Algebra
Linear Functions and Inequalities
Vertical Alignment
TEKS:
| 8th | 8.4(A)8.4(B) |
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Structured Conversation Questions
Observational
What is a similar right triangle?
A similar right triangle is...Relational
How is a similar right triangle related to congruence?
A similar right triangle is related to congruence because...Inferential
Why do you think it is important that the angles in similar right triangles are the same, even if the corresponding side lengths are different?
I think it is important that the angles in similar right triangles are the same, even if the corresponding side lengths are different because...
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Students might notice in this visual:
- The triangles have the same angle measures
- The triangles are different sizes but the same shape
- The side length values follow a pattern
- The ratios between the side length values are the same
- The triangles have the same shape, but different sizes.
EXTENDING THE DISCUSSION
After the observational question, randomly call on one or more students to share what they or their partner answered. Then ask the class, “Did anyone notice…?” using the suggestions above or anything else you’ve noticed.
After the observational question, randomly call on one or more students to share what they or their partner answered. Then ask the class, “Did anyone notice…?” using the suggestions above or anything else you’ve noticed.
Students might wonder:
- How do we know the triangles are proportional
- Why do the ratios stay the same
- How do corresponding sides match
- Do all triangles with the same angles have the same ratios
- Why angles matter for similarity
EXTENDING THE DISCUSSION
After students have shared what they notice, ask the class, “Did anyone wonder…?” using the suggestions above or anything else you might think is interesting or relevant to the lesson.
After students have shared what they notice, ask the class, “Did anyone wonder…?” using the suggestions above or anything else you might think is interesting or relevant to the lesson.
Example student responses
To the observational question, What is a similar right triangle?
LOW-LEVEL
A similar right triangle has the same shape but different side length values.
HIGH-LEVEL
A similar right triangle has congruent angles and proportional corresponding sides with equal ratios, even if the side length values are different.
RESPONDING TO RESPONSES
Emphasize and celebrate each student’s use of the key vocabulary to support a culture of “no wrong answers.”
Emphasize and celebrate each student’s use of the key vocabulary to support a culture of “no wrong answers.”
