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


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response:
Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

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


Standard options: 
A. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
B. Solve quadratic equations in one variable.


Your response:
Thought: This task shows one quadratic equation with one variable, x.
Answer: B

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 $P$.


Standard options: 
A. 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.
B. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.


Your response:
Thought: 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.
Answer: A

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
- 10 can be thought of as a bundle of ten ones — called a “ten.”
problem_activity: Narrative
The purpose of this activity is for students to
learn a new center called Greatest of Them All. Students use digit cards to create the greatest possible number. As each student draws a card, they choose where to write it on the recording sheet. Once a digit is placed, it can’t be moved. Students compare their numbers using <, >, or =. The player with the greater number in each round gets a point. Students think strategically about place value when they decide how to use the first of the 2 cards they draw (MP7).
Students should remove cards that show 10 from their deck.
Action and Expression: Internalize Executive Functions.
Check for understanding by inviting students to rephrase directions in their own words.
Supports accessibility for: Memory, Organization
Required Materials
Materials to Gather
Number cards 0–10
Materials to Copy
Greatest of Them All Stage 1 Recording Sheet
Launch
Groups of 2
Give each group a set of number cards and two recording sheets.
Ask students to remove the cards with the number 10.
“We are going to learn a new center called Greatest of Them All. You and your partner both make a two-digit number. Try to make the greatest number you can because the player with the greater number wins. Let’s play one round together.”
Display the number cards and recording sheet.
Invite a student to act as your partner.
Choose a number card.
“I can decide where to place this digit on the recording sheet. This digit can be my ones or my tens, but once I place it, it cannot be moved.”
“Where would you place this number on the recording sheet? Why would you place it there?” (I would put it in the tens place because 6 is a high number and I want to have a lot of tens. I would put this number in the ones place because I want to try to get a greater number for my tens.)
“After you place one number, your partner chooses a card and places the number on their recording sheet.”
Invite your partner to choose a card and decide where they will place the number.
Repeat until each of you has a two-digit number.
“Now we compare our numbers. Who has the greater number? How do you know?”
“Finally, we write a comparison using <, >, or =.”
Demonstrate writing the comparison statement on the recording sheet.
“The player with the greater number gets a point. Continue playing until someone reaches 5 points.”
Activity
10 minutes: partner work time
Activity Synthesis
Display a recording sheet with a 5 in the tens place for one partner and the rest blank.
“My partner has a 5 in the tens place. I choose a card and see that it is a 6. Where should I place the 6? Why would you place it there?” (Place it in the tens place because 6 tens is more than 5 tens so the number in the ones place won't matter. You will have the greater number.)


correct_option_index: 0

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