standard_description: Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.
problem_activity: Narrative
This Number Talk encourages students to use what they know about the meaning of fractions and about properties of operations to mentally relate fractions that are equivalent to whole numbers.
Launch
Display one fraction.
“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 fractions and work displayed.
Repeat with each fraction.
Student Facing
Find the whole number that each fraction is equivalent to.
\(\frac{16}{1}\)
\(\frac{16}{2}\)
\(\frac{16}{4}\)
\(\frac{20}{4}\)
Student Response
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Activity Synthesis
“How did the earlier fractions help you find the whole number for the last fraction?”
Consider asking:
“Did anyone have the same strategy but would explain it differently?”
“Did anyone approach the problem in a different way?”


aligns: no