few_shots: Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Standard options: 
A. Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Your response:
Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Your response:
Thought: This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).
Answer: B

Example 3:
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.


Your response:
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

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

fl_problem_001097

7

fl_problem_001894

HS_0
options: Define appropriate quantities for the purpose of descriptive modeling.

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
problem_activity: In Class Launch
Use after Unit 4, Lesson 8
Read the situation in the task statement aloud, or ask students to read it to themselves quietly.
Tell students to think about these questions:
“What might be some different ways of giving bonuses?”
“Does anyone have a job and has gotten a raise or a bonus? How are your allowances determined? Do they ever change?”
“What variables should be considered? What information do you need to know about the employees to compute bonuses for each of them?”
Give students a few minutes of quiet think time, then ask them to talk over their ideas with a partner. Finally, ask students to share their ideas with the whole class and record these ideas for all to see.
Ask students if they have any questions about the situation.
If students want to know what type of company it is and what jobs the employees are doing, tell them that they can make up a fake company with specific jobs.
Teacher Instructions
As students are considering the situation, prompt them with the following questions, as necessary:
"What are some variables you should consider?"
"Can you think of mathematically different methods to distribute the money?"
"What information would be helpful to know to compute the bonus for each employee?"
Tell students that they can make up the information they need to compute specific bonuses for 2 different methods and to apply them to the situation. In the proposal, students should compute the specific dollar amount each employee receives as a bonus.
If there is time, encourage students to try generalizing any values they invented to use variables instead.
Student-Facing Statement
A project at a large company was very successful, and the company made more money than expected as a result. Your boss has given you the task of coming up with different methods to distribute bonuses to the 5 employees that directly worked on the project. There is a total of
$
8,000 available to distribute.
The method for distributing the money will be shared with the entire company, so it is important that the employees feel the distribution is fair.
Make a proposal with at least two different methods for your boss to choose from. Describe the advantages and disadvantages of each method. Then give your recommendation and provide an argument in its support.
For each of the methods you propose, which of the five employees is most likely to complain about the method being unfair? How would you justify the method to this employee?
Teacher Instructions
As students are considering the situation, prompt them with the following questions, as necessary:
“Which of these variables should you consider?”
“Can you think of mathematically different methods to distribute the money?”
“What additional information would be helpful to know to compute the bonus for each employee?”
Tell students that they can make up any additional information they need to compute specific bonuses for 2 different methods and to apply them to the situation. In the proposal, students should compute the specific dollar amount each employee receives as a bonus.
If there is time, encourage students to try generalizing any values they invented to use variables instead.
Student-Facing Statement
A project in a large company was very successful, and the company made more money than expected as a result. Your boss has given you the task of coming up with different methods to distribute bonuses to the 5 employees that directly worked on the project. There is a total of
$
8,000 available to distribute.
Here is some information about the employees:
| employee | job description | hours working on project (per week) | annual salary | job experience |
|----------|-----------------|-------------------------------------|---------------|----------------|
|    A     |                 |                                     |               |                |
|    B     |                 |                                     |               |                |
|    C     |                 |                                     |               |                |
|    D     |                 |                                     |               |                |
|    E     |                 |                                     |               |                |
Make a proposal with at least two different methods for your boss to choose from. Outline the advantages and disadvantages of each method. Then give your recommendation and support your argument.
For each of the methods you propose, which of the five employees is most likely to complain about the method being unfair? How would you justify the method to this employee?


correct_option_index: 0

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