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: Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
problem_activity: Narrative
The purpose of this activity is for students to solve two story problems involving adding or subtracting multiples of 10. Students are presented with a familiar context from a previous lesson in which students counted cubes in different bags. The quantities of cubes are described using representations that students are familiar with, and students add or subtract in a way that makes sense to them. The familiar context and representations are used to help students make sense of adding and subtracting tens. In the synthesis, students compare and connect the different representations used for each problem (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 three 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 in towers of 10 and singles
Double 10-frames
Launch
Groups of 2
Give students access to connecting cubes in towers of 10 and singles and double 10-frames.
Activity
Read the task statement.
7 minutes: independent work time
3 minutes: partner discussion
Monitor for students who show:
towers of 10
base-ten drawings
__ tens and __ tens
expressions or equations
Student Facing
Jada is counting collections of cubes.
In Bag A there are 30 cubes.
In Bag B there are 2 towers of 10.
How many cubes are in the two bags all together?
Show your thinking using drawings, numbers, or words.
Tyler is counting a collection of cubes.
In Bag C there are 7 towers of 10.
He takes 40 cubes out of the bag.
How many cubes does he have left in the bag?
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.
Advancing Student Thinking
If students attempt to add or subtract using single cubes (or representations of single cubes), consider asking:
“How are you planning to find out how many cubes there are now?”
“How could you use what we've learned about tens to solve this problem?”
Activity Synthesis
Invite previously identified students to share their representations.
“How are these representations the same? How are they different?”


aligns: no