Learn · Illustrative Mathematics · Grade 6 · Unit 9
Short lessons you can play with. Shrink the world to a class, cut rectangles into squares, compare votes fairly, count supermajorities, count ranked ballots three ways, and share out representatives, then check yourself. When you’re ready, practice in Town Hall.
Six chapters follow the unit’s lessons in order. Each step shows one idea with something to change, then a quick check. A wrong answer names the likely mistake and gives one more try.
IM’s Unit 9 has no new standards: it puts the year’s math to work. Shrinking the world to a class uses ratios and rates (Units 2 and 3). Cutting a rectangle into squares finds the greatest common factor (Unit 7) and shows why a fraction like 16/5 is 3 1/5. Comparing votes, supermajorities, and turnout use percents (Unit 3). Sharing representatives uses “people per representative,” a unit rate.
The voting chapters keep coming back to one idea: groups of different sizes are compared by their shares, not their counts. A bigger class can have more yes votes and be less in favor, and 80% of the voters can be 4% of the town.
The same ranked ballots can pick three different winners: by plurality, by a runoff, and by instant runoff points. IM calls the points count (3, 2, 1, 0 for four choices) “instant runoff,” and these pages do too; elsewhere it’s often called a Borda count.
Each chapter ends with a link to the matching station in Town Hall, the practice game for this unit. Progress is saved on this device.
Lesson 1 (Fermi problems), making a class’s own “If Our Class Were the World” display, and designing district maps are open-ended, so they work better in class.