Answer Questions about Scaled Bar Graphs
10 min
Narrative
The purpose of this How Many Do You See? is for students to subitize or use grouping strategies to describe the images they see.
When students notice that some of the dots are in equal groups and skip-count to find the total number of dots, they are looking for and making use of structure (MP7).
Launch
- Groups of 2
- “How many do you see? How do you see them?”
- Flash the first image.
- 30 seconds: quiet think time
Teacher Instructions
- Display the first mage.
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
- Repeat for each image.
Student Task
How many do you see? How do you see them?
Solution Steps (4)
- 1Image 1: Identify groups→3 groups of 2 dots plus 1 extra dot
- 2Image 1: Skip count by 2s→2, 4, 6, then add 1 more = 7 dots
- 3Image 2: Identify groups→4 groups of 5 dots plus 2 extra dots in middle
- 4Image 2: Skip count by 5s→5, 10, 15, 20, then add 2 more = 22 dots
Sample Response
Sample responses:
- 7: I see 3 groups of 2 and 1 more.
- 22: I counted by 5 for the 4 groups of 5 to get 20, then added 2 more for the dots in the middle.
Activity Synthesis (Teacher Notes)
- “How did thinking about groups help you find the total number of dots?” (Some of the dots were in groups and some were not. I used skip-counting to count the groups that were the same size, then added on the rest of the dots.)
- Consider asking:
- “Who can restate the way _____ saw the dots in different words?”
- “Did anyone see the dots the same way but would explain it differently?”
Standards
Building On
- 2.OA.3·Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
- 2.OA.C.3·Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
Building Toward
- 3.MD.3·Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. <em>For example, draw a bar graph in which each square in the bar graph might represent 5 pets.</em>
- 3.MD.B.3·Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. <span>For example, draw a bar graph in which each square in the bar graph might represent 5 pets.</span>
15 min
20 min
Knowledge Components
All skills for this lesson
Role Legend
Target
Essential
Supporting
Foundational
All lesson KCs
3 skills
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Answer Questions about Scaled Bar Graphs
10 min
Narrative
The purpose of this How Many Do You See? is for students to subitize or use grouping strategies to describe the images they see.
When students notice that some of the dots are in equal groups and skip-count to find the total number of dots, they are looking for and making use of structure (MP7).
Launch
- Groups of 2
- “How many do you see? How do you see them?”
- Flash the first image.
- 30 seconds: quiet think time
Teacher Instructions
- Display the first mage.
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
- Repeat for each image.
Student Task
How many do you see? How do you see them?
Solution Steps (4)
- 1Image 1: Identify groups→3 groups of 2 dots plus 1 extra dot
- 2Image 1: Skip count by 2s→2, 4, 6, then add 1 more = 7 dots
- 3Image 2: Identify groups→4 groups of 5 dots plus 2 extra dots in middle
- 4Image 2: Skip count by 5s→5, 10, 15, 20, then add 2 more = 22 dots
Sample Response
Sample responses:
- 7: I see 3 groups of 2 and 1 more.
- 22: I counted by 5 for the 4 groups of 5 to get 20, then added 2 more for the dots in the middle.
Activity Synthesis (Teacher Notes)
- “How did thinking about groups help you find the total number of dots?” (Some of the dots were in groups and some were not. I used skip-counting to count the groups that were the same size, then added on the rest of the dots.)
- Consider asking:
- “Who can restate the way _____ saw the dots in different words?”
- “Did anyone see the dots the same way but would explain it differently?”
Standards
Building On
- 2.OA.3·Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
- 2.OA.C.3·Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
Building Toward
- 3.MD.3·Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. <em>For example, draw a bar graph in which each square in the bar graph might represent 5 pets.</em>
- 3.MD.B.3·Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. <span>For example, draw a bar graph in which each square in the bar graph might represent 5 pets.</span>