standard_description: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
problem_activity: Narrative
This warm-up prompts students to compare four area diagrams that have been decomposed into two areas, each representing a product. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as side lengths, area, parts, and decompose.
Launch
Groups of 2
Display the image.
“Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
2–3 minutes: partner discussion
Share and record responses.
Student Facing
Which one doesn’t belong?
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
“Why didn’t it make sense for the rectangle in C to be split in half?” (Because one part of the rectangle should have been larger than the other because 70 is greater than 28. The part with 28 should have been smaller than the part with 70.)
Consider asking: “Let’s find at least one reason why each one doesn’t belong.”


aligns: no