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.

A figure that represents a map of a town composed of 50 green and gold squares that are arranged in 5 rows with 10 squares in each row. The top 2 rows each contain 10 gold squares and the bottom 3 rows each contain 10 green squares.

1. 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?

2. 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?

   

   A figure that represents a map of a town composed of 50 green and gold squares that are arranged in 5 rows with 10 squares in each row. The top 2 rows each contain 10 gold squares and are labeled 1 and 2. The bottom 3 rows each contain 10 green squares and the rows are labeled 3, 4, and 5.  

   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

3. 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. The top 2 rows are gold and the bottom 3 rows are green. The grid is divided vertically into 5 equal rectangles labeled 1, 2, 3, 4, and 5. Each rectangle contains 4 gold squares at the top and 6 green squares directly underneath.

   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

4. 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. The top two rows are gold and the bottom 3 rows are green. Each numbered area contains a combination of 10 gold and green squares. Area 1: Starting on the first row, region 1 has the first 4 gold squares. Under the second gold square in the first row is a row of 2 gold squares. Directly under the 2 gold squares in row 2 are 2 green squares. Directly under the 2 green squares are another 2 green squares. Area 2: Starting on the first row, region 2 has the fifth and sixth gold squares. Under the 2 gold squares and 1 place to the left are 4 gold squares side by side. Under the 4 gold squares are 1 green square, 2 spaces, and another green square. Under that row is an identical row with 1 green square, 2 spaces, and another green square. Area 3: Starting on the top row, region 3 has the last 4 gold squares in the first row. Under the second gold square in the first row is a row of 2 gold squares. Under the 2 gold squares in row 2 are 2 green squares. Under the 2 green squares are another two green squares. Area 3 is identical to area 1. Area 4: Starting in row 2, region 4 has starts with a gold square. Directly below in row 3 is 1 green square, then 3 spaces, and 1 green square. Row 4 is identical to row 3. Row 5 has 5 green squares side by side. Area 5: Starting in row 2, region 5 has the 10th gold square. In row 3 has the 6th green square, then 3 spaces, and 1 green square. Row 4 is identical to row 3. Row 5 has 5 green squares side by side.10 squares over is 1 yellow. In the next row down, 6 squares over is 1 green, 3 spaces, and 1 green square. Under the green square in the previous row is 1 green, 3 spaces, and 1 green square. Under the previous green square on the left, are 5 green squares.  

   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

5. Write a headline for the local newspaper for each of the ways of splitting the town into districts.

6. Which systems of the three maps of districts do you think are more fair? Are any totally unfair?

1. 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:

   1. 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. The squares are arranged in the following order: Row 1: 8 green, 1 gold, 1 green. Row 2: 2 gold, 4 green, 1 gold, 1 green, 1 gold, 1 green. Row 3: 3 gold, 1 green, 1 gold, 2 green, 3 gold.  

      Table 1:

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

   2. 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. The squares are arranged in the following order: Row 1: 8 green, 1 gold, 1 green. Row 2: 2 gold, 4 green, 1 gold, 1 green, 1 gold, 1 green. Row 3: 3 gold, 1 green, 1 gold, 2 green, 3 gold.  

      Table 2:

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

2. 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:

   1. 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. The squares are arranged in the following order: Row 1: 10 green. Row 2: 2 gold, 5 green, 2 gold, 1 green. Row 3: 3 gold, 1 green, 1 gold, 2 green, 3 gold. Row 4: 5 green, 5 gold. Row 5: 4 green, 2 gold, 1 green, 1 gold, 1 green, 1 gold. Row 6: 3 green, 1 gold, 3 green, 1 gold, 1 green, 1 gold. Row 7: 4 gold, 3 green, 1 gold, 2 green. Row 8: 4 gold, 6 green. Row 9: 4 gold, 6 green. Row 10: 4 gold, 6 green.  

      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

   2. 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. The squares are arranged in the following order: Row 1: 10 green. Row 2: 2 gold, 5 green, 2 gold, 1 green. Row 3: 3 gold, 1 green, 1 gold, 2 green, 3 gold. Row 4: 5 green, 5 gold. Row 5: 4 green, 2 gold, 1 green, 1 gold, 1 green, 1 gold. Row 6: 3 green, 1 gold, 3 green, 1 gold, 1 green, 1 gold. Row 7: 4 gold, 3 green, 1 gold, 2 green. Row 8: 4 gold, 6 green. Row 9: 4 gold, 6 green. Row 10: 4 gold, 6 green.  

      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

3. 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.

   1. 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. Top row: 2 gold squares and 1 green square each side by side. Second Row: Starting under the green square in row 1, 1 gold square and 3 green squares each side by side. Third Row: Starting under the gold square in row 2, 1 gold square, 2 spaces, 2 green squares side by side, 2 spaces, and 3 gold squares each side by side. Fourth Row: Starting under the first green square in row 3, 3 green squares each side by side, then 1 gold square, and then 1 green square.  

      Table 5:

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

   2. 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. Top row: 2 gold squares and 1 green square each side by side. Second Row: Starting under the green square in row 1, 1 gold square and 3 green squares each side by side. Third Row: Starting under the gold square in row 2, 1 gold square, 2 spaces, 2 green squares side by side, 2 spaces, and 3 gold squares each side by side. Fourth Row: Starting under the first green square in row 3, 3 green squares each side by side, then 1 gold square, and then 1 green square.  

      Table 6:

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