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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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


Concept/skill: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with one variable, x.

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 $P$.


Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^(3) and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. [Excludes multiplicative comparison problems (problems involving notions of “times as much”)]
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