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: Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = �� – 3, 6 + 6 = ��.
problem_activity: Narrative
The purpose of this activity is for students to find the value of sums within 10. Students may apply what they learned about the commutative property and counting on. They may count on for certain equations, such as
\(+1\)
or
\(+2\)
equations as they can keep track easily, but count all for others. In the lesson synthesis, students return to the addition expressions cards they created in a previous lesson.
Action and Expression: Internalize Executive Functions
. Invite students to plan a method, including the tools they will use, for finding the sum. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Organization, Attention
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
Activity
Read the task statement.
5 minutes: independent work time
3 minutes: partner discussion
Student Facing
Find the value of each sum.
\(7 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(3 + 5 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} = 8 + 2\)
\(3 + 6 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(5 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} = 4 + 4\)
\(2 + 6 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} = 1 + 9\)
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
Display answers to problems.


correct_option_index: 1