Halloween candy math: mean, median and mode with dice, grades 6–8

1. Set the scene: "You visit five houses. At each house, roll two dice. The total is how many pieces of candy you get." Each student rolls five times and records the results.
2. Each student adds up their five rolls for a total haul. Ask: "What is the smallest total possible? The largest?" (10 and 60.)
3. Collect every total on the board. Students put them in order from least to greatest in their notebooks.
4. Find the four measures together. Mean: add all totals and divide by the number of students. Median: the middle value, or the average of the two middle values. Mode: the total that appears most. Range: largest minus smallest.
5. Add an outlier. Say: "One student found a house giving out 40 extra pieces. Add 40 to one total." Recalculate all four measures.
6. Discuss: "Which measure jumped? Which barely moved? If you wanted to describe a typical haul fairly, which would you use, and why?" Students should notice that the mean moves a lot and the median hardly moves.
7. Each student writes one sentence: "The median is a better summary here because…"

Extension: make a dot plot or box plot of the class totals before and after the outlier and compare them.

Not celebrating Halloween? Change the story to apples picked at an orchard or points scored in a fall tournament. The math is the same.

Differentiation: for students who are still building number sense, use one die and three houses so the totals stay small, and allow a calculator for the mean. For advanced students, ask what the mean of two dice should be over many rolls (7 per house, so 35 for five houses) and how close the class came. For English learners, post mean, median, mode, range and outlier with a tiny example beside each. For students with motor needs, use a dice app or let a partner roll while they record.

Quick check: "Five hauls are 20, 22, 25, 27 and 70. Which better describes a typical haul, the mean or the median? Explain in one sentence."

If you try it, tell us how far your class mean moved when you added the outlier.