M&M+double+bar+graph


 * NCTM Content Standards:**


 * NCTM.5-8.1.5.11 || ... use mathematical modeling to solve real-world problems ||
 * NCTM.5-8.1.5.12 || ... use counting to enumerate and order; use matrices, finite graphs, and trees to model problem situations; describe basic algorithms for accomplishing tasks ||
 * NCTM.5-8.1.5.5 || ... use both descriptive and inferential statistics to analyze data, make predications, and make decisions ||


 * Maryland Content Standards:**
 * MD.MA.5.4.A || STANDARD: KNOWLEDGE OF STATISTICS – Students will collect, organize, display, analyze, or interpret data to make decisions or predictions. ||
 * MD.MA.5.4.A.1 || >Collect, organize, and display data ||
 * MD.MA.5.4.A.1.1 || > Collect data by conducting surveys to answer a question ||
 * MD.MA.5.4.A.1.4 || > Organize and display data in double bar graphs · Assessment limit: Use no more than 4 categories and intervals of 1, 2, 5, or 10 and whole numbers (0 – 100) ||
 * MD.MA.5.4.B.1.3 || > Interpret and compare data in double bar graphs · Assessment limit: Use no more than 4 categories and intervals of 1, 2, 5, or 10 and whole numbers (0 – 1000) ||

The first thing that I would do is ask the class, “Have you ever wondered why it seems that there are always the fewest of your favorite M&M color in a bag of M&M’s?" Have students respond and then guide the class into a short discussion on how many M&M’s they think there should be of each color in a bag of M&M’s. Some students may think that the bag should be equal of each color and some students will think that there is definitely more of one color or another. Ask the class if it is the same for chocolate and peanut M&M’s or would the amount of each color be different for each type of M&M. After discussing their theories as a class, ask the class what can we do to try and figure out an answer to our question. The students should be able to tell you that we need to collect data.
 * Launch:**

Make sure the class understands that before we start no one is to open their bag of M&M’s or to eat their M&M’s until they are told to do so. Pass out a data sheet and a bag of chocolate and peanut M&M’s to each student. First the students record their estimates for home many M&M’s are in the bag and how many M&M’s there are of each color. After recording their predictions the students open the bags and record the total number of M&M’s for each bag and the number of M&M’s per color in each bag. After collecting data the students create a double bar graph to display their data. Show the students an example of a double bar graph and remind students to have a title, use appropriate intervals, and to make a key.
 * Explore:**

When students are finished they will discuss as a class what they had found. Discussion topics may include if there really is more of one color and if it is the same for chocolate and peanut M&M’s
 * Summerize:**

For students who finish early they can get in a small group and share their data. As a group they would then find the mean, median, and range for each color. They will they find the mode of the colors (which color appeared the most). If that is completed students may then write a short paragraph explaining the results of their study.
 * Extra Activities:**

For an extension you can have a large bag of M&M’s that have already been counted. You can give the class the data and have them use that to create a second double bar graph for homework. They can also analyze the data to see if there is a relationship between the small and large bags.
 * Extention:**

I feel that my lesson went very well. It was easy to launch the lesson because as soon as I started ranting about my there is never enough of my favorite color of M&M’s in the bag the class was hooked. A lot of the students had thought about this same question and they were motivated to see if there really was more of a certain color of M&M. My teacher had given me a few small suggestions such as showing the class that their estimates for each color need to add up to the total estimate. She also suggested that I show the class an example of a double bar graph since they were not that familiar with them. For the most part all of the graphs that the students made turned out really well. I did have one student make a line graph and I talked to him one on one and explained to him that line graph show something over time. Some students also made there graphs small, instead of spacing out the numbers on the y axis to make the graph more visible. The main consensus of the students was that they liked the activity but they did not like having to write the five sentences at the end describing their graph. It would be nice to just have a class discussion without making the students have to write anything. But in reality students are required to write across the curriculum. So even though they did not like having to write a few sentences they all liked the lesson and I feel that they all got a lot out of it.
 * Reflection:**

I would improve upon and do a few things differently if I were to be able to teach this lesson a second time. The first think that I would do a little differently would be to put numbers in the estimate section on the overhead and have the class tell me what is wrong. I would make sure that the estimate of each color did not add up to the estimate for the total of M&M’s this was a common mistake that the students had. They would guess that there were 15 M&M’s in the bag and then when they estimated how many there were of each color it added up to over 20 M&M’s. I would also discuss with the class on the purpose of a double bar graph is to compare two sets of data. In this case it would be peanut and chocolate and in my example of a double bar graph it was boys and girls.