“When you are at school, you make lots of choices. For example, at lunch you can choose between regular milk and chocolate milk. What are some other times you make choices at school?”
Allow students to share ideas and introduce them to the idea of a survey. Define the word survey. Make sure students understand that a survey can be about anything and that anyone can take a survey. “Under what circumstances would you take a survey? How do people take surveys? What do people do with the information they gather?”
Lead students to see that people take surveys by asking questions. They then gather the information together and display it in an easy-to-read format.
Brainstorm a list of things students would like to know about their classmates, such as their favorite pet, favorite hobby, what flavor of milkshake they like best, how many siblings they have, and so on.
Choose one suggestion from the list and turn it into a survey question. Explain that students will collect data based on this question and display it in different types of graphs.
“Let’s conduct a survey about everyone’s favorite flavor of milkshake. What flavor of milkshake do you like best? I am going to give everyone a sticky note. Draw a glass of your favorite flavor of milkshake. Color white for vanilla, brown for chocolate, or pink for strawberry. If you don’t drink milkshakes or don’t like them, draw the shape of a glass and put a big X on it. When you are done drawing, bring up your sticky note and place it anywhere on the chart paper.” The result should be a random collection of pictures on the front of the chart paper.
After everyone has added his/her picture to the collection, ask students to make observations. Ask them what flavor most of the class seems to prefer, how many like chocolate milkshakes best, and how many students do not like milkshakes. Lead students to see that since the notes are randomly placed on the chart paper, it is difficult to answer the questions.
Encourage students to suggest ways to organize the pictures so that it is easier to make observations and interpretations.
“We could group the responses by flavor, so chocolate would be in one group, vanilla would all be in a second group, and strawberry would all be in a third group. We would also make a group for people who don’t like milkshakes.”
“Let’s organize the data according to flavor.”
Take the first page of chart paper off, keeping the notes attached, and place it in the middle of the group, or display it to the side. Draw four columns on a new sheet of chart paper. Label the columns Vanilla, Chocolate, Strawberry, and None.
“I’m going to ask you to come up, one at a time, find your drawing, and place it in the appropriate column. Maybe that will help us to observe the data more clearly.”
Allow time for students to place their drawings on the page. Have students observe how the data is now displayed and compare it to the previous way it was displayed.
“Does the new chart display our data clearly?” (yes)
“What can we learn from our chart?” Prompt discussions about the choices students made. Compare the most popular flavor to the least popular flavor.
Discuss the parts of the graphs (title, axis labels). Make sure students understand that all graphs must have these important parts so people can understand the data on the graph.
“We are going to explore different ways to organize this data. First, we will use tally marks.” Remind students that one tally mark represents one vote for a specific flavor. Review the configuration for five tally marks. Take the review page off the chart paper pad and display it for all to see. On a clean sheet of chart paper, draw horizontal rows, one for each flavor of milkshake, and label each row accordingly.
Have a student come up to the chart with the pictures and count how many pictures there are in the vanilla column.
“How many people like vanilla milkshakes the best?” (six)
“Make six tally marks on the tally chart in the row labeled Vanilla.”
Continue this process with the remaining flavors; be sure to include a category for None. Have students discuss their observations of the data in the tally chart. Encourage them to compare data in the tally chart with the data in the first chart. Guide students in making the connection that both charts display the same information in different ways.
Draw a bar graph. Ask students if they can think of a good title for the graph. Model how to label the bottom of the graph with the milkshake flavors and number the left side of the graph from
0 to 10. Discuss the information presented in the tally chart. Model how to use the data in the tally chart to complete the bar graph by completing the first column. Remind them that for each tally mark they should color one square in that flavor’s column. Have students work with you to complete the remainder of the graph. Upon completion of the bar graph, ask students what they notice. Have them relate the bar graph to the tally chart and the first chart. Emphasize that the information remains the same even though it is displayed differently. Be sure to save all three displays. It will be important to keep these as models for work that students do independently or with partners.
Extension:
- Workstation: Use the list the class brainstormed earlier in the lesson and select a question to use for the workstation. Have each student take a copy of the survey form (M-1-6-1_Survey Form.doc), write a question at the top, and fill in the possible answer choices. Students will complete the survey by filling in one row next to their answer choice. When the survey is complete, the surveyor student should choose a way to display the data. S/he may use a chart, a tally chart (M-1-6-1_Blank Tally Chart.doc), or a vertical or horizontal bar graph (M-1-6-1_Blank Horizontal Bar Graph.doc).
- Small Group: “We are going to display the data we collected earlier in a new way. How might connecting cubes help us do this?” Take suggestions, and then guide students toward the idea of using one cube to represent each picture or tally mark.
“Let’s use red cubes to represent strawberry milkshakes.” Have a student count the number of students who chose strawberry as their favorite flavor of milkshake and connect the same number of red cubes to make a train. Repeat this with different colors representing each of the remaining flavors and the None category.
When all of the data is represented by cubes, have students work within their groups to arrange the cube train to look like a bar graph. Students might arrange the trains on a table side by side, creating a vertical graph, or lay them down to create a horizontal bar graph.
Lead a discussion comparing the data on the classroom chart to the cube trains.
“Are the results the same? Which is easier to understand, the chart or the cubes? Why?”
- Expansion: Demonstrate to students how to write number sentences that describe the relationships between the data. For example, ask students to compare the number of people who prefer chocolate-flavored milkshakes with the number of people who prefer strawberry-flavored milkshakes. If 8 people voted for chocolate and 3 people voted for strawberry you might write 8 > 3. If you ask how many more people prefer chocolate to strawberry, the expression might be 8 – 3 = 5. Encourage students to work together to write one mathematical expression that compares the data.
