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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”
problem_activity: Narrative
The purpose of this activity is for students to learn stage 1 of the Build Shapes center. Students use straws and clay to build a shape of their choice. Students check with their partner to be sure they both agree that the shapes match. The Build Shapes Cards are printed in the student book for this activity. The Build Shapes Cards blackline master is available for students to use during center activities in future lessons. Listen to how students create an argument and use or revise their language to make their argument clear to others (MP3, MP6).
After they participate in the center, students choose from any stage of previously introduced centers.
Counting Collections
Which One
Picture Books
Bingo
Shake and Spill
Required Materials
Materials to Gather
Materials from a previous activity
Materials from previous centers
Materials to Copy
Build Shapes Stage 1 and 2 Cards
Required Preparation
Students need the bags of straws and clay from the previous activity.
Gather materials from:
Counting Collections, Stage 1
Which One, Stage 1
Picture Books, Stages 1–3
Bingo, Stages 1 and 2
Shake and Spill, Stages 1 and 2
Launch
Groups of 2
Give each group clay and straws.
“We are going to learn a center called Build Shapes. You will choose a shape. Then you and your partner will both use the straws and clay to build that shape. When you are both finished, compare your shapes and make sure they both match the shape you chose.”
Activity
8 minutes: partner work time
Monitor for two students who build different rectangles to share in the lesson synthesis.
“Now you can choose another center. You can also continue playing Build Shapes.”
Display the center choices in the student book.
Invite students to work at the center of their choice.
8 minutes: center work time
If time, invite students to choose another center.
Student Facing
[IMG]
Choose a center.
Build Shapes
[IMG]
Counting Collections
[IMG]
Which One
[IMG]
Picture Books
[IMG]
Bingo
[IMG]
Shake and Spill
[IMG]
Activity Synthesis
Display a square built from 4 straws that are the same length.
Display a rectangle from the shape cards.
“Han was trying to build this shape. What should Han change so his shape will match the shape on the card?”


aligns: no