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: 
Construct a tangent line from a point outside a given circle to the circle.

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, 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_neg_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
In this activity, students find the value of sums with larger numbers using any method that makes sense to them. They may represent their thinking using connecting cubes, drawings, equations, or words. Monitor for the ways students use methods based on place value, including the language they use to describe composing a ten when adding tens and tens and ones and ones (MP3, MP6).
MLR8 Discussion Supports.
Synthesis: After a strategy is presented to the class, invite students to turn to a partner and restate what they heard in their own words. Encourage students to borrow language from a display with words and phrases collected from previous lessons.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Connecting cubes
Required Preparation
Create connecting cubes in towers of 10 and singles.
Launch
Groups of 2
Give students access to connecting cubes in towers of 10 and singles.
“Now we are going to add larger numbers. Think about how you can show your thinking so others can understand.”
“You have time to work independently before sharing your thinking with a partner.”
Activity
5 minutes: independent work time
5 minutes: partner discussion
Monitor for students who:
Add by place value (
\(27 + 15\)
,
\(20 + 10 = 30\)
,
\(7 + 5 = 12\)
,
\(30 + 12 = 42\)
)
Decompose 1 number to make a 10, then add the rest (
\(27 + 15\)
,
\(27 + 3 = 30\)
,
\(30 + 12 = 42\)
)
Student Facing
Find the value of each sum. Show your thinking using drawings, numbers, or words.
\(37 + 8\)
\(24 + 23\)
\(16 + 30\)
\(39 + 11\)
\(27 + 15\)
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
Display
\(27 + 15\)
.
Select previously identified students to share.


aligns: no