few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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:
Concept/skill: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

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


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
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.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
problem_activity: Narrative
The purpose of this activity is for students to add within 1,000 using any strategy that makes sense to them. The expressions in this activity give students a chance to use different strategies, such as adding hundreds to hundreds, tens to tens, and ones to ones, reasoning with numbers close to a hundred, or using a variety of representations. Students who use base-ten blocks or draw number line diagrams choose appropriate tools strategically (MP5).
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select 3 of the 4 expressions to complete. Encourage the completion of the last two expressions, as they will be the focus of the synthesis.
Supports accessibility for: Organization, Attention, Social-emotional skills
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
“Take a minute to think about how you could find the value of each sum.”
1 minute: quiet think time
Share responses.
Activity
“Work with your partner to add these numbers in any way that makes sense to you. Explain or show your reasoning.”
5-7 minutes: partner work time
Monitor for an expression for which students use a variety of representations, such as:
Using base-ten blocks
Drawing a number line
Writing their reasoning in words
Writing equations
Identify students using different representations to share during synthesis.
Student Facing
Find the value of each sum in any way that makes sense to you. Explain or show your reasoning.
\(325 + 102\)
\(301 + 52\)
\(276 + 118\)
\(298 + 305\)
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
Select previously identified students to display their work side-by-side for all to see.
“Which representations show the same idea or help us find the sum the same way?” (The base-ten blocks and equations show adding hundreds to hundreds, tens to tens, and ones to ones. The number line and the words both added on the second number to the first number in parts.)


aligns: no