Lesson 3
Scaled Picture Graphs
Warmup: Number Talk: Addition (10 minutes)
Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 100. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to add up the total number of students represented in a picture graph. When students use strategies based on place value to add they look for and make use of structure (MP7).
Launch
 Display one expression.
 “Give me a signal when you have an answer and can explain how you got it.”
 1 minute: quiet think time
Activity
 Record answers and strategy.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
Find the value of each expression mentally.
 \(50 + 10\)
 \(50 + 12\)
 \(60 + 13\)
 \(65 + 13\)
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 “How was place value helpful as you added these numbers?” (I was able to use tens and ones to help me find the sum.)
 Consider asking:
 “Who can restate _____’s reasoning in a different way?”
 “Did anyone have the same strategy but would explain it differently?”
 “Did anyone approach the problem in a different way?”
 “Does anyone want to add on to _____’s strategy?”
Activity 1: So Many Responses (15 minutes)
Narrative
The purpose of this activity is for students to read a scaled picture graph. A scale of 5 is used to encourage skipcounting because students skipcounted by 5 in grade 2. The questions in the task focus on the structure of a scaled picture graph and strategies for reading them.
Launch
 Groups of 2
 “What is your favorite sport or activity outside of school?”
 Share responses.
 Display the first image of the singleunit scale picture graph.
 “What do you notice? What do you wonder?” (Students may notice: The graph is about students’ favorite sports. There are a lot of smiley faces. Each smiley face represents 1 student. It takes a lot of time to count up the students in each category. Students may wonder: How many student responses are shown in the whole graph? How could we make the graph take up less space?)
 1 minute: quiet think time
 “Discuss your thinking with your partner.”
 1 minute: partner discussion
 Share and record responses.
Activity
 “Work with your partner to find how many students are represented in the graph.”
 3–5 minutes: partner work time
 Monitor for students who group the smiley faces by 2, 5, or 10 to make them easier to count.
 Have students who grouped the smiley faces share their strategies for how they found the total number of students represented in the graph.
 If no students use this strategy ask, “How could grouping the pictures in the graph make them easier to count?” (We could circle tens so we could count by ten. It would be easier to keep track of your count than by counting by ones.)
 Display the second image of the scaled picture graph.
 “How could we count the total number of students in this graph?”
 2 minutes: partner work time
 Math Community: As students work, monitor for examples of the “Doing Math” actions.
Student Facing
 A group of students were asked, “What is your favorite sport?” Their responses are shown in this picture graph:
How many students are represented in the graph?

Their responses are also shown in this picture graph:
How is counting the total number of students in this graph different from counting the total number of students in the first graph?
Student Response
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Advancing Student Thinking
 “How did you find the total number of students represented in the graph?”
 “How could you use counting by 5 to find the total number of students represented in the graph?”
Activity Synthesis
 “In a graph where there’s a lot of data we can adjust the scale so each picture represents more than 1 object. When each picture represents something other than 1, we say that it’s a scaled picture graph. The key tells us that in this graph, each smiley face represents 5 students.”
Activity 2: Questions about Scaled Picture Graphs (20 minutes)
Narrative
The purpose of this activity is for students to interpret a scaled picture graph and write questions that can be asked based on the data represented in a scaled picture graph.
Advances: Listening, Representing
Supports accessibility for: Conceptual Processing
Launch
 Groups of 2
 Display the graphs for all to see.
 “What are some strategies you could use to read the graphs?” (In the Flowers I Saw on the Way Home graph I could count each category by 5 since each picture represents 5 flowers.)
 1 minute: quiet think time
 Share and record responses.
Activity
 “Now, we’re going to answer some questions about the scaled picture graphs. You will also have a chance to write your own question that can be asked based on each graph.”
 8–10 minutes: partner work time
 If there is time, have groups trade books and answer each other’s questions.
 Math Community: As students work, monitor for examples of the “Doing Math” actions.
Student Facing

Andre collected data to see how many of each type of flower he saw on the way home. The data is shown in this picture graph:

How many of each type of flower did Andre see on the way home?
roses _____
tulips _____
daisies _____
violets _____
 Write 2 questions that you could ask about the flowers Andre saw on his way home.


A group of students were asked, “What is your favorite type of book?” Their responses are shown in this picture graph:
 How many students liked each type of book? How do you know?
 Write 2 questions that you could ask about students’ favorite types of books based on the graph.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
 “How did you answer the questions about the graph?”
 “What does the key tell us about each picture in the graph?”
Activity Synthesis
 Have students share responses to the questions they answered and explain their reasoning.
 Consider asking:
 “How did you use the scale to answer the questions?” (I counted by the number that each picture represented, like by 5 for the flowers and by 2 for the students.)
 Share a variety of student written questions.
 Consider asking:
 “How did you know your question could be answered with the graph?” (The data you needed to answer the question was in the graph.)
 If time ask, “What questions cannot be answered by this graph?” (How many students' favorite type of book is graphic novels?)
Lesson Synthesis
Lesson Synthesis
Display the images of the two “Favorite Sports” graphs.
“Today we learned about scaled picture graphs. Why would we make a scaled picture graph?” (When there is a lot of data to represent, it is faster to use a scale.)
“How is reading scaled picture graphs different from reading graphs that have a scale of 1?” (Each picture doesn’t represent 1 thing so you need to look at the scale. In a scaled picture graph you can count by the scale to find the total in each category instead of counting by 1.)
Math Community
After the cooldown, ask students to individually reflect on the question “Which ‘Doing Math’ action did you feel was most important in your work today, and why?” Have students write their responses on the bottom of their cooldown paper, on a separate sheet of paper, or in a math journal.
Collect and read their responses after class. These responses will offer insight into how students feel about their own mathematical work and help you make personal connections to the norms they will be creating during days 4–6.
Cooldown: Birds in the Park (5 minutes)
CoolDown
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