Geometry
Geometric Figures and Angles
Vertical Alignment
TEKS:
| 7th | 7.9(C)7.9(D) |
| 8th | 8.7(B) |
| Geom | G.10(A)G.11(C)G.11(D) |
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Structured Conversation Questions
Observational
What is total surface area?
Total surface area is...Relational
How is total surface area different from lateral surface area?
Total surface area is different from lateral surface area because...Inferential
Why do you think manufacturers/designers consider the total surface area of gift boxes?
I think manufacturers/designers consider the total surface area of gift boxes because...
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Students might notice in this visual:
- The rectangular prism has a Base and lateral faces
- The pyramid has a Base and triangular lateral faces
- The formulas show how to calculate total surface area
- Each face’s area is calculated and then added together
- The final answer is written in square units
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:
- Why do we multiply by 2 in the prism formula?
- Do all shapes have the same number of faces?
- How do you know which measurements to use for each face?
- Why is the pyramid calculated differently than the prism?
- When would I use total surface area in real life?
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 total surface area?
LOW-LEVEL
Total surface area is adding up all the sides of a shape.
HIGH-LEVEL
Total surface area is the sum of the areas of all the faces of a three-dimensional figure, including the base and lateral faces.
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.”
