Pizza Anyone?

Students survey their class and analyze data about favorite pizza toppings.

This activity is meant to be fun and engaging, with the class participating and making decisions as a whole.

A lesson plan for grade 6 Mathematics

By Jack Hunter

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Learning outcomes

Students will:

• take part in a survey and discuss principles of surveying and data gathering.
• use graphs and tables to display survey data.
• use fractions, percents, and ratios to report results.

Teacher planning

Time required for lesson

90 minutes

Materials/resources

Chalkboard or whiteboard, or overhead projector.

Technology resources

Basic calculator.

(optional) Computer with internet access for making graphs.

Pre-activities

Basic understanding/number sense with fractions and percents.

Understanding of phrases like “50% of the class” and “one-fourth of the trees in the yard” etc.

Activities

Day 1:

1. As students begin class, hand out the Student Sheet (attached) then draw their attention to the question on the board/overhead “What toppings do you like on your pizza? Answer in the first box on your paper. Keep your answer secret — no discussion.”
2. Give the students a minute or two to get settled and think about their answers.
3. Choose one student to be “Survey engineer” (this student will survey the class) and another to be “Data technician” (this student will record responses. Make sure s/he has legible handwriting). Be sure these two students are comfortable with this and not surprised by speaking to them before class.
4. The Survey engineer will read directions to the class (to circle their one favorite topping out of the ones they have written) and then circulate and read each student’s circled topping out loud. Give this student the attached document “Survey Engineer.”
5. The Data technician will go to the board and record responses as tallies. Give this student the attached document “Data Technician.”
6. After the responses are recorded for the class to see, have the students turn their papers face down, then talk with them about expressing these data in ratios like “8 out of 22 people chose pepperoni.” Have each student answer the question on their own paper about the ratio of their favorite topping.
7. Lead a discussion of ways to display this data, and create graphs on the board. “How might you see this data displayed in a newspaper?” is a good example of a question to get this started. Students will come up with their own answers. The teacher, directed by the class, will make a pictograph, a bar graph, and a cirle graph (see below), then the class can decide which they like best and why. Many students will have seen these before, so as you make them on the board ask questions to see what students know about them. For example: “What does a pictograph look like when it is finished?” “How do I make it?”
   • Pictograph - Make this vertical, not horizontal, so it can easily be transformed into a bar graph. Let students choose the symbol to use, (the unit measured is people: a smiley face perhaps?). Label the axes “Topping” and “Number of people.” Depending on your class size, one smiley face may represent 2, 4, or 5 students. Let the class decide this, and be sure to include a legend on the graph explaining it.
   • Bar Graph - Make this right on top of the pictograph. Explain to the class that this is really the same as a pictograph, except with bars instead of symbols. The main labeling difference: we don’t have the symbols and legend, so we need the vertical axis to say how many people each bar represents.
8. Before making the circle graph, have the students convert the ratios on their papers into fractions, “8/22 of the class chose pepperoni” for example. Then draw the circle, and let the students help decide how big to make each slice of the circle graph. For example “If the whole circle is our whole class of 22 people, how should I make the section for the 8 people who chose pepperoni?” Use the reference points of halves and quarters of the circle to guide the class. Label each slice with a number of people. This can be a rich discussion of fractions and estimation depending on how the class reacts and where you want to take it. For example, 8/22 is less than 1/2 (which is exactly 11/22) but more than 1/4 (which is about 5/ or 6/22). Use the calculators to find 1/2 or 1/4 of 22 if you want.

Before the next class meeting, have the students answer the questions in the homework section. For the question “Which graph do you like best, and why?”, make sure they understand that there is no right or wrong graph, and that their reasons why are the most important part of their answer. Day 2:
First, check students’ homework for effort and completion.

9. Now have the class help you put percents on the circle graph. Start with the largest fraction, and ask “If this was your chosen favorite, and you can tell me how to make this fraction a percent, raise your hand.” If necessary show students, or let them show each other, how to convert a fraction to a percent using the calculator… divide the numbers in the fraction and move the decimal two places to the right (or more simply in this case, the first two digits are your percent). Label the circle graph with percents in parenthesis next to the numbers of people, 8(36%) for example.
10. Lead a discussion about the percents on the graph. Show students that this is similar to the way we looked at the fractions, but now 50% and 25% of the circle are the reference points. Ask questions out loud like “If 18 of your classmates had said Shrimp, is that more than 50% of the class?”, “What is the total of all the percents in the graph?”, and “What percent of the class did NOT say ‘Shrimp’” to test for understanding; these questions can be answered without doing much math if the students have a good understanding of percents. Questions like “If there were 45 people in our class, how many do yo think would choose pepperoni?” require some calculation, but these questions are also appropriate.
11. Discuss homework question #1, and lead this into a discussion of the relative merits of these graphs. Encourage students to discuss their reasons for choosing one graph or another. For example, some students might say pictographs are easiest for most people to understand, while others might think circle graphs are easier. Both are correct. This part of the lesson could be done in small groups at the teacher’s option; if you do this in groups, make sure you group students with differing opinions.
12. Use the remaining homework questions to launch a discussion of bias in surveying. In particular, compare the methods of surveying (HW question #3), and make sure students understand that hearing others’ answers before giving your own answer can cause bias (this would happen if we all called out our answers). Have fun with the mushrooms question, for example, imagine starting this activity with the question “Isn’t your favorite topping yummy, delicious mushrooms? If not, what is it?” Make sure students understand that bias can easily make survey results meaningless.
13. The follow-up project (attached) has students design a survey and use it in their community, collaborating in small groups on the design and then gathering and displaying data individually.

Assessment

Orally check for understanding through discussion.

Homework questions (see Student Sheet).

Follow-up project.

Supplemental information

Attachments:

• Data Technician
• Survey Engineer
• Student sheet
• Survey project

Related websites

National Center for Education Statistics has a website that students can use to create graphs from data (optional). This should not take the place of making graphs by hand! http://nces.ed.gov/nceskids/graphing/index.asp

Comments

This plan was inspired by a discussion of who likes what on pizza. My classes were starting a pizza concession at our school (a charter school with no cafeteria) and wanted to know what types of pizza to order. This plan was the result of our discussion: an impromptu lesson and a real “teachable moment” that was well worth moving my teaching schedule back a day or two!