few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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

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: 
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, 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_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
problem_activity: Narrative
The purpose of this optional activity is for students to practice the verbal count sequence to 10. This activity is optional because it is an opportunity for extra practice that not all students may need. Based on formative assessment data and observation from previous sections and during the first activity, this activity will be helpful for students who are not yet saying the count sequence to 10. English learners in particular will benefit from this additional opportunity to practice the verbal count sequence.
This activity can be used with a small-group or the whole class. Students who do not need this optional activity may benefit from additional time working in centers. Some students may benefit from working on the concepts in this optional activity more than one time. Consider incorporating counting and counting songs throughout the day and during transitions.
Launch
Groups of 2
“I’m going to count to 10.”
Count to 10.
Activity
“Let’s count to 10 all together.”
Count to 10 all together.
“Let’s count to 10 and clap our hands when we say each number.”
Count to 10 and clap all together.
“Let’s count to 10 and touch the table when we say each number.”
Count to 10 and touch the table all together.
“Let’s count to 10 and put up 1 finger when we say each number.”
Count to 10 and put up each finger all together.
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 “sing” the count sequence without separating each number word, prompt them to count slowly and match a gesture or movement with each number.
Activity Synthesis
“Take turns counting to 10 with your partner. You can clap your hands or touch the table when you say each number. You can also think of your own movement for each number.”
1 minute: partner discussion


aligns: no