standard_description: Verify experimentally the properties of dilations given by a center and a scale factor:
- A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
problem_activity: Narrative
The purpose of this activity is for students to compare different methods for solving problems within 100 using data presented in a bar graph. Students may use whatever method makes the most sense to them. The synthesis focuses on sharing multiple methods that students use to find the difference. Monitor for students who use methods that rely on using the bar graph to count on or count back and those that use more abstract methods, such as adding or subtracting by place value.
For example, when combining categories, some students may choose to use the graph to count on. Other students may choose to combine tens and ones with or without drawing a base-ten diagram or other representation.
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to choose a strategy and tool that works for them. Encourage students to use that same strategy and tool for both problems so they are not overwhelmed.
Supports accessibility for: Conceptual Processing, Organization, Attention
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Required Preparation
Create towers of 10 with the connecting cubes.
Have single connecting cubes available.
Launch
Groups of 2
Display the bar graph.
“What does this graph tell us?” (students’ favorite movie snacks, students picked their favorite movie snacks)
1 minute: quiet think time
1 minuter: partner discussion
Share responses.
Give students access to connecting cubes in towers of ten and singles.
Activity
“Use the bar graph to answer the questions. Show your thinking using drawings, numbers, or words.”
“You can use the connecting cubes or any of the other representations we saw in the warm-up to help you.”
8 minutes: independent work time
“Now compare your methods with your partner. How are they similar or different?”
4 minutes: partner discussion
As students work, monitor for students who:
use the bar graph to count on or count back
use the connecting cubes or base-ten drawings to show adding or subtracting tens with tens and ones with ones
Student Facing
Use the bar graph to answer the questions.
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What is the total number of students that chose popcorn or pretzels? Show your thinking.
How many more students chose nachos than chose popcorn? Show your thinking.
[IMG]
Student Response
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Activity Synthesis
Invite previously identified students to share the method they used to find how many more students chose nachos than chose popcorn.
As needed, record student methods using equations.
Consider asking:
“How are these methods the same? How are they different?”
“How does the method work? Why does each method find the same value?”


aligns: no