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 activity gives students opportunities to practice explaining or showing whether two fractions are equivalent. Students may do so using a visual representation, by reasoning about the number and size of the fractional parts in each fraction, or by thinking about multiplicative relationships between the numbers in the given fractions.
Students participate in a gallery walk in which they generate equivalent fractions for the numbers on the posters. Students visit at least two of six posters (or as many as time permits)—at least one poster with two fractions (posters A–C) and one poster with three fractions (posters D–F). Here are the sets shown on the blackline master:
A
​​​​​
\(\frac{2}{10}\)
,
\(\frac{20}{100}\)
B
\(\frac{6}{4}\)
,
\(\frac{18}{12}\)
C
\(\frac{3}{5}\)
,
\(\frac{60}{100}\)
D
​​​​​​
\(\frac{1}{4}\)
,
\(\frac{3}{12}\)
,
\(\frac{30}{100}\)
E
\(\frac{15}{6}\)
,
\(\frac{7}{4}\)
,
\(\frac{30}{12}\)
F
\(\frac{7}{3}\)
,
\(\frac{21}{10}\)
,
\(\frac{28}{12}\)
Because at the posters with two fractions (A–C) students would need to generate an equivalent fraction that hasn’t already been written by others, generating equivalent fractions becomes more difficult as the activity goes on. Consider using this to differentiate for students who may need an additional challenge: start them at the posters with three fractions (D–F).
MLR8 Discussion Supports.
Synthesis. Display sentence frames to support whole-class discussion: “I agree because . . .” and “I disagree because . . . .”
Advances: Speaking, Conversing
Required Materials
Materials to Gather
Sticky notes
Materials to Copy
How Do You Know
Required Preparation
Each group needs 4 sticky notes.
Launch
Groups of 3–4
Give each group 4 sticky notes
Read the task statement as a class. Solicit clarifying questions from students.
Invite a couple of students to recap the directions in their own words or to demonstrate the process, if helpful.
Consider assigning each group a starting poster and giving directions for rotation.
Activity
10 minutes: gallery walk
Tell students who are visiting posters A–C that they could leave feedback about the fraction on a sticky note if they disagree that it is equivalent to the fractions on the poster. They should include their name and be prepared to explain how they know.
Student Facing
Around the room you will find six posters, each showing either two or three fractions.
With your group, visit at least two posters: one with two fractions and one with three fractions.
[IMG]
For the set of 2 fractions:
Explain or show how you know the fractions are equivalent.
Write a new equivalent fraction on a sticky note and add it to the poster. Think of a fraction that hasn’t already been written by someone else.
We visited poster __________, which shows __________ and __________.
New equivalent fraction: __________
For the set of 3 fractions:
Identify 2 fractions that are equivalent. Explain your reasoning.
We visited poster __________, which shows __________, __________, and __________.
Student Response
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Activity Synthesis
See lesson synthesis.


aligns: no