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Launch

Arrange students in groups of 2–4. If needed, remind students of the school-level vote for the new mascot from an earlier activity.

Representation: Develop Language and Symbols. Use virtual or concrete manipulatives to connect symbols to concrete objects or values. Provide snap cubes for students to build and manipulate the districts they are creating.
Supports accessibility for: Visual-Spatial Processing, Conceptual Processing

Activity

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After the school mascot voting, the whole town gets interested in choosing a mascot. The mayor of the town decides to choose representatives to vote.

There are 50 blocks in the town, and the people on each block tend to have the same opinion about which mascot is best. Green blocks like sea lions, and gold blocks like banana slugs. The mayor decides to have 5 representatives, each representing a district of 10 blocks.

Here is a map of the town, with preferences shown.

30 green and 20 gold squares that are arranged in 5 rows with 10 squares in each row.

Suppose there were an election with each of the 50 blocks getting one vote. How many votes would be for banana slugs? For sea lions? Which mascot would win this election and what percentage of the votes would they get?

Suppose the blocks are in districts 1–5, as shown here. What did the people in each district prefer? What did their representative vote? Which mascot would win the election?

20 gold and 30 green squares in 5 rows of 10.

Complete the table with this election’s results.

district	number of blocks for banana slugs	number of blocks for sea lions	percentage of blocks for banana slugs	representative’s vote
1	10	0		banana slugs
2
3
4
5

Suppose, instead, that the 5 districts are as shown in this new map. What did the people in each district prefer? What did their representative vote? Which mascot would win the election?

50 gold and green squares are arranged in 5 rows with 10 squares in each row.

Complete the table with this election’s results.

district	number of blocks for banana slugs	number of blocks for sea lions	percentage of blocks for banana slugs	representative’s vote
1
2
3
4
5

Suppose the 5 districts are designed in yet another way, as shown in this map. What did the people in each district prefer? What did their representative vote? Which mascot would win the election?

A 10 by 5 grid of squares with specific area boundaries numbered 1 through 5 indicated

Complete the table with this election’s results.

district	number of blocks for banana slugs	number of blocks for sea lions	percentage of blocks for banana slugs	representative’s vote
1
2
3
4
5

Write a headline for the local newspaper for each of the ways of splitting the town into districts.
Which systems of the three maps of districts do you think are more fair? Are any totally unfair?

Student Response

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Building on Student Thinking

9.2

Activity

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

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Materials

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Activity Narrative

Students design districts in three towns to “gerrymander” the results of elections. In two of the towns, the election results can be skewed to either color. In the third, it isn’t possible to skew the results. When students design and defend their districts, they construct arguments and critique the reasoning of others (MP3).

Launch

Arrange students in groups of 2–4.

Explain the history of gerrymandering: Sometimes people in charge of designing districts make them in strange shapes to produce the election results they want. One of the first was Elbridge Gerry (governor of Massachusetts in 1812), whose party designed a district that many people thought looked like a salamander. They called it a Gerrymander, and the name stuck. It means a very strangely shaped, spread-out district designed to produce a certain result.

Usually, districts are required to be connected: A person traveling to all parts of the district should be able to stay inside the district. There should be no “islands” that are separated by parts of other districts.

Activity

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Smallville’s map is shown, with opinions shown by block in green and gold. Decompose the map to create three connected, equal-area districts in two ways:

Design three districts in which green will win at least two of the three districts. Record results in Table 1.

A figure that represents a district composed of 30 green and gold squares that are arranged in 3 rows and 10 columns.<br>

Table 1:

district	number of blocks for green	number of blocks for gold	percentage of blocks for green	representative’s vote
1
2
3

Design three districts in which gold will win at least two of the three districts. Record results in Table 2.

A figure that represents a district composed of 30 green and gold squares that are arranged in 3 rows and 10 columns.<br>

Table 2:

district	number of blocks for green	number of blocks for gold	percentage of blocks for green	representative’s vote
1
2
3

Squaretown’s map is shown, with opinions by block shown in green and gold. Decompose the map to create five connected, equal-area districts in two ways:

Design five districts in which green will win at least three of the five districts. Record the results in Table 3.

A figure that represents a district composed of 100 green and gold squares that are arranged in 10 rows and 10 columns.<br>

Table 3:

district	number of blocks for green	number of blocks for gold	percentage of blocks for green	representative’s vote
1
2
3
4
5

Design five districts in which gold will win at least three of the five districts. Record the results in Table 4.

A figure that represents a district composed of 100 green and gold squares that are arranged in 10 rows and 10 columns.<br>

Table 4:

district	number of blocks for green	number of blocks for gold	percentage of blocks for green	representative’s vote
1
2
3
4
5

Mountain Valley’s map is shown, with opinions by block shown in green and gold. (This is a town in a narrow valley in the mountains.) Decompose the map to create 3 connected, equal-area districts in 2 ways.

Design three districts in which green will win at least 2 of the 3 districts. Record the results in Table 5.

A figure that represents a district composed of 18 green and gold squares that are arranged in the following order.

Table 5:

district	number of blocks for green	number of blocks for gold	percentage of blocks for green	representative’s vote
1
2
3

Design three districts in which gold will win at least 2 of the 3 districts. Record the results in Table 6.

A figure that represents a district composed of 18 green and gold squares that are arranged in the following order.

Table 6:

district	number of blocks for green	number of blocks for gold	percentage of blocks for green	representative’s vote
1
2
3

Student Response

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Building on Student Thinking

Activity Synthesis

The goal of this activity is to understand that it is possible to design fair districts (where the result of the vote is similar to the vote if all individual votes were counted) and unfair districts. Here are some questions for discussion:

“In the Smallville maps, which map is more fair, the one where green wins or the one where gold wins?” (Green because there are 18 green blocks and 12 gold blocks, so a green result better represents what the people want.)
“In the Squaretown maps, which map is more fair, the one where green wins or the one where gold wins?” (Green because there are 60 green blocks and 40 gold blocks, so a green result better represents what the people want.)
“All of the maps we made followed the rules: Districts must be the same size and connected. Are there reasons maps would be made that are unfair?” (If the people designing the maps are biased, they could make maps that favor their choice.)
“What other rules about drawing maps could we add to make sure the maps are as fair as possible?”