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 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_pos_0

HS_2
standard_description: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
problem_activity: Narrative
The purpose of this activity is for students to add 2 two-digit numbers within 100 and show their thinking with equations. Although some students may write each step of their thinking with equations, it is not required that they do so. Students can write one equation that shows the sum and represent their solution pathway in their drawings. In the activity synthesis, students present their method verbally to a new partner.
This activity uses
MLR8 Discussion Supports. Advances: listening, speaking, conversing
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Launch
Groups of 2
Give students access to connecting cubes in towers of 10 and singles.
“We have been learning about different ways to add within 100. You are going to find sums using a method that makes most sense to you for each problem. Record equations to show your thinking.”
Activity
5 minutes: independent work time
“Compare your work with your partner’s. Did you use the same method? Did you represent your method in the same way? How is your work the same? How is it different?"
5 minutes: partner work time
Monitor for a student who wrote equations related to making ten and one who wrote equations related to adding by place.
Student Facing
Find the value of each sum using any method that you want.
Show your thinking using drawings, numbers, or words.
Write equations to represent your thinking.
\(48 + 15\)
\(57 + 36\)
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
MLR8 Discussion Supports:
Display sentence frames to support students when they explain their method as equations:
“First, I _____ because . . .”
“I noticed _____ so I . . .”
“You are going to explain your method to another student in the class. Practice what you will say with your partner. Use these sentence starters to help you.”
3 minutes: partner discussion
“Find a new partner and explain your method.”
2 minutes: partner discussion


aligns: yes