48.1: How Do We Choose?
Lesson
Let's vote and choose a winner!
Exercise \(\PageIndex{1}\): Which Was "Yessier"?
Two sixth-grade classes, A and B, voted on whether to give the answers to their math problems in poetry. The “yes” choice was more popular in both classes.
| yes | no | |
|---|---|---|
| class A | \(24\) | \(16\) |
| class B | \(18\) | \(9\) |
Was one class more in favor of math poetry, or were they equally in favor? Find three or more ways to answer the question.
Exercise \(\PageIndex{2}\): Which Class Voted Purpler?
The school will be painted over the summer. Students get to vote on whether to change the color to purple (a “yes” vote), or keep it a beige color (a “no” vote).
The principal of the school decided to analyze voting results by class. The table shows some results.
In both classes, a majority voted for changing the paint color to purple. Which class was more in favor of changing?
| yes | no | |
|---|---|---|
| class A | \(26\) | \(14\) |
| class B | \(31\) | \(19\) |
Exercise \(\PageIndex{3}\): Supermajorities
- Another school is also voting on whether to change their school’s color to purple. Their rules require a \(\frac{2}{3}\) supermajority to change the colors. A total of 240 people voted, and 153 voted to change to purple. Were there enough votes to make the change?
- This school also is thinking of changing their mascot to an armadillo. To change mascots, a 55% supermajority is needed. How many of the 240 students need to vote “yes” for the mascot to change?
- At this school, which requires more votes to pass: a change of mascot or a change of color?
Exercise \(\PageIndex{4}\): Best Restaurant
A town’s newspaper held a contest to decide the best restaurant in town. Only people who subscribe to the newspaper can vote. 25% of the people in town subscribe to the newspaper. 20% of the subscribers voted. 80% of the people who voted liked Darnell’s BBQ Pit best.
Darnell put a big sign in his restaurant’s window that said, “80% say Darnell’s is the best!”
Do you think Darnell’s sign is making an accurate statement? Support your answer with:
- Some calculations
- An explanation in words
- A diagram that accurately represents the people in town, the newspaper subscribers, the voters, and the people who liked Darnell’s best