M&M+Activity

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**M&M Distributions** **Adapted From:** “Variability in Categorical Data” from Data Distributions, //Connected Math 2// **Reference:** Lappan, G. Michigan State University. National Science Foundation (U.S.). Pearson Education, I., & Connected Mathematics (Project). (2009). //Connected mathematics//. 2[nd ed.] Boston, Mass.: Pearson. (M&M company data is no longer available on their website. Email the manufacturer to verify the information.)

**CCSS-M Content Standards: 7.SP.1, 7.SP.2** **CCSS-M Practices: 2, 3, 4, and 5**

**Task:** **Day 1:** > Teacher circulates around the room posing questions to guide the students, since comparing the number of each color will not work if the bags have different quantities. The goal here is to have students calculate the percentage of each color in terms of the number of M&Ms in their bag. **Day 2:** > >
 * 1) Teacher provides students with a mini history of M&Ms including how they began as a treat for soldiers.
 * 2) Students should be seated in groups of 3. Teacher passes out a bag of M&Ms to each student. Students are directed to create a frequency table for the colors of the M&Ms in their bag. Once each student has created their table, each group should discuss the following questions:
 * Is there an even number of each color in a bag of M&Ms?
 * Is the number of each color of M&Ms the same as your group members?
 * 1) Once a group of students has calculated relative frequencies, teacher poses the following question to them: "Does the M&M company have a specific distribution of colors in each bag?" Students should be prepared to justify their reasoning.
 * 2) Teacher brings the class back together and chooses a few groups to share their results with the class.
 * 3) Teacher collects the data from each student in the class and compiles it into a frequency table. Teacher should compute the percentages for each color and list in the table as well.
 * 1) Teacher passes back students’ data from previous day.
 * 2) Teacher displays the table created with the data from the whole class. Teacher leads a discussion about the class percentages of the compiled samples on the following topics:
 * Difference between student sample, class sample and population of M&Ms
 * If and how the percentages changed with a larger sample.
 * If the class sample represents the population distribution supplied by the M&M company. (24% blue, 20% orange, 16% green, 14% yellow, 13% red and 13% brown)
 * 1) Teacher explains more of the history of the M&Ms company that in 2004 M&Ms were only black and white for a short amount of time and then the colors came back. Teacher poses a question to the class: "What are some of the reasons that M&M could have stopped production of colored M&Ms for a while?" Sample answers: Packaging, change in colors, number of colors, and distribution of colors. Teacher should probe to get distribution of colors as a possibility.
 * 2) Teacher passes out one of three random samples from pre-2004 to each group. Students in their groups should examine this data to discover what the M&M company did in 2004. Students should discover that the colors and number of colors stayed the same and question the distribution of colors.
 * 1) Teacher brings the class back together to have a discussion about the students’ findings. After the concept of distribution of colors and sample size comes up, teacher will provide the students with a larger sample, 30, of pre-2004 distribution.
 * 1) Each group compares the pre-2004 data to the post-2004 data and draw inferences on how the distribution of colors changed.
 * 2) Teacher then brings the class back together and has groups share their conclusions.
 * 3) Teacher closes the lesson by summarizing the importance of sample size when making inferences and how large of a difference constitutes a change in distributions.

**PD Agenda:** **Length of session:** 1.5 hours **Materials needed:** Pre-2004 M&M data, Bag of M&Ms for each participant ***Note: Facilitators will model how the lesson should be carried out in the classroom with pedagogical discussions interwoven throughout. All time lengths listed below following each component of the activity are estimates and not strict time allotments.**
 * 1) Participants (teachers) are seated in groups of 4-6 to encourage discussion and collaboration.
 * 2) Participants begin the activity just as students would. As groups finish collecting their data from the bags of M&Ms, they enter the data into a Google document spreadsheet. Facilitators circulate around the room monitoring, facilitating and selecting and sequencing solutions that they would like to highlight in the whole group discussion. (20 minutes)
 * 3) Facilitators choose a few groups and they present their findings. (10 minutes)
 * 4) Participants will now complete the day 2 portion of the task just as students would. (20 minutes)
 * 5) Facilitators choose a few groups to present their findings. (10 minutes)
 * 6) Facilitators lead a whole group discussion using the following questions as a start: (20 minutes)
 * Did you like this task? Why or why not?
 * What struggles did you face completing this task?
 * Do you think your students will like this task? Why or why not?
 * What struggles do you anticipate your students having?
 * What can you do as a teacher to overcome the students’ misconceptions and struggles? (Identified in previous question)
 * What are possible extensions of this task?
 * 1) Facilitators review the session’s task with the group and bring it to a close by emphasizing the key concepts (sample size, proportional reasoning, variation, compelling evidence, and informal inference) discussed in the session. (10 minutes)

**Why the task would promote conceptual understanding of this topic and if it lays the foundation for other topics in statistics:** This task promotes the understanding of informal inference by having students explore how sample size affects their inferences about the whole population. This task also introduces students to comparing two distributions and identifying if variation exists between them. This lays the foundation for more formal variation in samples.