standard_description: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
problem_activity: Narrative
This Number Talk encourages students to look for and make use of structure to mentally evaluate a series of subtraction expressions. The numbers preview some benchmark angle measurements students will see in upcoming lessons.
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: quiet think time
Activity
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Facing
Find the value of each expression mentally.
\(90 - 45\)
\(270 - 45\)
\(270 - 135\)
\(360 - 135\)
Student Response
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Activity Synthesis
“What do these expressions have in common?” (The first number in each sequence is a multiple of 90.)
“How did this observation—that the first numbers are all multiples of 90—help you find the value of the differences?”
Consider asking:
“Who can restate _____’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone approach the expression in a different way?”
“Does anyone want to add on to _____’s strategy?”


aligns: no