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: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
problem_activity: Narrative
This activity prompts students to use multiplicative comparison to determine the cost of different living expenses in Bermuda and in India. Students use these costs to interpret and solve a multi-step problem. The multi-step problem can be solved in more than one way. Students might use multiplication or division. They may also choose to estimate rather than perform each calculation. Encourage students to use the Three Reads routine as needed to solve problems.
When finding the missing prices in the table, students also have an opportunity to reason about how to find a value that is 2.5 times as much. Students are not expected to multiply whole numbers by decimals in grade 4, but may use their understanding of decimal notation and decimal fractions to estimate the cost by doubling the price in India and adding half the price or by reasoning that 2.5 is close to 3.
MLR8 Discussion Supports.
Prior to solving the problems, invite students to make sense of the situations. Monitor and clarify any questions about the context.
Advances: Reading, Representing.
Launch
Groups of 2
“We saw one example of how the same items can vary a lot in cost depending on where you live in the United States. Let’s look at the costs of some other things in two different countries—one known to be very expensive and the other known to be inexpensive.”
Activity
5 minutes: independent work time on the first question
Monitor for students who use the multiplication or division algorithm, draw diagrams, write equations, or use estimation to find the missing values.
Pause for a discussion. Select students to share their responses and reasoning for finding the costs in the table.
Highlight that to find the missing cost in Bermuda, we can multiply the cost in India by the number in the middle column, and to find the cost in India, we divide the cost in Bermuda by the number in the middle column.
4 minutes: independent work time on the second question
4 minutes: partner discussion
Student Facing
Bermuda is the most expensive country in the world and India is one of the least expensive.
[IMG]
The table shows how prices of some things in the two countries compare. Estimate or calculate the missing costs and complete the table.
[IMG]
In India, rent for a 1-bedroom apartment outside of a city center costs about \$76 per month. A similar apartment in Bermuda costs 23 times as much.
Utilities (electric, gas, water, and heating) for a small apartment costs about \$27 per month in India and 7 times as much in Bermuda.
If a person earns \$2,000 per month, can they afford to pay rent and utilities in Bermuda?
Student Response
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for free access to Student Response.
Activity Synthesis
Select students to share their responses and strategies for how they determined if they can afford to live a month in Bermuda with \$2,000.


correct_option_index: 0

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