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: 
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).

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


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
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.

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: 
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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

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: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
problem_activity: Narrative
The purpose of this activity is for students to discuss different ways to solve a three-addend story problem in which none of the addends can be combined to make 10 without being decomposed. Students solve the problem in a way that makes sense to them. Some students may build each number separately on the 10-frames and see both are filled. Some students may manipulate the numbers and think
\(8 + 7 + 5 = 8 + 2 + 5 + 5\)
. Different methods for solving are highlighted in the synthesis. It is important that the teacher represents student thinking, so that these methods are visible to all.
When students make sense of the story problems and connect the quantities in the story to an equation, they reason abstractly and quantitatively (MP2).
MLR6 Three Reads.
Keep books or devices closed. To launch this activity, display only the problem stem, without revealing the question. “We are going to read this story problem 3 times.” After the 1st Read: “Tell your partner what happened in the story.” After the 2nd Read: “What are all the things we can count in this story?” Reveal the question. After the 3rd Read: “What are different ways we can solve this problem?”
Advances: Reading, Representing
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Double 10-frames
Launch
Groups of 2
Give students access to double 10-frames and connecting cubes or two-color counters.
Activity
Read the task statement.
4 minutes: independent work time
2 minutes: partner discussion
Monitor for students who:
place 8, 7, and 5 counters on the 10-frames and see that they are both full
count on
represent the problem as
\(8 + 2 + 5 + 5\)
use a known sum like
\(8 + 8\)
and then add 4 more.
Student Facing
Jada went to the zoo with her family.
They went to the reptile exhibit and saw 8 snakes, 7 iguanas, and 5 frogs.
[IMG]
How many reptiles did Jada's family see?
Show your thinking using drawings, numbers, or words.
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 previously identified students to share.
“What did they do to find the sum?”
Record each method with an equation.


aligns: no