few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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:
Concept/skill: 
Solve quadratic equations in one variable.

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


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

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
problem_activity: Narrative
The purpose of this activity is for students to apply what they’ve learned about quadrilaterals to design a wax print pattern. First, students analyze wax prints that have quadrilaterals incorporated into the pattern. Then, students design their own wax print that incorporates rhombuses, rectangles, or squares and a quadrilateral that doesn’t belong to any of these subcategories.
MLR8 Discussion Supports.
Synthesis: During group presentations, invite the student(s) who are not speaking to follow along and point to the corresponding parts of the display.
Advances: Speaking, Representing
Action and Expression: Internalize Executive Functions.
To support working memory, provide students with access to sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization
Required Materials
Materials to Gather
Colored pencils, crayons, or markers
Materials to Copy
Square Dot Paper Standard
Launch
Groups of 2
Display the image.
“Today’s lesson is going to focus on African wax prints. African wax prints are colorful cotton fabrics commonly used for clothing in West Africa. Take a minute to think about the pattern. What do you notice? What do you wonder?” (Students may notice: The pattern is colorful. There are rhombuses in the pattern. There are triangles in the pattern. There are quadrilaterals that aren’t rhombuses, rectangles, or squares in the pattern. Students may wonder: How do they make these patterns? What other shapes could be used to make these patterns? What types of clothing are made with this cloth? Where can you buy this type of fabric?)
1 minute: partner discussion
Share responses.
“You’re going to create your own wax print pattern. Independently read over the directions and think about how you’ll create your pattern.”
2–3 minutes: quiet think time
“Are there any questions about how you’ll create your wax print pattern?”
Answer any questions students have.
Give each student a sheet of dot paper and colored pencils, crayons, or markers.
Activity
“Work independently to create your wax print pattern.”
5–7 minutes: independent work time
“You can continue working on your own or work with a partner or small group to finish your pattern. Even if you choose to work alone, be available if your partner wants to think through something together.”
3–5 minutes: partner, small group, or independent work time
Monitor for students who use a rhombus, rectangle, or square in their pattern to highlight in the synthesis. Adjust the synthesis if all shapes aren’t used.
Student Facing
Your teacher will give you some dot paper for drawing.
Use the dot paper to design your own wax print pattern. Your pattern should:
use a rhombus, rectangle, or square
use a quadrilateral that is not a rhombus, rectangle, or square
have each shape repeat at least 5 times
Color the pattern in a way that highlights the shapes you chose or choices you made.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Display previously selected patterns one at a time.
For each pattern, ask, “How did this student use rectangles (or rombuses, or squares) in their design?”


aligns: no