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: 
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_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Order three objects by length; compare the lengths of two objects indirectly by using a third object.
problem_activity: Narrative
The purpose of this activity is for students to think of questions that can be answered using the data representation they create as they collect data from the class. Although there are two different sets of data, all of the questions students ask should be able to be answered using either data set. Questions are compiled during the synthesis and will be used in the following activity.
If necessary, use the provided blackline master instead of collecting data from the class. Cut the blackline master in half and give half the class data from Group A and the other half data from Group B.
Required Materials
Materials to Copy
Favorite Special Class Data
Launch
Groups of 2
“We are going to take another survey and ask questions about the data.”
Decide on a survey question the class would like to answer and three possible responses.
“Record the title of the data representation and each category.”
Demonstrate recording the titles.
Divide the class into Group A and Group B. Each partnership should have one person from each group.
“Group A is going to take the survey first. If you are in Group B, record the data in your book as I record it for all to see.”
Ask students in Group A the survey question and record the data on the table using tally marks and numbers.
“Now Group B is going to take the survey and Group A will record the data.”
Ask students in Group B the survey question and record the data on the table using tally marks and numbers.
Activity
“Now, think of as many questions as you can that can be answered using your data representation. Record your questions in your book if you would like.”
5 minutes: independent work time
Student Facing
Our favorite __________________________________________________
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "width:33%"}, "p": [{"_attributes": {"style": "text-align:center"}, "_value": "category 1"}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}]}, {"_attributes": {"scope": "col", "style": "width:33%"}, "p": [{"_attributes": {"style": "text-align:center"}, "_value": "category 2"}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}]}, {"_attributes": {"scope": "col", "style": "width:33%"}, "p": [{"_attributes": {"style": "text-align:center"}, "_value": "category 3"}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}]}]}]}], "tbody": [{"tr": [{"td": [{"p": [{"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}]}, {}, {}]}]}]}]}
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 make statements instead of questions, consider asking:
“What is the question you want your partner to answer?”
“How could you finish this question, ‘How many students chose _____?’”
Activity Synthesis
Share and record the students’ questions about their data.
“Now we will ask our partner some of these questions.”


aligns: no