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: 
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: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Answer: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
problem_activity: Narrative
The purpose of this activity is for students to interpret a scaled picture graph and write questions that can be asked based on the data represented in a scaled picture graph.
MLR8 Discussion Supports.
Use multimodal examples to show the meaning of a symbol. Use verbal descriptions along with gestures, drawings, or concrete objects to show how each flower on the graph is a symbol that represents five flowers that were seen in the park.
Advances: Listening, Representing
Representation: Internalize Comprehension.
Synthesis
:
Invite students to identify which details were needed to solve the problem. Display the sentence frame, “The next time I read a scaled picture graph I will pay attention to . . . .“
Supports accessibility for: Conceptual Processing
Launch
Groups of 2
Display the graphs for all to see.
“What are some strategies you could use to read the graphs?” (In the Flowers I Saw on the Way Home graph I could count each category by 5 since each picture represents 5 flowers.)
1 minute: quiet think time
Share and record responses.
Activity
“Now, we’re going to answer some questions about the scaled picture graphs. You will also have a chance to write your own question that can be asked based on each graph.”
8–10 minutes: partner work time
If there is time, have groups trade books and answer each other’s questions.
Math Community: As students work, monitor for examples of the “Doing Math” actions.
Student Facing
Andre collected data to see how many of each type of flower he saw on the way home. The data is shown in this picture graph:
[IMG]
How many of each type of flower did Andre see on the way home?
roses _____
tulips _____
daisies _____
violets _____
Write 2 questions that you could ask about the flowers Andre saw on his way home.
A group of students were asked, “What is your favorite type of book?” Their responses are shown in this picture graph:
[IMG]
How many students liked each type of book? How do you know?
Write 2 questions that you could ask about students’ favorite types of books based on the graph.
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 answer questions about the graph with numbers that don’t match the graph, consider asking:
“How did you answer the questions about the graph?”
“What does the key tell us about each picture in the graph?”
Activity Synthesis
Have students share responses to the questions they answered and explain their reasoning.
Consider asking:
“How did you use the scale to answer the questions?” (I counted by the number that each picture represented, like by 5 for the flowers and by 2 for the students.)
Share a variety of student written questions.
Consider asking:
“How did you know your question could be answered with the graph?” (The data you needed to answer the question was in the graph.)
If time ask, “What questions cannot be answered by this graph?” (How many students' favorite type of book is graphic novels?)


aligns: yes