M&M's®

Task

Conduct an investigation to determine the validity of these numbers. Do your investigation results agree with these numbers? Are the officials right?

I read this interesting "Did You Know...." tidbit in the February 1995 NCTM Bulletin. I had used M&M's® in the past for calculating fractions, percents, assigning probability and collecting statistical data. As I was in the middle of working with my heterogeneous group of sixth and seventh grade students on fractions and percents, I thought they might enjoy testing the credibility of the Mars® Corporation.

What This Task Accomplishes

This task addresses nine of the 13 NCTM Curriculum Standards for grades 5 - 8. (See the Exemplars matrix.) It definitely engaged the students and provided an opportunity to use skills for scientific discovery, as well as math problem-solving skills.

What the Student Will Do

Students were asked to bring in 47.9 gram (1.67 ounce) bags of plain M&M® candies as a homework assignment. I suggest you ask them to bring them in the day before you want them, as some are bound to forget. A few brought different sized bags and that only added to the complexity of the task, as the news item did not specify any one size of bag. If students were without M&M's®, I paired them up with those who had them. You can do very nicely with two students per bag.

I had them estimate the number of M&M's® in the bag before opening as an added exercise. They then sorted, counted, established fractions and percents for each color. At this point they posted individual results onto a class chart and determined the percentages from the larger sample. They then decided if they agreed with the Mars® statement. Many attempted to determine why the numbers might be different. Most were concerned since the net weight of the package was listed to the nearest tenth of a gram, and if each M&M® weighed almost a gram that there was a range of 10 M&M's® per bag in the class sample. They felt that the company should be more consistent than that. They were madly calculating the mass of various M&M's® at press time, looking for an explanation.

Time Required for Task

60 minutes

Some groups did work outside of class time to complete the write up of the task.

Interdisciplinary Links

Learning to question statistics read in the press is a useful life skill and crosses all disciplines. Students used their science discovery skills to carry out the investigation.

Teaching Tips

Have the students bring in the M&M's® the day before you do the investigation to be sure they do not forget them. Have them empty the bags onto clean paper rather than desk tops if they plan to eat them at the end. The task of compiling class data is easier if all students use the same size bag. Perhaps challenging them to compare results with large size bag numbers, as an at home assignment, would be interesting. It takes a long time to count them all in class. Encourage kids to think of reasons for the wide range of numbers of candies in the bags within the class. Have a scale or balance available to mass a sample.

Suggested Materials

• Calculators


• Balances or scales (for massing/weighing M&M® samples)


• Extra bags of candy (for those you know are unable to bring one)

Possible Solutions

Solutions will vary. The larger your sample size, the closer to the Mars® percentages you will come. Their numbers are quite close to those we found.

Benchmark Descriptors

Novice
This student does not recognize the difference between the number of candies and the percent of each color candy in the bag. The student managed to count and sort the colors. S/he did attempt a mathematical representation (the original was color coded). The final chart contains information about the individual bag only and not the class result figures.

Apprentice
This student has a basic understanding of the task, but fails to communicate the solution clearly. "Using a chart" is not actually the way in which the solution was derived. The chart does list the student's percentages as compared to Mars® percentages, but the "Class Average" column leaves one guessing. The student makes no attempt to explain the origin of the percentages listed. While the "connection to life" comments are interesting, they are not mathematically relevant comments.

Practitioner
This student understood the task and set about successfully finding percentages of each color in one bag and comparing those percentages with the class average percentages. The bar graphs are accurate, but might have been more effective as a communication tool if all three sets of percentages (individual, class avg. and Mars®) were graphed on the same axes for comparison purposes. Additionally, I wish the student had pursued the point that, "All the percentages equaled 114%." I think it had to do with "rounding up" both by individuals and again in finding the class average.

Expert
This student communicated understanding of the task clearly. While lacking a title, the chart does present information clearly. The observation that the results might not agree with Mars®, "because the numbers are way off from each other," shows good reasoning. In the discussion of finding percents, the student uses the term "estimating" in place of "rounding", which is actually what was done. A true Expert might have gone further by trying to account for the discrepancy between Mars'® claim and the students' findings, but this student did Expert work to this point. Perhaps a discussion of "next steps" would encourage students to take the initiative to do so.