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: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only 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: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Answer: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
problem_activity: Narrative
The purpose of this activity is for students to identify examples of circles and triangles. The geometric terms
circle
and
triangle
are formally introduced, though some students may already be familiar with the terms and may have heard or used them in previous lessons. This activity exposes students to a wider variety of circles and triangles than they may have seen previously, which encourages students to expand their concepts of the shapes. Students may incorrectly identify some shapes as triangles or circles, particularly distactors, such as a shape that looks like a triangle but has 4 sides. These shapes can be discussion points and are expected throughout kindergarten. Students distinguish between defining and non-defining attributes of shapes in grade 1.
MLR8 Discussion Supports.
To support the transfer of new vocabulary to long term memory, invite students to chorally repeat these words in unison 1–2 times: circles, triangles.
Advances: Listening, Speaking
Representation: Access for Perception.
Synthesis: Students might need extra support determining that the oval and the pizza slice shapes are not circles or triangles. Hold up a triangle and circle next to the shapes to visually show that the oval and pizza slice shapes do not match the triangle and circle.
Supports accessibility for: Visual-Spatial Processing
Required Materials
Materials to Gather
Colored pencils or crayons
Required Preparation
Each student needs at least 2 different colored crayons or colored pencils.
Launch
Groups of 2
Give each student access to 2 different color crayons or colored pencils.
Display the image from the book.
“Mai put her shapes into 2 groups. What do you notice? Why do you think Mai put these shapes together?”
30 seconds: quiet think time
Share responses.
“What can we name each group?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
“We can call this group
circles
. All of the shapes in this group are circles. We can call this group
triangles
because all of the shapes in this group are triangles.”
“What do you know about circles?”
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
“What do you know about triangles?”
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
Display student workbook.
“Color all of the circles that you find with 1 color. Then color all of the triangles that you find with another color.”
Activity
4 minutes: independent work time
“Choose 1 triangle that you colored in. Tell your partner 1 thing that you know about that shape.”
30 seconds: quiet think time
30 seconds: partner discussion
“Write a number to show how many triangles you colored. Write a number to show how many circles you colored.”
1 minute: independent work time
“Did you color more triangles or more circles? How do you know?”
30 seconds: quiet think time
30 seconds: partner discussion
Student Facing
[IMG]
[IMG]
[IMG]
[IMG]
[IMG]
[IMG]
[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 shape from student book or draw shape:
[IMG]
“Did you color this shape? Why or why not?” (I didn’t color the shape. It looks like a triangle but one of the sides is round.)
Display shape from student book or draw shape:
[IMG]
“Did you color this shape? Why or why not?” (I didn’t color this shape. It looks like a circle but it is stretched out.)


aligns: no