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: 
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_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Count to 100 by ones and by tens.
problem_activity: Narrative
The purpose of this activity is for students to put numbers 1–20 in order.
MLR8 Discussion Supports.
Invite each group to chorally read numbers 1–20 in order once the group agrees on the order. Listen for and clarify questions.
Advances: Speaking, Conversing
Required Materials
Materials to Copy
Number Cards 1-20
Required Preparation
Create a set of cards from the blackline master for each group of 4.
Launch
Groups of 4
Give each group of students a set of number cards, not in sequence.
Activity
“Work with your group to put the numbers in order from 1 to 20.”
3 minutes: small-group work time
“Once your group agrees that the numbers are in the correct order, write the numbers in order from 1 to 20.”
3 minutes: independent work time
Student Facing
Write the numbers in order.
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
_________
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
“How did you decide the order of the numbers?”
Display numbers 1–12 in order.
“Clare is putting the numbers in order. What would you say to her to help her find the number that comes next?” (Look for 13 because it comes after 12. Look for the number that has a 3 because the last number has a 2.)


aligns: yes