Illustrative Mathematics · Grade 6 · Unit 9 · Putting It All Together
The town needs your math. Shrink the world to a class, cut rectangles into squares, decide which class was more in favor, count supermajorities, find who really decided, count ranked ballots three ways, and share out representatives fairly. Each station matches a lesson from class. New to this? Learn it first →
Each station deals 8 fresh problems (Town Meeting deals 10). A right answer on the first try earns 10 points. After a wrong answer, the game names the likely mistake and gives one more try for 5 points. A question with only two choices (does a vote pass, which mascot wins) gets one try.
This optional unit uses the year’s math on real questions: ratios and percents (Units 2 and 3) to shrink the world to a class and to compare votes, common factors (Unit 7) to cut rectangles into squares, and rates (“people per representative”) to share seats fairly.
World facts are rounded to friendly shares like “about 1 in 4” from recent UN and ITU figures. Classes have 20 to 36 students, percents come out whole, rectangles are at most 30 long, and elections have three choices and up to 36 voters, so the challenge is the reasoning, not the arithmetic.
Hints show the class as dots, cut the rectangle into its squares, draw bars inside bars for a percent of a percent, and spell out each voting rule.
The people who would not instead of who would, 1 in 4 read as 4 students, comparing yes counts instead of shares, rounding a supermajority down, exactly half taken for a majority, a percent of the voters taken for a percent of everyone, the winner by a different voting rule, forgetting 2nd-choice points, and one representative per group no matter its size.
IM calls the points count (2 for a 1st choice, 1 for a 2nd, 0 for a 3rd) “instant runoff,” and the game does too. Elsewhere this is often called a Borda count, and “instant runoff” can mean a ranked runoff counted all at once.
Lesson 1 (Fermi problems), making a class’s own “If Our Class Were the World” display, and drawing district maps (Lesson 6) are open-ended, so they work better in class than as scored problems.