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: 
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_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
problem_activity: Narrative
The purpose of this activity is for students to use given information to ask and answer different questions. Students may ask Put Together or Compare problems using the given information. A representation of the information is also provided. This representation is a precursor to the tape diagrams students will use to represent and solve Compare problems in grade 2.
When students recognize the mathematical features of things in the real world and ask questions that arise from a presented situation, they model with mathematics (MP4).
MLR2 Collect and Display.
Circulate, listen for and collect the language students use as they create questions to match each task statement. On a visible display, record comparison words and phrases such as: more than, less than, how many fewer, and how many more. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Launch
Groups of 2
Give each group access to connecting cubes in towers or 10 and singles.
Activity
Read the task statement.
15 minutes: partner work time
Monitor for students who can explain how the representation helps them answer the question they asked.
Student Facing
Write and answer 2 questions using the information.
Use the picture for the first one if it is helpful.
Diego went on 7 rides.
Priya went on 11 rides.
[IMG]
Jada went on 3 rides.
Kiran went on 6 rides.
Noah went on 9 rides.
Student Response
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for free access to Student Response.
Activity Synthesis
Display the representation in the student book.
Invite previously identified students to share their question and how the representation helps them find the answer to the question.


aligns: no