few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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

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:
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_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: In Class Launch
Use after Unit 1, Lesson 15
Ask students to think about a question they are interested in that they would need to gather data in order to answer. They will choose one of these questions, find data relevant to it, and present their results with a data display or an infographic. Either show students examples of infographics or ask them to look up a few examples.
Students can be arranged in groups in advance, or they can choose groups based on the questions they are most interested in.
Teacher Instructions
Students may not be able to find the information they need to answer the question they were originally interested in. They can refine and change their question to align with the data available.
If students are not sure where to begin, it might be helpful for them to think about questions that compare two groups, since they have been doing a lot of work with comparing data sets using measures of center and variability, and this is the kind of data analysis they will be expected to do.
Student-Facing Statement
Choose a question that you think is interesting and that you do not know the answer to. You will gather data relevant to this question by either doing an experiment or researching available data, so choose a reasonable question.
Write your question.
What do you predict you will learn from the data?
Next, gather your data. Then choose one of these options for displaying your data and answer the questions about it.
Option 1: Create a display that shows the distribution of the data. Include both measures of center and measures of variability.
Why is the data display you selected the best way to summarize your data?
Is any of the data surprising?
Are there any outliers? If so, tell their story. If not, why do you think not?
Describe the shape of the distribution.
Option 2: Use an infographic to summarize what you found.
Why is an infographic the best way to summarize your data?
Is any of the data surprising?
What story does your infographic tell?
Now that you have seen some data, is there another, related question you would like to study or some additional data you would like to collect?
Teacher Instructions
Give students a source of data and let them explore it for a few minutes and share observations in pairs or groups before they begin working on the task statement. This task can be further scaffolded by giving students data that is easier to work with.
If students are not sure where to begin, it might be helpful for them to think about questions that compare two groups, since they have been doing a lot of work with comparing data sets using measures of center and variability, and this is the kind of data analysis they will be expected to do.
Student-Facing Statement
What are some questions that you might be able to answer with the given data?
Choose one of your questions to try to answer. What do you predict the data will tell you?
Look for data that’s relevant to your question. You might have to change your question a little if you can’t find the data you need to answer the original question. When you have an answer, choose a way of displaying the data that will help other people understand what you learned.
Option 1: Create a display that shows the distribution of the data. Include both measures of center and measures of variability.
Why is the data display you selected the best way to summarize your data?
Is any of the data surprising?
Are there any outliers? If so, tell their story. If not, why do you think not?
Describe the shape of the distribution.
Option 2: Use an infographic to summarize what you found.
Why is an infographic the best way to summarize your data?
Is any of the data surprising?
What story does your infographic tell?
Now that you have seen some data, is there another, related question you would like to study or some additional data you would like to collect?


aligns: no