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: 
Solve quadratic equations in one variable.

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


Answer: 
Yes. This task shows one quadratic equation with 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_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
problem_activity: Narrative
The purpose of this activity is for students to describe coordinates for points. After playing a round of What’s the Point, students have an opportunity to write a description of the location of a point in the coordinate plane. The structure of this part of the activity mirrors what students did in the previous lesson when they were describing a rectangle. Some students may use the coordinates on the grid while others may use words to describe the location of the point.
Students make choices about how to revise their thinking based on what makes the description stronger and clearer to them. This activity not only supports students developing language to describe the location of a point but also develops a deeper understanding of the coordinate grid (MP6). Invite students to use language from the display from an earlier lesson if they find it helpful.
This activity uses
MLR1 Stronger and Clearer Each Time
. Advances: Reading, Writing.
Required Materials
Materials to Copy
What's the Point
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2.
Activity
10 minutes: partner work time
Monitor for students who:
revise their thinking
refer to the numbers on the coordinate grid to communicate the location of the point
MLR1 Stronger and Clearer Each Time
“Share your description of the location of the point on the grid with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3–5 minutes: structured partner discussion
Repeat with 1–2 different partners.
If needed, display question starters and prompts for feedback, such as:
“Can you use the numbers on the coordinate grid in your explanation?”
“Revise your initial draft based on the feedback you got from your partner.”
2–3 minutes: independent work time
Student Facing
Play 2 rounds of What’s the Point so each partner gets a chance to draw.
Sit back to back with your partner.
Partner A: Choose a card. Then, describe the location of the point to your partner.
Partner B: Draw the point on the blank coordinate grid.
Compare the card with your partner’s diagram.
Discuss: What’s the same? What’s different?
[IMG]
[IMG]
Use words to explain the location of the point on the grid.
[IMG]
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 do not reference the axes or the directionality of the gridlines, show them point
\((3, 4)\)
and point
\((4, 3)\)
on a grid and ask, “What is the same and different about these two points?”
Activity Synthesis
Select previously identified students to share how they revised their explanation for the location of the point in the last problem.
Display the image of the coordinate grid with a point from the student workbook.
“The point can be described using the
coordinates
\((3, 4)\)
. Where do you think these coordinates come from?” (They describe the location of the point. The point is on gridline 3 and gridline 4. The point is where these gridlines intersect.)


aligns: no