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: 
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).

Answer: 
No. This task does not involve an equation in two variables. There is only 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 following problem or activity 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_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
problem_activity: Narrative
The purpose of this Choral Count is to invite students to practice counting by
\(\frac{1}{2}\)
and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students recognize and generate equivalent fractions. In the synthesis, students have the opportunity to notice that
\(\frac{2}{2}\)
and
\(\frac{4}{4}\)
are both equal to 1 whole.
Required Preparation
Have recording of choral count by one-fourth available, from a previous lesson.
Launch
“Count by
\(\frac{1}{2}\)
, starting at
\(\frac{1}{2}\)
.”
Record as students count. Record 2 fractions in each row, then start a new row. There will be 4 rows.
Stop counting and recording at
\(\frac{8}{2}\)
.
Activity
“What patterns do you see?”
1–2 minutes: quiet think time
Record responses.
Student Response
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Activity Synthesis
Display count by
\(\frac{1}{4}\)
from the previous lesson. There should be 4 rows and 4 fractions in each row with the count ending at
\(\frac{16}{4}\)
.
“How are these two counts the same? How are they different?” (The denominator stays the same in both counts—4 for the last count, and 2 for today’s count. The numerators change in the same way because they both count by one. They start a new line at
\(\frac{2}{2}\)
and
\(\frac{4}{4}\)
, which are both whole numbers.)
Consider asking:
“Who can restate the pattern in different words?”
“Does anyone want to add an observation as to why that pattern is happening here?”
“Do you agree or disagree? Why?”


aligns: no