# Decisions, Decisions

## Objective

SWBAT apply principles of probability to analyze quality control systems.

#### Big Idea

Can we be sure about our candy if we're only examining one package out of one thousand? Use probability to help answer this question

## Set the Stage

5 minutes

I begin class with this short clip about making M&M's.

This gets my students engaged and ready to participate in a discussion about just how well the packages of M&Ms actually do match up for color and size.  There always seems to be at least one student with an anecdote to share about getting a bag with an odd-sized or odd-colored M&M, which just adds to the discussion.  I ask questions to lead them to consider what level of consistency might be reasonable, given the millions of M&Ms made and sold.  It's often difficult for my students to propose an appropriate gauge of consistency, so I tell them that today they will apply mathematics and look at probabilities to answer that question.

## Put It Into Action

35 minutes

For this activity I have my students working with M&M candies, but you could use other candies that come in small packages like Smarties or Skittles.  I explain why candies are important to this lesson in my video.  I also have access to electronic balances to measure mass, but if you don't, you can have your students measure the diameter of each candy at its widest point instead.  I tell my students that they will be working with their back partner for this part of the lesson.  I distribute the Candy Quality Control Challenge, ask if there are any questions, and tell them they have about 35 minutes to complete this activity.  (MP1, MP3, MP4)  While they're working I walk around offering encouragement and redirection as needed.  One of the first questions asked is always "Can we eat these?" to which I reply "Read your handout."  Questions that require a bit longer response might be "We don't remember how to measure mass?" or "How do we create a table?  What should we include?"  For the first team, I'll give direct instruction, demonstrating how to use the balance.  For the second team I'll ask questions to give them guidance like "What kinds of information are you supposed to record or measure?" or "How many different things will you need to make columns for? rows?".  After about 35minutes or when everyone is done, I remind them to turn in their work and "dispose" of the candies.

## Wrap It Up

10 minutes

I close this lesson by asking my students to write a letter to the Mars Candy Company either congratulating or castigating them, and offer their recommendations, depending on their results.  I tell them they need to write using proper grammar and complete sentences and should include the mathematics that supports their statements. (MP3) This gives them an opportunity to put their thoughts into writing and to reinforce what they've learned.