Lesson 2
Represent Data and Solve Problems
Warmup: How Many Do You See: Dots in Groups (10 minutes)
Narrative
The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the number of dots they see. They also make connections between the images to determine the number of dots. Grouping strategies and skipcounting by 2, 5, and 10 offer a review of grade 2 work and build toward multiplication in future lessons. In the synthesis, students revisit the language of “how many more” to prepare them to use data from a bar graph to solve “how many more” problems throughout this lesson.
Launch
 Groups of 2
 “How many do you see? How do you see them?”
 Flash the image.
 30 seconds: quiet think time
Activity
 Display the image.
 “Discuss your thinking with your partner.”
 1 minute: partner discussion
 Record responses.
 Repeat for each image.
Student Facing
How many do you see? How do you see them?
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 “How many more dots were in the third image than in the second image? What equation matches your thinking?” (There were 2 more dots in the image. \(8 + 2 = 10\).)
Activity 1: How We Get Home (15 minutes)
Narrative
The purpose of this activity is for students to create a bar graph that includes features that help communicate the data clearly. A class picture graph is created, and students make a bar graph using that data. During the synthesis, focus attention on similarities and differences between picture and bar graphs. When you create the blank “ways to get home” picture graph for the launch, feel free to adjust the categories based on how your students get home from school. When students label their graphs, including a title, a key, and numbers if they make a bar graph, they are communicating clearly and precisely (MP6).
Advances: Speaking
Required Materials
Materials to Gather
Required Preparation
 Create a visual display with a blank bar graph that will be large enough to fit a column of sticky notes in each category.
Launch
 Groups of 2
 Display an empty picture graph with labels along the bottom axis for bike, walk, van, bus, car, and train.
 Give each student a small sticky note.
 Have each student draw a smiley face on their sticky note.
 “Put your smiley face on the graph based on how you get home from school.”
 “What needs to be added to the class picture graph to communicate the data clearly?” (A title. A key so we know what each smiley face represents.)
 Facilitate addition of title and key to class picture graph.
Activity
 “Represent the data shown in the class picture graph on a bar graph with your partner. Make sure to include the parts of the graph that will help someone else read it.”
 5–7 minutes: partner work time
Student Facing
 Follow your teacher’s instructions to organize and represent the class data in a picture graph.
 Represent the same data that shows how our class gets home on a bar graph.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
If students create bar graphs that do not match the data in the class picture graph, consider asking:
 “Tell me about how you made your bar graph.”
 “How could we use the data in the class picture graph to help make the bar graph?”
Activity Synthesis
 “How are our picture graph and bar graph alike?” (They both show the same data. They have the same categories.)
 “How are our picture graph and bar graph different?” (The picture graph has a key, but the bar graph has a scale. For the picture graph, you have to count each picture but in the bar graph, you can use the numbers on the side to tell how many.)
Activity 2: Questions About a Bar Graph (20 minutes)
Narrative
The purpose of this activity is for students to answer one and twostep “how many more” questions using data represented in a bar graph. Students decide if statements about the data in the bar graph from the previous activity are true or false and then answer questions about the data. When students use expression, equations, or describe adding or subtracting to find how many more or less, they show they can decontextualize and recontextualize the data to make sense of and solve the problems (MP2). You will generate the questions students answer in this task from the class graph.
Supports accessibility for: Language
Launch
 Groups of 2
Activity
 “Now you’re going to use your bar graph to decide if statements are true or false.”
 1–2 minutes: independent work time
 3–5 minutes: partner discussion
 As students work, decide which categories will go in the question stems for the next problem.
 Consider providing these sentence stems if students need support explaining their reasoning:
 “I knew the statement was false because . . .”
 “I knew the statement was true because . . .”
 “How did you know if each statement was true or false?”
 Share responses.
 Guide the whole class to fill in blanks in question stems using the previously identified categories.
 “Use the data in your bar graph to answer the questions.”
 3–5 minutes: partner work time
Student Facing

Decide if each statement is true or false about how our class gets home. Explain your reasoning to your partner.
 More students walk than go home any other way.
 More students ride home on a bus than in a car.
 Fewer students walk home than ride their bikes.
 More students walk or ride their bikes than ride in a van.

Fill in the blanks as directed by your teacher, then answer each question.

“How many more students \(\underline{ \phantom{{\Huge{0000000000}}}}\) than \(\underline{ \phantom{{\Huge{0000000000}}}}\)?”

“How many more students \(\underline{ \phantom{{\Huge{0000000000}}}}\) or
\(\underline{ \phantom{{\Huge{0000000000}}}}\) than \(\underline{ \phantom{{\Huge{0000000000}}}}\)?”

Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
 “How did you answer the questions?”
 “How could you use the graphs to answer the questions?”
Activity Synthesis
 Ask students to share their responses to each compare problem.
 “Do you have any lingering questions about how to answer these questions from the bar graph?”
 Consider asking: “What equation matches your thinking?”
Lesson Synthesis
Lesson Synthesis
Display a studentcreated bar graph.
Generate a few questions for students to answer about how they get home using the bar graph. For example, you might ask:
 “How many more students _______________ than _______________?”
 “How many fewer students _______________ than_______________?”
 “How many more students _______________ or _______________ than _______________?”
Have students answer the questions and share their reasoning.
Math Community
After the Cooldown, give students 2–3 minutes to discuss any revisions to the “Doing Math” actions in small groups. Share ideas as a whole group and record any revisions.
Cooldown: Questions About a Bar Graph (5 minutes)
CoolDown
For access, consult one of our IM Certified Partners.