.  Students participate in a Think Pair Share with a partner about what it looks like and feels like to persevere.  I ask students, “Does it take courage to persevere?”  I want students to recognize that problem solving is difficult and can be frustrating, but it is important to work through it and keep trying.

Students participate in a Think Write Pair Share.  Some students may share about strategies like drawing a picture or using manipulatives, while other students may talk about taking a break and then going back to the problem or rereading information.  I want students to write down these strategies so they can revisit this page if they get stuck later while working on the problem.  

Note:

• Dan Meyer’s video can be found at http://threeacts.mrmeyer.com/nana/act1/act1.mov

I ask students if they have ever had to follow a recipe to make something.  I tell students they are going to see a problem involving a recipe.  I preview what students should be looking for on page 3. 

We watch the video and students take notes on what happened.  After the video, I ask students, “How can Dan fix the glass he has just created?”  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 the students to have the recipe and what Dan actually made written down so they can refer to it later.

Note:

• I may start this section on one day and have students revisit and finish brainstorming the next day.

Students participate in a Think Write Pair Share about ideas on how to fix Dan’s glass of chocolate milk.  Before students share out, I remind them that I am not asking for an answer.  I am asking for a general idea.  I record students’ ideas on the board.  Students will say to start over, and I tell them that this is not an option.  I repeat the question, “How can Dan fix this glass of milk?”  Students will mention add more milk, add more milk and chocolate, take out some chocolate, among other ideas.

Notes:

• Once students are finished with this part, I collect student work.  I read over students’ ideas and I write 1-2 questions that I have about their idea.  Some of these questions are, “How much milk are you going to add?  Why?”  “How could you use math to show that your idea will work?”  “Why are you adding _______ milk/chocolate?” Many students start with an idea that needs more details and specifics.
• A common misunderstanding is some students think they can remove some of the chocolate.  I remind them that Dan has already stirred the milk so that all of the chocolate has dissolved.
• If students are struggling, I may give them red/yellow counters or double number lines so that they can create a visual of the recipe and what Dan did.

We watch the Act One Video again.  I ask a volunteer to explain the question.  Students need to understand that “starting over” is not an appropriate response to this question.  I tell students that I will be collecting their work and reading over their idea.  I remind students that they need to show their work so that I can easily understand their idea.  If they are drawing pictures I want them to label the picture and explain what they are doing.

I pass back students’ work so they can read over my questions.  I explain that they are going to find out some new information that may affect their idea.  I tell students, “The glass won’t hold two cups of liquid.  How does that affect your solution?”  This serves as a way to challenge students who came up with the idea of adding another cup of milk and 3 scoops of chocolate to create a double batch of chocolate milk. 

I ask students if someone has an idea that now won’t work.  I have a student explain the double batch idea and why they think it would have worked.  This explanation can help other students who are still struggling.  

I ask students to share the new information that we found out.  Students work on revising and changing their work independently.  I walk around and monitor student progress.

I may ask some of the following questions:

• What is your plan?  Why will it work?
• Exactly how much __________ are you planning on adding?  Why?
• How could you use math to show that Nana will approve of your glass of chocolate milk?
• What kind of diagram can you create to show your thinking?

If students come up with a correct plan, I will ask them some of the following questions:

• What is another way you could solve this problem?
• What if Nana wanted the same kind of “chocolateyness” but…
  • Only had 1 scoop of chocolate?  How much milk should she add?
  • Only had ¾ cup of milk?  How much chocolate should she add?
  • Used 9 scoops of chocolate?  How much milk should she add?
  • Was making a large batch?  If she used 5 ½ cups of milk, how many scoops of chocolate should she add?

I ask students to think about these things, “What makes useful feedback?” “When giving feedback I should…” “When receiving feedback I should…”  I review the rubric for showing work.

I give examples of how to give constructive feedback:

• It’s good that you have created a picture to show your work, but I am confused about what it means.
• You explain your plan but you don’t use math to prove that it will work.
• You have a good start with adding milk, but you don’t say exactly how much you will add and why.
• Why do you think your plan will work?

Students switch papers with a neighbor and take a few minutes to silently read their partner’s work.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.  They record their feedback.  Then students talk with their partner and share their feedback and ask questions.  I ask students, “How did it feel to receive feedback?  What did you partner do well?  Why is getting feedback important?”  I explain that as students and adults they will receive feedback from teachers and employers.  Nobody’s perfect and feedback helps us to keep improving!

I review the rubric for showing and explaining work.  Students take a minute to review their feedback from their peer.  Then they work independently to revise their solution so that they show and explain their mathematical thinking (MP1).  I walk around and monitor student progress.

Students put their revised solution on their desks with a peer feedback sheet (students can also create their own feedback sheets on notebook 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.

With about 10 minutes remaining, students return to their seats to read over their feedback.  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?”

We watch the Act 3 video (http://threeacts.mrmeyer.com/nana/).   I ask students to explain why Dan’s solution works.  I tell students there is more than one way to solve this problem.  I ask other students to share out other ideas for solving the problem.

Once students have started learning about ratios, I will bring up Nana’s Chocolate Milk problem to see how their thinking has evolved.