*All solutions and teacher notes in blue* Algebra Handout Key: Lesson 1.1 Topics: functions as maps, non-functions Lesson 1.1 Guided Notes We elect our president using the Electoral College. The Electoral College requires a candidate to win 270 electoral votes to win the presidency, regardless of popular vote. 2016 Election Clinton Trump 48.2% 46.1% 227 Lost 304 Won Today’s Key Analysis: Are electoral votes a function of people’s votes? Functions as maps 1. Imagine you were asked to find the place associated with the name “Connecticut.” The map given to the right would not be helpful. Explain why. The name Connecticut is labeled on two different places on the map (the yellow and brown areas). We wouldn’t know which region to visit based on the input name “Connecticut.” 2. Imagine you were asked to find the y-value associated with the x-value of -3. The map given to the right would not be helpful. Explain why. The x value of -3 has two arrows that point to two different y-values: 2 and -7. It’s a confusing map: we don’t know which y-value is associated with the x input of -3. Material adapted from the Skew The Script curriculum (skewthescript.org) Lessons made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License (https://creativecommons.org/licenses/by-nc-sa/4.0) Popular Vote Electoral College Result 2 3. For each example, say whether the table of values describes a function. Justify your answer. a) b) a. is a function because each x-value maps to exactly one y-value. b. is not a function because -3 maps to two y-values: 2 and -7. 4. Describe what needs to be true for a relationship to be considered a function: Every x-value (input) is associated with only one possible y-value (output) Non-functions Are these functions? Provide an answer and justify. 1. Yes. Each input (each x value) has only one output (one possible y value). For every vertical line we could draw (for every x value), there is only one intersection with the graph (one mapped y value). 2. No. Certain x-values map to more than one y-value. There are places where a vertical line (one x value) has two intersections (two mapped y-values). 3. Yes. Each input (each x value) has only one output (one possible y value). For every vertical line we could draw (for every x value), there is only one intersection with the graph (one mapped y value). The Electoral College Material adapted from the Skew The Script curriculum (skewthescript.org) Lessons made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License (https://creativecommons.org/licenses/by-nc-sa/4.0) 3 In the Presidential Election, each state’s electoral vote total is equal to its number of senators (two per state) plus its number of Congressional House representatives (number depends on state’s population size). Candidates need 270 total electoral votes to win the Presidency. Are electoral votes a function of people’s votes (voter share)? Justify your answer using the table to the right. Electoral votes are not a function of people’s votes. The voter share value of 46% (input) maps to two possible electoral vote outcomes (outputs): 304 for Trump in 2016 and 173 for McCain in 2008. Interestingly, the same voter share of 46% also mapped to different final results: winning and losing. Lesson 1.1 Discussion Only consider the three states below. For each of the following vote scenarios, which party (Democrat or Republican) would win the popular vote? Which would win the electoral college? Show your work: a) California: 10 million Republican, 14 million Democrat Texas: 10 million Republican, 7 million Democrat Ohio: 3 million Republican, 4 million Democrat Popular Vote: 10 + 10 + 3 = 23 million Republican votes 14 + 7 + 4 = 25 million Democrat votes Electoral votes: 38 Republican (TX), 73 Democrat (CA + OH) Democrat wins both popular vote and electoral college Popular Vote: 10 + 10 + 3 = 23 million Republican 14 + 7 + 4 = 25 million Democrat b) California: 10 million Republican, 14 million Democrat Texas: 9 million Republican, 8 million Democrat Ohio: 4 million Republican, 3 million Democrat Electoral: 56 Republican (TX+OH), 55 Democrat (CA) Democrat wins popular vote, Republican wins electoral college Discussion: Should electoral votes be a function of people’s votes? Answers will vary. Here are some possible responses: Recommended discussion norms: skewthescript.org/discussion-norms Yes: The state-by-state “winner take a
1.1.Alg.STS.Handout.Key
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