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 the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
problem_activity: Narrative
The purpose of this activity is for students to practice adding within 1,000 with an emphasis on adding by place. Throughout the activity, students have opportunities to explain their methods and representations to peers. In the synthesis, students have opportunities to question and critique the work of their peers as they compare different methods for adding three-digit numbers and different representations that show composing units when adding by place (MP3).
This activity uses
MLR8 Discussion Supports
. Advances: conversing
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to decide which problem to start with and the strategy they feel most comfortable solving with.
Supports accessibility for: Social-Emotional Functioning, Organization, Attention
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“We are going to practice adding 2 three-digit numbers. You can find the value of each sum in any way that makes sense to you. After some time working independently, you can continue working with a partner.”
MLR8 Discussion Supports
Display sentence frames to support students when they explain their strategy:
“First, I _____ because . . .”
“I noticed _____ so I . . .”
5 minutes: independent work time
4 minutes: partner work time
“Choose one expression and share how you found the value of the sum with a new partner.”
3 minutes: partner discussion
Monitor for students who use base-ten blocks, base-ten diagrams, or other representations that clearly show adding by place.
Student Facing
Find the value of each expression. Show your thinking.
\(384 + 409\)
\(757 + 152\)
\(262 + 438\)
\(575 + 166\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students lose track of the tens or hundreds they compose (for example,
\(384 + 409 = 783\)
) or do not compose a ten or hundred, prompt students to explain their thinking and any representations they use. Consider asking:
“How does your representation show that you composed a new unit?”
“What could you add to your representation to help you keep track of any tens or hundreds you compose?”
“How could you use base-ten blocks to show your thinking?”
Activity Synthesis
Invite 2–3 previously identified students to share their representations and how they found the value of the sums.
“How are these methods the same? How are they different?”


aligns: no