few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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:
Concept/skill: 
Solve quadratic equations in one variable.

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


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

Example 3:
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.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 100 can be thought of as a bundle of ten tens — called a “hundred.”
- The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
problem_activity: Narrative
In this activity students compare two book sale scenarios in which there is a different base price of a book for the fundraiser. Students notice that when you increase the price by a lot, you make more profit per book, but you may also sell fewer books. On the other hand, if you increase the price by less money, you have to sell more books to make the same profit.
MLR6 Three Reads.
Keep books or devices closed. Display only the problem stem, without revealing the questions. “We are going to read this question 3 times.” After the 1st Read: “Tell your partner what this situation is about.” After the 2nd Read: “List the quantities. What can be counted or measured?” Reveal the question(s). After the 3rd Read: “What strategies can we use to solve this problem?”
Advances: Reading, Representing
Launch
Groups of 2
“When a school plans a book sale fundraiser, the school orders books from the publisher, or bookseller, for a certain price. Then the school sells it for a different price at the book fair.”
“Let’s imagine the school buys a book for \$10. Should they sell the book for more or less than \$10 at the book fair? Why?” (More if they want to make money from the sale.)
“This is called the mark-up price. For every book they sell, the bookseller will get \$10 and the school keeps the amount they added. The amount they add is called the profit.”
Activity
1 minute quiet think time
5 minutes: group work time
Monitor for students who consider the profit per book in their justifications.
Student Facing
Two schools buy science books for \$8 from a publisher to sell at their book sale. School A sells the books for \$12. School B sells the books for \$12.90.
Who do you think sells more science books? Why?
How much profit does each school make if they each sell 35 books?
School B sells 10 science books. How many science books does School A have to sell to raise about the same amount of money?
Student Response
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Activity Synthesis
“What is a reasonable mark-up price?”
“What do you need to consider when deciding a mark-up price?”


aligns: no