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: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 2 of the Target Numbers center. Students start with 25, choose a number card and decide whether to add that number of tens or ones. Students play six rounds and the student who gets as close to 95 as possible without going over is the winner.
MLR8 Discussion Supports.
Prior to playing the game, invite students to make sense of the directions and take turns sharing their understanding with their partner. Listen for and clarify any questions about the directions.
Advances: Reading, Representing
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Number cards 0–10
Materials to Copy
Target Numbers Stage 2 Recording Sheet
Launch
Groups of 2
Give each group a set of number cards, two recording sheets, and access to connecting cubes in towers of 10 and singles.
“Take out all of the cards that show 0 or 10.”
“We are going to learn a new way to play Target Numbers. This time, your goal is to get as close to 95 as you can, without going over. You only get 6 turns. On each turn, you get to decide whether you want to add tens or ones to your number. Let’s play a round together. Each partner starts at 25.”
Demonstrate drawing a number card.
“I drew a [4]. Should I add 4 ones or 4 tens? Why?” (You can add 4 tens because that will give you 65. You still have 5 rounds to get to 95. You can add 4 ones to make 29. That gives you more time to add tens.)
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
“I’m going to add 4 tens, 2 tens and 4 tens is 6 tens. So my sum is 65.”
“Once my partner and I agree on the sum, the partner who drew the number card records an equation. Since 25 is already filled in for me, I will record the number as tens (or ones) and the sum.”
Demonstrate completing the equation.
“After I write my equation, the sum becomes my starting number for the next round, so I write it in as the first number in the next equation.”
If needed, play another round with the class.
“Take turns drawing the number card, finding the sum and writing an equation. Each player plays 6 rounds. Whoever gets closest to 95 without going over is the winner.”
Activity
10 minutes: partner work time
Activity Synthesis
“When you draw the number card, what is your method for deciding whether to add that many tens or ones?” (I think about how close I am to 95. That helps me think about whether to add ones or tens.)


aligns: yes