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: 
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.

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, 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_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
problem_activity: Narrative
This optional activity gives students another opportunity to practice identifying multiples of some powers of 10 that border a given number and identify the nearest ones. As before, students may use number lines to support their reasoning, but here the number lines are unlabeled.
Launch
Groups of 2
Activity
“Work independently for a few minutes. Then, discuss your responses with your partner.”
5 minutes: independent work time
2 minutes: partner discussion
Student Facing
Answer each question. Label and use the number lines if they are helpful.
Is 425,193 closer to 400,000 or 500,000?
[IMG]
Is 425,193 closer to 420,000 or 430,000?
[IMG]
Is 425,193 closer to 425,000 or 426,000?
[IMG]
Is 425,193 closer to 425,100 or to 425,200?
[IMG]
Is 425,193 closer to 425,190 or to 425,200?
[IMG]
For the number 425,193:
The nearest multiple of 100,000 is _______________.
The nearest multiple of 10,000 is _______________.
The nearest multiple of 1,000 is _______________.
The nearest multiple of 100 is _______________.
The nearest multiple of 10 is _______________.
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
Invite students to share their responses and reasoning.
“Which nearest multiples were you able to identify fairly easily?”
“Which were a bit more challenging, if any? Why might that be?”


aligns: no