few_shots: 
Example 1:
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.

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


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

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: 
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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
problem_activity: Narrative
The purpose of this warm-up is for students to consider concepts of number in a familiar context. Students may use the structure of the chart and the 5-frames to determine how many students made each choice (MP7). Students have an opportunity to hear and practice the count sequence. Adjust the context and choose a different question with 3 possible responses to better reflect students’ interests and experiences as needed.
MLR8 Discussion Supports.
Display an image or drawing of each type of pet above the corresponding 5-frame. Invite students to respond to the question using the sentence frame, “My favorite pet is a . . .”
Advances: Speaking, Representing.
Required Materials
Materials to Copy
Questions About Us Chart 5-Frame Template
Required Preparation
Cut out enough 5-frames to make a chart with a space for each student to answer the survey question.
Launch
Groups of 2
Display Questions About Us chart.
“Which pet is your favorite: dogs, cats, or rabbits?”
30 seconds: quiet think time
Record each student’s choice with a circle in a 5-frame.
Activity
“How can we figure out how many students chose dogs?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students chose dogs?”
“How many students chose cats?”
30 seconds: quiet think time
Share responses.
“How many students chose rabbits?”
30 seconds: quiet think time
Share responses.
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
“What was different about the question that we answered today?” (There were 3 choices instead of 2.)


aligns: yes