The next day, Martina produced the first draft of a circle graph to represent her survey data. She agreed to have her teacher begin the whole-class discussion by asking the students to critique Martina's graph:

Here is Martina's data table:

Look at Martina's data and graph:

• Why do you think she chose a circle graph for her data?
• Are the sectors the correct size for each category of data?
• Explain your reasoning.

Naseem and Vanessa, his sixth-grade partner, are discussing their thoughts about the questions their teacher posed:

Naseem: I think our bar graph was much easier to make.
Vanessa: I know, but a circle graph is a good way to compare everyone at once. Remember how the circle represents the total -- the whole group?

Naseem: Well, you can compare bars, too, but I guess the circle graph does show that, for example, baseball was about twice as popular as football, and soccer and basketball were about the same. Maybe she chose the circle graph because it shows the results for the whole group all in one circle, out of 100 percent.
Vanessa: Yeah. Next question. Do you think Martina made her graph right?

Naseem: I'm not sure. Is the part for soccer the right size? Her table says it's 20%. What fraction is it?
Vanessa: It looks like less than a quarter. Let's match it to a Fraction Circle piece. It seems closest to 1/5.

Naseem: Her table says the soccer group is 12 out of 60. Is that close to, or the same as, 1/5?
Vanessa: Well, she already figured that it is 20%. Actually, I know that 1/5 equals 20%. You could divide it again on the calculator.

Naseem: Hmm, I divided 12 by 60 and got 0.2. Is that 20%?
Vanessa: Yeah, 0.2 is like two-tenths. It is 20%. Think about it -- it's easy to change 1/5 to a percent, just make it out of 100. Multiply by 20 over 20. It's 20 out of 100, so it's 20%.

Naseem: So, the graph is correct.
Vanessa: Well, what about the other colors? Basketball looks good; it's supposed to be 23%, and that's almost a quarter, and it's about 1/4 of the graph. Also, kickball is 33%, and that's like 1/3, and it looks right. I think it's easier if we write those numbers on the graph, too.

Naseem: The smallest sections are supposed to be for baseball and football, and that's how they look. Also, they're probably right because the part for football is about half the size of the baseball section, and 8% is about half of 15%. I guess Martina did a good job. What do we have to write down?

  Reflect on the Circle Graph problem