few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Concept/skill: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_pos_0

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im_task_000870_pos_0

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im_task_001160_neg_0

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standard_description: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
problem_activity: Narrative
The purpose of this activity is for students to sort triangles into more specific categories. This requires students to attend to an attribute other than the number of sides. As students sort the triangles, monitor for students who sort by the number of equal side lengths or the presence of a right angle (MP7). Although the terms “equilateral,” “isosceles,” and “scalene” are not introduced in this lesson it is fine if students already know them and use them to describe the groups of triangles.
MLR2 Collect and Display.
Direct attention to words collected and displayed from the previous lesson. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Representation: Access for Perception.
Synthesis: Use gestures during explanation of triangle sorting to emphasize side lengths of triangles.
Supports accessibility for: Visual-Spatial Processing
Required Materials
Materials to Copy
Triangle Cards Grade 3
Required Preparation
Create a set of cards from the blackline master for each group of 2 or 4.
When copying the card sort triangles, use colored paper to distinguish these cards from the cards in the next activity.
Launch
Groups of 2 or 4
Distribute one set of pre-cut cards to each group of students.
“What do you notice about the shapes on the cards?” (The shapes are all triangles. They all look different. Some of them have sides that are the same length.)
1 minute: quiet think time
Activity
“Work with your partner to sort the triangles into categories. Be sure to explain your categories.”
8 minutes: partner work time
Monitor for students that sort the triangles into groups based on:
the number of sides with equal length (all, two, none)
the sides and corners having the same size (the triangles being identical)
the presence of right angles
Student Facing
Sort the triangles into categories. Record your categories and be prepared to explain how you sorted the shapes.
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Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students say they aren’t sure how to sort the shapes because they are all triangles, consider asking:
“What other attributes have you used before to sort shapes?”
“How are some of the triangles different?”
Activity Synthesis
Select groups to share their categories and how they sorted their cards.
Allow as many categories to be presented as time permits, but be sure to highlight categories based on the number of sides with equal length.
Highlight the use of terms like “equal side lengths” and “angles.”
Record and display the attributes students use to categorize the triangles.


aligns: no