Students gain an understanding of how tally charts, titles, and labels, among other components of a graph or other data display, work together in this lesson. Students are going to:
- select the proper labels and title to rebuild a graph.
- learn more about the use of bar graphs for information display.
- put data in order and sort it for bar graphs.
- identify discrepancies in labels, data, graphs, etc.
- How accurate must calculations and measurements be?
- How are mathematical properties of things or processes measured, computed, and/or interpreted?
- What does it mean to evaluate or estimate a numerical quantity?
- What qualifies a tool or strategy as suitable for a particular task?
- How can information be presented and arranged to shed light on the relationship between different quantities?
- Data: Information that is gathered.
- Tally Chart: A chart that organizes data using tally marks.
- copies of the Mystery Graph Examples page (M-2-6-2_Mystery Graph Examples)
- copies of pages 1–4 of Matching Mystery Graphs (M-2-6-2_Matching Mystery Graphs)
- Watch the students work through the first exercise using the think-pair-share method.
- Observe students as they work through the M-2-6-2_Matching Mystery Graphs activity, and use the results to formally evaluate students' comprehension of bar graphs.
Modeling, Active Participation, and Scaffolding
W: The lesson prompts students to reflect more deeply on the key features of bar graphs. This covers the labels, titles, and tally charts that go with it.
H: Get students to assist you in piecing together graphs that have broken apart. Tell them that the task is similar to solving a mystery.
E: Assign students to work in pairs to determine the best way to reassemble the divided graphs, labels, and titles.
R: Bring the class together and ask them to discuss how they would reconstruct the graphs, taking into account the labels and titles. Once you've put the mystery graphs back together, ask them questions to help steer them in the right direction. Compare and contrast the graphs and tally tables.
E: Assign students to complete the Matching Mystery Graphs exercise in pairs. Based on the tally marks in the matching tables, students should make the bar graphs.
T: Assist students in obtaining information from friends, family, and classmates throughout the academic year. Next, assist them in interpreting the data and making bar graphs from the information they collected. Favorite color, the students' daily mode of transportation (bus, car, bike, walk), and other subjects can be discussed.
O: The main points of this lesson are bar graphs and their associated tally charts, titles, and labels. With all of these details available, students reconstruct mystery graphs. Students are still learning how to make and read bar graphs.
Copy the M-2-6-2_Mystery Graph Examples file, which contains the Mystery Graph Examples.
"I need your help because I have a problem. When I attempted to enter the classroom this morning, I was holding all of the materials for our math class. I accidentally dropped all my papers while trying to unlock the door. Everything spilled onto the floor, getting muddled. I'm stuck figuring out which titles and labels belong with each bar graph, so I need your help. Do you think you could help me?"
Most likely, your students will be excited to help you in solving the puzzle of which graph's title belongs to which. Make the three graphs visible to every student by putting them on display.
"I've got three tally tables. I produced three graphs. I also have a lot of labels and three titles. Which titles and labels are going to be used with each tally table? I'll show you the tally tables, categories, and titles."
Show the M-2-6-2_Mystery Graph Examples
"All right, now I want you and your partner to look at my tally charts and search for any hints on each chart that could help you match the title and labels to the graph. In your math journal, you are welcome to jot down any thoughts you may have. This could aid in your idea recall."
Give the class a few minutes to concentrate on the tally tables and engage in discussion about their thoughts.
"As I walked around, I heard many good suggestions about how to align the titles and labels of the tally charts with them. I want you to discuss your ideas with another pair before we share them with the whole class."
As the class gathers together, discuss matching the tally charts, titles, and labels. Ask students to present their clues to the class.
Students may say, "This tally chart needs three labels because I noticed it has three rows. I knew the labels needed to have numbers because one title discussed people's ages." "I noticed that there were two rows in each of the tally charts. I simply cannot decide which graph title to use. I need more help."
Talk to the students about what titles to use for each table and how to label the tally charts. To assist students in accurately labeling the graphs, you might need to delve deeper or pose questions.
Some examples of questions you could pose to students are
"How many rows are there on each graph? Why might this occur?"
"What does the quantity of tallies indicate to us?"
"How do you locate the appropriate bar graph using the table of tallies?"
"How many items or people are shown on each of our charts? How are you aware?"
"In your opinion, why do some charts have three rows while others only have two?"
Once students have successfully matched every tally chart to its matching bar graph, label each category and write the chart's title.
Making Mystery Graphs
"After that, you will be expected to work in pairs to piece together another set of mystery graphs by searching for hints. You will also be required to create bar graphs using the tally charts once you have sorted the data."
Give page 1 of the Matching Mystery Graphs (M-2-6-2_Matching Mystery Graphs) to each student pair, then instruct them to get to work. Provide pages 2, 3, and 4 of Matching Mystery Graphs to every student once they have all successfully matched the labels and titles with the corresponding tally charts. Give students the tally charts to use in making bar graphs. Remind students to label and title each graph appropriately.
Extension:
Utilize the subsequent exercises in your classroom to address your student's needs all year long:
Routine: Mysterious Graphs: Post samples of two or three graphs on the board without titles or labels at the beginning of the school year. Ask students to suggest labels and titles. Alternatively, make the labels and titles first, then ask the students to match them to the appropriate graphs. Students should be asked to describe the hints they utilized to properly match the objects.
Small Groups: Use the Mystery Graphs from this lesson to review the material. Likely, students who require additional practice did not comprehend the process and rationale behind the choices made during graph reconstruction. To help the group with the thinking required to reconstruct the mystery graphs, pose targeted questions to them. Once completed, create a label-free tally chart. Ask students to create the matching bar graph and offer names for the tally chart. Remind students that the bar graph needs labels and a title.
Expansion: My Own Mystery Graphs: As students work at their workstations, ask them to create their mystery graphs. As soon as a few students have created their graphs, assign the class to match the title with the appropriate graph.
