Ticket Goal: The Pizza Party Mean

Ticket Goal: The Pizza Party Mean. A Grade 6 activity on the mean as a fair share

Most students can recite “add them up and divide,” but far fewer can tell you what the mean actually means. This worksheet builds that understanding first, then the procedure, through a story students care about: Lincoln Middle’s homerooms are selling raffle tickets, and a homeroom earns a pizza party if its students average 8 tickets each. Some students sold a lot, some sold a few, and one sold none.

Each student’s tickets appear as a tower of cubes, so students can see the data and not just read it. Over five problems they:

• Level the towers by hand. In Problem 1, students move tickets from tall towers to short ones until every tower is the same height. Their moves have to add up to zero, which shows that sharing never changes the total. The level height is the mean.
• Connect the picture to the calculation. Students check their leveled height with total ÷ number of students and complete a definition of the mean in their own words.
• See what a zero does. Homeroom 6A includes a student who sold nothing. Students compute the mean with her included and watch the towers level at their answer.
• Watch one value change the mean. A late ticket sheet turns up, and students find the new mean and explain why five extra tickets raise it by only half a ticket per student.
• Work backwards from a goal. Students figure out how many tickets one more student must sell for the homeroom to hit a mean of exactly 8.
• Compare groups of different sizes. Homeroom 6B sold more tickets in total but has more students. Students compute both means and discover that the bigger total does not win the party.

What’s included

• A two-slide student intro deck that sets up the mission and shows how leveling works, written for students to read on their own
• 5 problems with 26 auto-graded answers and instant correct/incorrect checks
• Interactive tower graphs that level at the student’s own answer, so they can see a wrong answer before anyone tells them
• Numbers chosen to give clean answers, so the arithmetic never gets in the way of the idea
• About 30 minutes of class time

Standards alignment

• 6.SP.A.3: Recognize that a measure of center summarizes all of the values with a single number
• 6.SP.B.5c: Give quantitative measures of center (mean) and relate them to the context of the data
• Supports 6.EE.B.7 in Problem 4, where students solve for an unknown value to reach a target mean

Good for

• Introducing the mean before students memorize the formula
• Reteaching students who can calculate the mean but can’t explain it
• Leading into median and outliers, since the “student who sold zero” sets up why the mean is sensitive to extreme values
• Independent work, small groups, or sub days, since students read the intro deck themselves and the worksheet grades itself