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: Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Fluently add and subtract within 5.

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students to find the missing value in addition and subtraction equations. This activity is optional because determining the missing value of an equation is not required by the standards. Students may “just know” some of the answers or they may use counting forward or backward (MP7) or they may draw a picture.
MLR8 Discussion Supports.
Invite students to read their completed equations aloud.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to connecting cubes or two-color counters.
Display the student book.
“What do you notice? What do you wonder?” (The equations have a number missing. Why are there numbers missing?)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“FIll in the missing part of each equation.”
Activity
10 minutes: partner work time
Monitor for students who use two-color counters or connecting cubes.
Monitor for students who draw pictures.
Student Facing
Fill in the missing part of each equation.
\(3 - \underline{\hspace{1.1 cm}} = 2\)
\(2 + \underline{\hspace{1.1 cm}} = 2\)
\(5 - \underline{\hspace{1.1 cm}} = 2\)
\(1 + \underline{\hspace{1.1 cm}} = 2\)
\(5 - \underline{\hspace{1.1 cm}} = 3\)
\(2 + \underline{\hspace{1.1 cm}} = 3\)
\(4 - \underline{\hspace{1.1 cm}} = 3\)
\(0 + \underline{\hspace{1.1 cm}} = 3\)
\(5 - \underline{\hspace{1.1 cm}} = 4\)
\(3 + \underline{\hspace{1.1 cm}} = 4\)
\(4 - \underline{\hspace{1.1 cm}} = 4\)
\(2 + \underline{\hspace{1.1 cm}} = 4\)
\(1 + \underline{\hspace{1.1 cm}} = 5\)
\(4 + \underline{\hspace{1.1 cm}} = 5\)
\(5 - \underline{\hspace{1.1 cm}} = 5\)
\(3 + \underline{\hspace{1.1 cm}} = 5\)
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
Invite previously identified students to share.


correct_option_index: 2