Question

make picture graphs
ron asked his classmates about their favorite kind of tv show. he recorded their responses in a frequency table. use the data in the table to make a picture graph.
follow the steps to make a picture graph.
step 1 write the title at the top of the graph
step 2 look at the numbers in the table. tell how many students each picture represents for the key
step 3 draw the correct number of pictures for each type of show.
use your picture graph for 1–4.

1. what title did you give the graph?
2. what key did you use?

problem solving real world

1. how many pictures would you draw if 12 students chose game shows as their favorite kind of tv show?
2. what key would you use if 10 students chose cartoons?
3. write ➤ math describe why it might not be a good idea to use a key where each symbol stands for 1 in a picture graph.

table: favorite tv show (type: cartoons 9, sports 6, movies 3)
graph: favorite tv show (drawn), key: each ■ = 3

Explanation:

Question 3:

Step1: Determine the key value

From the original problem, the key used for the initial data (Cartoons: 9, Sports: 6, Movies: 3) is that each picture (square) represents 3 students (since \( 9\div3 = 3 \) pictures for Cartoons, \( 6\div3 = 2 \) for Sports, \( 3\div3 = 1 \) for Movies, which matches the partial graph shown).

Step2: Calculate the number of pictures for 12 students

To find the number of pictures for 12 students, we divide the number of students by the value each picture represents. Let \( n \) be the number of pictures. Then \( n=\frac{12}{3} \).
\( n = 4 \)

Step1: Analyze the requirement

We need to find a key (a number that each picture represents) such that when we use it to represent 10 students who chose cartoons, the number of pictures is a whole number (since we can't draw a fraction of a picture, usually). We need to find a divisor of 10 (or a number that 10 is divisible by, or we can use a number that makes the number of pictures reasonable). Common choices are 1, 2, 5, 10. But if we use 1, we would draw 10 pictures; if we use 2, we draw \( \frac{10}{2}=5 \) pictures; if we use 5, we draw \( \frac{10}{5} = 2 \) pictures; if we use 10, we draw 1 picture. A reasonable key (not too big or too small) could be 2 or 5 or 1 or 10. Let's pick a common one, say each picture represents 2 students (or 5, etc. But let's check the original data: original numbers were 9, 6, 3 which are multiples of 3. For 10, a common factor or a number that makes the number of pictures manageable. Let's take key as each picture = 2. Then number of pictures is \( \frac{10}{2}=5 \), which is reasonable. Or key as each picture = 5, then \( \frac{10}{5}=2 \). Or key as each picture = 1, then 10. But a good key is one where the number of pictures is not too large. So a possible key is each picture represents 2 students (or 5, or 1, or 10). Let's go with a common one, say each \( \square = 2 \) (or another valid divisor).

Step2: Verify

If each picture represents 2 students, then for 10 students, number of pictures is \( 10\div2 = 5 \), which is a whole number. If we use each picture = 5, then \( 10\div5 = 2 \), also whole number. If we use each picture = 1, then 10 pictures. All are valid, but a typical choice could be each picture represents 2 (or 5) students. Let's choose each picture represents 2 students (or 5, but let's see the original key was 3, which was a factor of 9,6,3. For 10, factors are 1,2,5,10. So a valid key is each picture represents 2 (or 5, 1, 10). Let's pick 2 as an example.

If each symbol stands for 1, and the number of students is large (e.g., 50), we would need to draw 50 symbols. This makes the picture graph very long and cluttered, hard to read and take up too much space. It's inefficient for representing large data sets as the graph would be too big and messy.

Answer:

4

Question 4: