Make a copy of the Mystery Graph Examples (M-2-6-2_Mystery Graph Examples.docx).
“I have a problem, and I need your help. This morning I had all of my materials for our math class in my hands when I tried to enter the classroom. When I tried to unlock the door, I accidentally dropped all of my papers. Everything fell to the floor and became mixed up. I need your help because I can’t figure out which title and labels go with each bar graph. Do you think you can help me?”
Students will most likely be eager to help you solve the mystery of which title belongs to which graph. Display the three graphs so all of the students can see them.
“I have three tally tables I made for three graphs. I also have three titles and many labels. I wonder which title and labels will go with each tally table. Let me show you the titles, categories, and tally tables.”
Display the Mystery Graph Examples (M-2-6-2_Mystery Graph Examples.docx).
“Okay, I want you and your partner to look at my tally charts and look for clues on each chart that may help you match the title and labels to the graph. You can write your ideas down in your math journal if you wish. This may help you remember your ideas.”
Give students a few minutes to focus on the tally tables together and allow them to discuss their ideas.
“As I was walking around I heard a lot of good ideas on how to match up the tally charts and their titles and labels. Before we share with the entire class, I want you to find another pair and discuss your ideas.”
Bring students back together for a class discussion on how to match up the tally charts, titles, and labels. Have students share their clues with the class.
Students might say: “I noticed that this tally chart has three rows so it has to have three labels.” “One title talked about ages of people, so I knew that the labels had to have numbers.” “I noticed that two of the tally charts had two rows each. I just can’t decide which title goes with which graph. I need a little more help.”
Discuss with students how the tally charts should be labeled and what title they should use for each table. You may need to probe or ask questions in order to guide students to correctly labeling the graphs.
Sample questions to ask students include
- “How many rows are on each chart? Why would this be?”
- “What does the number of tallies tell us?”
- “How can you use the table of tallies to find the right bar graph?”
- “How many people or things are represented on each of our charts? How do you know?”
- “Why do you think this chart has three rows and the others only have two?”
After students have correctly matched all of the tally charts with the corresponding bar graphs, write the title on each chart and label each category.
Making Mystery Graphs
“Now you will be asked to work in pairs to look for clues to reconstruct another set of mystery graphs. As soon as you sort out the information, you will also be asked to construct bar graphs using the tally charts.”
Hand out page 1 of Matching Mystery Graphs (M-2-6-2_Matching Mystery Graphs.docx) to each pair of students and ask them to begin working. After students have successfully matched the labels and titles with the appropriate tally charts, distribute pages 2, 3, and 4 of Matching Mystery Graphs to all students. Ask students to create bar graphs using the tally charts. Remind students to put the appropriate title and labels on each graph.
Extension:
Use the following activities in your classroom to meet the needs of your students throughout the year:
- Routine: Mystery Graphs: Throughout the year, place examples of two or three graphs on the board without labels or titles. Have students come up with titles and labels. Or create the titles and labels first and have students match them to the correct graphs. Ask students to explain the clues they used to correctly make a match.
- Small Groups: Use the Mystery Graphs from this lesson, and review the lesson. Students who need more practice likely did not understand how and why the decisions were made when reconstructing the graphs. Ask specific questions of the group to help guide them through the thinking needed to reconstruct the mystery graphs. When finished, draw a tally chart with no labels. Ask students to suggest labels for the tally chart and construct the corresponding bar graph. Remind students to put the labels and a title on the bar graph.
- Expansion: Mystery Graphs of My Own: Have students make up their own mystery graphs during workstations. When a couple of students have made up their own graphs, ask the class to match the title to the correct graph.
