# Lift the Rainbow

Deepen your students’ understanding of volume with this sweet weightlifting challenge:

### Challenges

1. How many Skittles are in Marshawn Lynch’s barbell plates?
2. How much do the Skittles weigh?

### Setting

All of the images above were created for a football-themed promotional series (Fall 2014) posted on the official Skittles tumblr website.

### Lesson Notes

Play this video to set the stage. Then display the following image…

…and ask students to record 2-3 things they notice. After a moment or two, ask volunteers to share one or more of their responses. Make a record of their observations. Then ask: “How many Skittles do you think are in those plates?” (As an alternative, you could turn this into a more open-ended task by inviting students to notice and then wonder, and then develop the lesson by pursuing one or more of these student-generated questions.)

Have students write down three guesses (here I’m borrowing heavily from Dan Meyer, Andrew Stadel, James Cleveland, and someone else):

• A guess that is too low
• A guess that is too high
• A guess that is just right

The too low and too high guesses will help students build a framework for their “true” estimate. Students who might otherwise decline to participate in estimating—because they “have no idea”—will often join in when asked for these boundary guesses at the outset.

Another advantage to having students make guesses (and actually write them down) at the start of a problem is that it increases their interest in the problem, anywhere from marginally to dramatically. This is no longer just a math problem. It’s an opportunity to be more or less right than a classmate, to get closer than the try before, to reason at the end about our “offness” (or lack thereof), etc.

With the guesses recorded, now comes the task of calculating an answer. Students will need some additional information before they can proceed. Display the following image…

…and then ask them how they think these official plates compare to those filled with Skittles. My estimate (I am still waiting for a reply from @Skittles regarding exact dimensions) is that the Skittles-filled plates (or cylinders) have roughly the same diameter (17.5 inches), and that their height (measured horizontally here) is slightly less than that measure. (I went with 15 inches.)

Two cylinders, each with diameter 17.5 inches and height 15, give a total volume of:

Next, students will need to relate the volume back to the original question (number of Skittles). To do so, it would be helpful to have a smaller reference point relating volume and number of Skittles. To fill that need, display this image:

With that information, we are now just a few calculations away from the answer:

On the one hand, I’m feeling pretty amazing about the “offness” of our answer (less than 1%). However, I’m not sure if “more than 100,000” refers only to the Skittles in the barbell setup, or to all of the Skittles in the photo shoot.

Questions for students to consider before moving forward:

• How did your answer compare to the one given (indirectly) by Mars Inc.?
• Whose answer do you think is more reliable? Why?
• Describe one or two ways you could go about reducing your error.

To determine the weight, students will need some additional information:

There are a number of ways to proceed. Here is one approach:

According to a Mars Inc. spokesperson, more than 100,000 Skittles weighing more than 500 pounds were used in the photo shoot:

If our assumptions (and calculations) are accurate, it appears that there might have been as many as 300,000 Skittles in the shoot—if indeed the total weight was over 500 pounds. (If you watch the video again—or look at this photo—you can see that the Skittles in the barbell plates account for well under 50% of the Skittles in the room.)

Whatever the case, there are a number of rich discussions that might follow this task depending on what your students focused on, struggled with, etc.

### Extensions

1. How much would it cost to purchase that many Skittles?
2. How many Skittles are in a “rainbow”?
3. How many Skittles are in this container?

Two additional images that may help with the extensions:

### Super Extension (via @mathbutler)

• Have students design barbells they think they could lift.

### Key Standards

• CCSS 8.G.C
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
• CCSS HSG.GMD.A
Explain volume formulas and use them to solve problems

### Supporting Standards

• CCSS 6.RP.A
Understand ratio concepts and use ratio reasoning to solve problems.
• CCSS 7.RP.A
Analyze proportional relationships and use them to solve real-world and mathematical problems.