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Student Page 4.1.2 Batty Functions
A4US

1.

Listen to the story, Bats on Parade, by Kathi Appelt. (Find online a YouTube video of someone reading Bats on Parade.) Read the scenarios found in or adapted from the story. Scenario A describes the characters in the story as they appear in the book. In Scenario B, you will also count the flag bearer as shown in the story. In Scenario C, the story is adapted to include more flag bearers.

Scenario A

The first group has 1 marcher in 1 row. The second group has 2 marchers in each of 2 rows. The third group has 3 marchers in each of 3 rows, and so on.

Scenario B

Each group that joins the parade also has a single flag bearer. Include the flag bearer in the number of marchers in each group.

Scenario C

Each group that joins the parade has as many flag bearers as columns in the group. For example, the third group of bats marches in 3 rows and 3 columns and has 3 flag bearers.

(a)

In Table 4.1.2.1, draw a tile pattern to match each Scenario A, B, and C.

(b)

Write the numbers of tiles for each of Scenarios A, B, and C in Table 4.1.2.2. The step number above becomes the group number in Table 4.1.2.2.

Table 4.1.2.1. Bats on Parade Tile Patterns
Scenario Step 1 Step 2 Step 3 Step 4 Step 5
A  
 
 		  
 
 		  
 
 		  
 
 		  
 
 
Number of Tiles  
 		  
 		  
 		  
 		  
 
B  
 
 		  
 
 		  
 
 		  
 
 		  
 
 
Number of Tiles  
 		  
 		  
 		  
 		  
 
C  
 
 		  
 
 		  
 
 		  
 
 		  
 
 
Number of Tiles  
 		  
 		  
 		  
 		  
 
D  
 
 		  
 
 		  
 
 		  
 
 		  
 
 
Number of Tiles  
 		  
 		  
 		  
 		  
 
Table 4.1.2.2. Number of Marchers
  Scenario A Scenario B Scenario C Scenario D Scenario E
Group
Number		 Number of
Marchers
in the Group		 Number of
Marchers
in the Group		 Number of
Marchers
in the Group		 Number of
Marchers
in the Group		 Number of
Performers So Far
1          
2          
3          
4          
5          
6          
7          
8          
9          
10          
\(x\)          

2.

For each of Scenarios A, B, and C:

(a)

What patterns do you see in the data?

(b)

Are any of the patterns linear? How do you know?

(c)

How are the columns of data related to each other?

3.

(a)

Graph each set of data with Group Number as the independent variable and the number of marchers for the scenario as the dependent variable.

(b)

How are the graphs related to each other?

4.

(a)

For each data set, find an equation giving the number of marchers in group \(x\text{.}\) Write the equations in the last row of Table 4.1.2.2.

(b)

Are any of the equations linear? Should they be? Explain.

5.

Listen to another story, Bat Jamboree, also by Kathi Appelt. (Google Bat Jamboree to find this story online in a YouTube video.) Complete Table 4.1.2.1 and Table 4.1.2.2 for Scenarios D and E.

Scenario D

Each group has the same number of performers as the group number.

Scenario E

The number of performers who have appeared so far is the number of new performers and all performers who appeared before the new group. For example, when Group 3 performs, the number of performers who have appeared so far plus the new group are \(1 + 2 + 3 = 6\) performers.

6.

(a)

Compare the data for Scenario E to the data for Scenarios A, B, and C. What do you notice?

(b)

Is the data for any of Scenarios A, B, or C related to Scenario E? How?

(c)

Graph the data with Group Number as the independent variable and Scenario E as the dependent variable.

(e)

Determine an equation to model the data for Scenario E as it relates to group number.

7.

Share your work on Batty Functions. Resolve differences and ask questions before continuing.