Warm-up: Number Talk: Twos and Fives (10 minutes)
The purpose of this Number Talk is to elicit strategies students have for counting by 2 and 5. These understandings help students develop fluency and will be used later in this lesson when students will need to be able to scale bar graphs.
When students notice the number of equal addends are doubled in the second expression, they are looking for and making sense of structure (MP7). When they notice the pattern repeats in the second pair of expressions and use the pattern to find the value of the sum, they are also looking for and expressing regularity in repeated reasoning (MP8).
- Display one expression.
- “Give me a signal when you have an answer and can explain how you got it.”
- 1 minute: quiet think time
- Record answers and strategy.
- Keep expressions and work displayed.
- Repeat with each expression.
Find the value of each expression mentally.
- \(2 + 2 + 2 + 2\)
- \(2 + 2 + 2 + 2 + 2 + 2 + 2 + 2\)
- \(5 + 5 + 5 + 5\)
- \(5 + 5 + 5 + 5 + 5 + 5 + 5 + 5\)
- “How did the first two expressions help you solve the third and fourth expressions?” (If you notice there are double the number of twos or fives you can just double your 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: Compare Bar Graphs (10 minutes)
- Groups of 2
- Display the images.
- “How are these bar graphs alike? How are they different?”
- 1 minute: quiet think time
- 4 minutes: partner discussion
A class was asked, “How do you get home from school?” Their responses are shown in these two bar graphs:
Discuss with your partner: How are the two graphs alike? How are they different?
- “What was the same? What was different?”
- Share and record responses.
- If it doesn't come up, elicit the idea that the scale on the second graph counts by 2.
- “When each jump on the scale is some number other than 1, we say that it’s a scaled bar graph.”
- “Why would it be helpful to make a scaled bar graph?” (If you didn't want to count one by one. If you wanted to show larger numbers on your graph.)
Activity 2: Create a Scaled Bar Graph (25 minutes)
The purpose of this activity is for students to create a scaled bar graph. Students decide on a scale of 2 or 5, so it will be important to ask students why they chose their scale and how accurately they can tell the exact number the bar represents (MP6). In the activity synthesis, students discuss how they represented an odd number of students with a scale of 2 and a number of students that was not a multiple of 5 on a scale of 5. This question should be adjusted based on the data your class collects.
Advances: Representing, Speaking
Supports accessibility for: Organization, Attention
Materials to Gather
- Each student needs the picture graph they creaed in the previous lesson.
- Groups of 2
- Make sure each student has their scaled picture graph from the previous lesson.
- “Today, we will represent the data we collected yesterday about ways we would like to travel in a scaled bar graph.”
- “Decide with your partner whether you want to use a scale of 2 or 5. Be prepared to explain your choice. If you have time, try making one graph with a scale of 2 and one with a scale of 5.”
- 12 minutes: partner work time
- Consider asking, “How did your scaled picture graph help you to make your scaled bar graph?”
Represent the data we collected earlier in a scaled bar graph.
Use the graph with a scale of 2 or the graph with a scale of 5. If you have time, you can make 2 graphs. Be sure to label your title and categories.
Advancing Student Thinking
- “How did you decide where the top of the bar would end?”
- “How could you use counting by 2 (or 5) to help you decide where the top of the bar should end?”
- “What scale did you and your partner choose? Why?”
- Display student work with both scales.
- “How did you represent a way of travel that didn’t land right on the numbers in the scale?” (It was between the 2 numbers, so I had to make a guess about where the bar should stop.)
- “What differences do you notice when the graph is with a scale of 2 and when the graph is with a scale of 5?” (Sample responses: The bars look taller when the scale is 2. It's hard to tell what number some bars represent when the scale is 5. It was easier to count up to larger amounts when the scale was 5.)
Display a scaled bar graph from the lesson.
“We’ve been learning about how to make scaled bar graphs. If you were going to help a friend create a scaled bar graph, what advice would you give them?” (I would tell them that means that the scale goes up by numbers other than 1. They should look at the number of people in each category and think about whether those numbers are easy to count by 2 or 5 or some other number.)
Be sure to highlight ideas about using scales of 2 or 5.
After the cool-down, give students 2–3 minutes to discuss in small groups any revisions to the “Norms” section. Collect and record any revisions.