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 following problem or activity 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: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students to use their data to generate questions and represent the answer using an equation. Then students take turns asking and answering each other’s questions.
Action and Expression: Internalize Executive Functions
.
Check for understanding by inviting students to rephrase directions in their own words.
Supports accessibility for: Memory, Organization
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Students need access to the survey data used in the previous activity.
Launch
Groups of 2
“We’re going to use our data again. This time we will create how many more and how many fewer questions about your data that you will ask your classmates to answer.”
Read the task statement.
“Use the categories in your survey data to complete the questions. You do not need to answer the questions."
3 minutes: independent work time
Activity
"Take turns asking and answering questions with your partner. After asking your question, let your partner show their work in your book."
10 minutes: partner work time
Student Facing
How many more students liked________________________________
than liked _______________________________?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
How many fewer students liked ________________________________
than liked _______________________________?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Write another story problem you could ask about your data.
Equation: ________________________________
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
"Clare asked, 'How many more students like pizza than burgers?' Her partner said six more people like pizza than burgers and wrote
\(10 - 4 = 6\)
."
“How could we turn this ‘more than’ question into a ‘fewer than’ question? Does this change the equation you would write? Why or why not?"


aligns: yes