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


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Standard options: 
A. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
B. Solve quadratic equations in one variable.


Thought: This task shows one quadratic equation with one variable, x.
Answer: B

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 $P$.


Standard options: 
A. 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.
B. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.


Thought: 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.
Answer: A

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: 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.

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
problem_activity: Narrative
In this activity, students create a line plot using the measurement data that they generated earlier and display their group’s line plot for all to see.
Encourage students to plan their line plot using the blank line in the activity statement before creating a poster version for display in a gallery walk. A template for a larger line plot is provided in the blackline master. Students can join the number lines on two copies of the blackline master to create a longer number line.
[IMG]
As students visit others’ data displays, they consider how the line plots are alike and how they are different, as well as why different scales might have been chosen for different objects measured.
Representation: Access for Perception.
Synthesis: Use gestures during the explanation of the line plot to emphasize important aspects of the line plot.
Supports accessibility for: Conceptual Processing, Attention
Required Materials
Materials to Gather
Glue or tape
Scissors
Tools for creating a visual display
Materials to Copy
Let's Make a Line Plot
Launch
Groups of 4
“Look at the data your group collected. What do you need to know to make a line plot that represents the data?” (The longest and shortest measurements. Whether the lengths are whole numbers or include halves and fourths of an inch.)
1 minute: group discussion
Share responses.
Give each group 2 copies of the blackline master, scissors, glue or tape, and tools for creating a visual display.
Activity
“Work with your group to create a line plot that represents your data. You will share your line plot with the class later.”
“You can use the blank number line on your page to plan your line plot before creating a final one to display.”
Consider asking:
“How do you plan to make the scale for the line plot so that it can show all your measurements?”
“What information or labels could be included to help others understand your line plot?”
Demonstrate how to join and tape (or glue) the 2 copies of the blackline master to make a large line plot.
“After you complete your final line plot, tape (or glue) your line plot on a poster.”
12–15 minutes: group work time
Student Facing
Create a line plot to represent the measurement data you collected. You will display and share your line plot with your class later.
You can use the blank number line here for your draft. Think about:
how to label the tick marks so that all the measurements are included
details to help others understand the data you collected
[IMG]
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
Ask students to display their posters.
MLR7 Compare and Connect
“As you visit the posters with your group, think about how the line plots are alike and how they are different. Be prepared to share your observations.”
5 minute: gallery walk
See lesson synthesis.


correct_option_index: 0