standard_description: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
problem_activity: Narrative
The purpose of this activity is for students to compare methods that can be used to count numbers between 100 and 999. Students see images of beans that are put in groups of 5 and another in groups of 10. A third image uses groups of 100, groups of 10, and single beans. Students make connections to place value and their understanding of the base-ten structure (MP2, MP7). They also consider opportunities for accuracy and efficiency when they articulate pros and cons for each method.
Launch
Groups of 2
Display image of a cup of beans or display a cup of beans.
Read the context aloud.
Activity
1 minute: quiet think time
5 minutes: small-group discussion
Monitor for students who:
describe the organization and group sizes in each method
describe Clare’s method in terms of hundreds, tens, and ones
discuss ideas such as efficiency (how long it takes) and accuracy (chances of mistakes)
Student Facing
[IMG]
Clare, Noah, and Jada counted a cup of dried beans. They each came up with 529 beans. The following pictures show how each of them counted.
Jada’s counting strategy:
[IMG]
Noah’s counting strategy:
[IMG]
Clare’s counting strategy:
[IMG]
What do you notice about each of their strategies?
What is helpful about each strategy?
What is challenging about each strategy?
Student Response
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Activity Synthesis
Invite previously selected students to share their observations.
“Which of these strategies do you believe would be the fastest or slowest? Explain.”
“Do you think it would be easier to make a mistake using one of these strategies? Which one and why?”
“Which strategy do you prefer? Why?”


aligns: no