Warm-up: Number Talk: Repeated Addition (10 minutes)
The purpose of this Number Talk is to elicit strategies and understandings students have for adding groups of 2 and groups of 5. These understandings help students develop fluency and will be helpful later in this lesson when students need to be able to use data in scaled bar graphs to solve one- and two-step “how many more” and “how many fewer” problems. Students use the structure of the expressions and repeated reasoning when they use methods based on skip-counting by 2 or 5 or counting on 2 or 5 from a previous known value (MP7, 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.
- \(2 + 2 + 2 + 2 + 2\)
- \(2 + 2 + 2 + 2 + 2 + 2\)
- \(5 + 5 + 5 + 5 + 5 + 5\)
- \(5 + 5 + 5 + 5 + 5 + 5 + 5\)
- “What is a strategy that you hadn’t used before that you might use in the future?” (Thinking about one more group if I already know part of the problem. Skip-counting.)
- Consider asking:
- “Who can restate _____’s reasoning in a different way?”
- “Did anyone have the same strategy but would explain it differently?”
- “Did anyone solve the problem in a different way?”
- “Do you agree or disagree? Why?”
Activity 1: New School Year (20 minutes)
The purpose of this activity is to introduce MLR6, Three Reads, and solve a two-step “how many fewer” problem using data presented in a scaled bar graph. The routine prompts students to read a problem three times for different purposes to support them in making sense of the problem (MP1).
- Groups of 2
MLR6 Three Reads
- “Keep your books closed.”
- Display only the graph, without revealing the question.
- “We are going to read this graph 3 times.”
- 1st read: “Take a moment to read the data displayed by this graph”
- “What is this graph about?” (It’s about how students are feeling about the new year.)
- 1 minute: partner discussion
- Listen for and clarify any questions about the context.
- 2nd read: “Read and interpret the graph a second time. What quantities are represented? What can be counted or measured in this situation?” (We can count the number of students in each category.)
- 30 seconds: quiet think time
- 2 minutes: partner discussion
- Record quantities on a display for all to see.
- Reveal the question.
- 3rd read: Read the question aloud.
- “What are some strategies we can use to solve this problem?” (We could add the 24 plus 25 to see how many students are nervous or curious. We could subtract how many students are nervous or curious from the number of students that are excited.)
- 30 seconds: quiet think time
- 1–2 minutes: partner discussion
- 5-7 minutes: partner work time
- Monitor for students who:
- add 25+23 and then subtract 55-48
- subtract 55-23 and then subtract 32-25
- subtract 55-25 and then subtract 30-23
A group of students were asked, “How are you feeling about the new school year?” Their responses are shown in this bar graph:
How many more students are excited about the new school year than are nervous or curious?
- Have 1-2 selected students share their solution and strategy.
- Display the steps of Three Reads routine and keep displayed for the next activity.
- “How did reading the problem three times help you make sense of the problem?” (I was more comfortable with the problem each time I read it. It made more sense every time I read the problem. I noticed different details each time I read it.)
Activity 2: Use Bar Graphs to Solve Problems (15 minutes)
The purpose of this activity is for students to practice the Three Reads math language routine on their own and use data presented in a scaled bar graph to solve a two-step “how many more” situation. The Three Reads routine has students read a problem three times for different purposes to support them to make sense of the problem and persevere in solving it (MP1).
Advances: Listening, Speaking
Supports accessibility for: Social-Emotional Functioning
- Groups of 2
- “What types of plants do you see on your way home from school?” (Trees. Bushes. Flowers. Vines.)
- Share responses.
- Display the graph.
- “Work independently to use the graph to solve the problems. You can use the Three Reads routine if it’s helpful to you.”
- 7–10 minutes: independent work time
- Monitor for students who solve the one-step problems by:
- using the bars on the graph to count up to or back from one number to another.
- using equations to show adding or subtracting by place.
- Monitor for students who solve two-step problems by:
- adding two numbers then subtracting the sum from another number.
- subtracting a number, then subtracting again from the difference.
The bar graph shows how many of each type of tree Clare saw on the way home. Use the graph to answer the questions. Show your thinking using expressions or equations.
- How many more pine trees did Clare see than fir trees?
- How many more pine trees did Clare see than oak or maple trees?
- How many fewer oak trees did Clare see than pine trees?
- How many fewer maple or oak trees did Clare see than fir trees?
Advancing Student Thinking
If students find the sum of all categories or don't find a solution to the problems, consider asking:
- “Tell me about how you started this problem?”
- “How could you use the information from the graph to solve the problem?”
- Have 1-2 students share the method, including any expressions or equations they used to solve the first problem.
- Have 2-3 students share the expressions or equations they used to solve the last problem.
- “How are these methods the same? How are they different?” (Some people added the maple and oak trees together and then subtracted it from the number of fir trees. Some people subtracted the number of maple trees from fir trees and then subtracted the number of oak trees. Each way found the same number of trees.)
Display equations from the first problem in the last activity.
“How did you use what you know about tens and ones to solve the problems?” (Some questions I saw I could just count by 10 on the graph because the scale was 10. We didn’t subtract all at once. We subtracted the tens, then the ones. We were thinking about how to get to the next ten to make adding the tens easier.)
“In the future, how could you use the Three Reads strategy on your own, without a partner?” (We could use it any time by thinking what the problem is about. We can read the problem to look for what can be measured or counted in the problem. We can read it to think about strategies we could use to solve the problem.)
Cool-down: Reading Time (5 minutes)
Student Section Summary
In this section, we created scaled picture graphs and scaled bar graphs.
We asked and answered questions that could be answered by the graphs.
- How many more daisies were seen than violets?
- How many fewer students walk home than bike home?
- How many more students bike home than walk or ride in a car?