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.


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.


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.


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: Read, write, and compare decimals to thousandths.

Use place value understanding to round decimals to any place.

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
problem_activity: Narrative
The purpose of this activity is for students to convert from meters to centimeters using the context of a standing broad jump, a common test for physical fitness. Students may multiply by 100 to convert from meters to centimeters or divide by 100 to convert from centimeters to meters. Students should be encouraged to use whatever strategy makes sense to them. Future lessons will focus specifically on conversion from centimeters to meters. Give students access to meter sticks.
MLR8 Discussion Supports.
Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Required Materials
Materials to Gather
Metersticks
Launch
Groups of 2
Display the image from student workbook.
Give students access to meter sticks.
“What do you notice? What do you wonder?” (The girl is jumping. There are numbers on the mat. Did she start where the footprints are? How far did she jump?)
Activity
1–2 minutes: quiet think time
6–8 minutes: partner work time
Monitor for students who:
use their result for Tyler’s jump in centimeters to find his jump in millimeters
use the result in meters to find how far Tyler jumped in millimeters
Student Facing
[IMG]
[IMG]
Here are the distances that each student jumped.
| student |  distance   |
|---------|-------------|
|   Mai   | 1.61 meters |
|  Tyler  | 1.43 meters |
|  Clare  | 1.57 meters |
The average standing broad jump distance for 5th graders is 148 centimeters. Are each of the students in the table below, at, or above the average? Explain or show your reasoning.
The world record for the standing broad jump is 337 centimeters. Jada says that’s more than Mai and Clare jumped combined. Do you agree with Jada? Explain or show your reasoning.
Tyler says his jump sounds more impressive if he reports it in millimeters.
How far is Tyler’s jump in millimeters? What about Mai’s and Clare’s jumps?
Which unit do you think is best for reporting the jumps? Explain your reasoning.
Student Response
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Advancing Student Thinking
If students do not know the relationship between millimeters, centimeters, and meters, show them a meter stick and ask “How can you use the meter stick to figure out how many millimeters are in 1 meter?”
Activity Synthesis
Display the expression:
\(1.43 \times 100\)
.
“How does this expression represent Tyler’s jump in centimeters?” (There are 100 centimeters in a meter.)
Invite students to share how they found Tyler’s jump in millimeters.
Display the expression:
\((1.43 \times 100) \times 10\)
.
“In what unit of measurement does this expression represent Tyler's jump? How do you know?” (It represents Tyler’s jump in millimeters. There are 10 millimeters in a centimeter and
\(1.43\times100\)
represents the centimeters, so if we multiply the number of centimeters by 10, we will get the number of millimeters.)
Display the expression:
\(1.43 \times 1,\!000\)
.
“How does this expression represent Tyler’s jump in millimeters?” (There are 1,000 millimeters in a meter so I have to multiply by 1,000 to get millimeters from meters.)
Display the equation:
\(1.43 \times 1,\!000 = (1.43 \times 100) \times 10\)
.
Invite students to share which unit they prefer to express the distances that the students jumped.
“It’s important to choose a unit that makes sense to you.”


correct_option_index: 2