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: Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.
problem_activity: Narrative
The purpose of this activity is for students to write numbers between 95 and 120. Groups create posters that show a drawing of how they counted their animal measurements from the last activity. Groups should not write a number for the final measurement on the poster. Students do a gallery walk to interpret each representation and record the count with a number in their workbooks. Group members then compare their counts and written numbers.
When students look at the different representations and determine the length of each animal, they may notice that the representation may help to accurately find the value. For example, students may draw groups of 10 cubes rather than every individual cube (MP7).
This activity uses
MLR7 Compare and Connect
. Advances:
representing, conversing.
Required Materials
Materials to Gather
Tools for creating a visual display
Launch
Groups of 3
Give each group tools for creating a visual display.
Activity
MLR7 Compare and Connect
“Create a poster to show how you counted the cubes you used to measure the length of the animal in the measuring animals activity. Do not write the number of cubes your animal measured on your poster.”
5 minutes: group work time
“Now we will do a gallery walk to see different representations of your measurements. As you look at each poster, use the representation to determine the length of the animal. Write the number of cubes that represents its length in your book.”
7 minutes: gallery walk
Student Facing
For each animal, write the number of cubes that represent its length.
The beaver is ______________________ long.
The dog is ______________________ long.
The giant anteater is ______________________ long.
The raccoon is ______________________ long.
The red fox is ______________________ long.
The snake is ______________________ long.
[IMG]
Student Response
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Activity Synthesis
Display the snake and giant anteater posters.
“How do I write the number that represents the length of the snake?”
“Where do you see 100 in this poster? Where do you see 5?”
Repeat for giant anteater.


aligns: no