“We have been working with graphs for a while now. We have studied bar graphs, picture graphs, and have started working on line plots. Today we are going to continue with our graphing unit.”
Make an overhead copy of the first page of Matching Mystery Graphs (M222_Matching Mystery Graphs.doc). For examples of graphs you could make, look at M222_Graph, Title, and Label Examples.doc.
“As I was walking into the room this morning, I had all of my materials for our Math class in my hands and I tried to unlock the door and I accidentally dropped them. Everything I had in my hands 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 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. Place the three graphs on the chalk board so all of the students can see them.
“Let’s see, I have the three tally tables I made for three graphs. I also have three titles and three labels. I wonder which title and labels will go with each tally table. Let me show you the titles, categories, and tally table.”
Put up the overhead copy of the first page of Matching Mystery Graphs (M222_Matching Mystery Graphs.doc).
“Okay, I want you and your partner to look at my tally tables and look for clues on each table that may help us 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 tables and their titles and labels. Before we share with the entire class, I want you to find another group of partners and discuss your ideas.”
Bring students back to their desks or carpet for a class discussion on how to match up the tally tables, titles, and labels. Have students share their clues with the class. [IS.3  All Students]
Students might say: “I noticed that this tally table 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 tables had two rows each. I just can’t decide which title goes with which graph. I need a little more help.”
Discuss with your students how the tally tables should be labeled, and what title they should go with. 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 table? Why would this be?”

“What does the number of tallies tell us?”

“How many people or things are represented on each of our tables? How do you know?”

“Why do you think this table has three rows and the others only have two?”
After students have correctly matched all of the tables, write the title on each table and label each category. Then ask them to return to their seats.
Making Mystery Graphs
“We talked about looking for clues to make sure our data, titles, and labels match. You will now be asked to construct your own graph now that we have all of the information sorted out.”
Hand out the second, third, and fourth page of Matching Mystery Graphs (M222_Matching Mystery Graphs.doc) to your students and ask them to begin working. Give students at one table different graphs to work on.
“Raise your hand if you have a question and I will come see you. When you are finished, please leave the paper on your desk and go to a math workstation.”
After students have completed the graphs, discuss the similarities and differences between the graphs and the tally tables. Did the graphs turn out the way they expected?

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 to 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.

Workstation: 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. You could also use studentmade graphs during the Mystery Graphs activity.
Through various activities, students spend time thinking about the best way to display data and about which combinations of graphs, titles, labels, etc. would make sense together. If the label says “time” and the tic marks are letters, students should be able to recognize this as an inconsistency and to recommend a better label or tic mark. Students are asked to look at data in the graph as well as to find clues that would help them best match the title and labels to a graph.