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


Topic options: 
A. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
B. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
C. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
D. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
E. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
F. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
G. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
H. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
I. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
J. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
K. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.


Thought: This problem pertains to functions because it asks students to find the general solution to a trigonometric function.
Answer: B

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


Topic options: 
A. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
B. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
C. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
D. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
E. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
F. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
G. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
H. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
I. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
J. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
K. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.


Thought: This task asks students to reason with equations, specifically a quadratic equation. Since the problem asks for as many different methods as possible, it's possible that students would discover solution methods that include graphing both sides of the equation with a graphing calculator and finding the x coordinates of where the two functions intersect.
Answer: B, G

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 $P$.


Topic options: 
A. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
B. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
C. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
D. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
E. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
F. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
G. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
H. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
I. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
J. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
K. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.


Thought: This task involves geometric concepts including angles, circles, and rays.
Answer: H

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
problem_activity: Optional activity
The purpose of this activity is for students to make preparations to create their scale drawings. They sketch a rough floor plan of the classroom.
In groups, they plan the steps for making measurements and then carry out their plan.
Some things to notice as students work:
As they draw their sketch, encourage them to focus on big-picture elements and not on details. It is not important that the sketch is neat or elaborate. What matters more is that it does not omit important features like the door.
As they make plans for measuring and recording, encourage them to work systematically to minimize omissions and errors.
Urge students to measure twice and record once. It is better to take a little more time to double check the measurements than to find out during drawing that they are off.
Launch
Give students 1–2 minutes to read the task statement individually and to ask any clarifying questions. Consider displaying a floor plan sketch of another room in the school. Emphasize that the sketch serves a similar purpose as an outline in writing. It does not need to be to scale, accurate, or elaborate, but it should show all the important pieces in the right places so it can be a reference in creating the scale drawing.
Arrange students in groups of 2–4. Smaller groups means that each individual student can be more involved in the measuring process, which is a benefit, but consider that it might also make the measuring process more time consuming (as it would mean more groups moving about in a confined space).
Distribute blank paper and give students 4–5 minutes to draw a sketch and to share it with a partner. Provide access to measuring tools. Give students another 4–5 minutes to plan in groups, and then time to measure (which may vary depending on size of classroom and other factors).
Representation: Internalize Comprehension.
Activate or supply background knowledge about measurement. Check to see that students are able to use measuring tools and record measurements accurately.
Supports accessibility for: Memory; Conceptual processing
Student Facing
On a blank sheet of paper, make a
rough sketch
of a floor plan of the classroom. Include parts of the room that the class has decided to include or that you would like to include. Accuracy is not important for this rough sketch, but be careful not to omit important features like a door.
Trade sketches with a partner and check each other’s work. Specifically, check if any parts are missing or incorrectly placed. Return their work and revise your sketch as needed.
Discuss with your group a plan for measuring. Work to reach an agreement on:
Which classroom features must be measured and which are optional.
The units to be used.
How to record and organize the measurements (on the sketch, in a list, in a table, etc.).
How to share the measuring and recording work (or the role each group member will play).
Gather your tools, take your measurements, and record them as planned. Be sure to double-check your measurements.
Make your own copy of all the measurements that your group has gathered, if you haven’t already done so. You will need them for the next activity.
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
After groups finish measuring, ask them to make sure that every group member has a copy of the measurements before moving on to the next part.
Consider briefly discussing what was challenging about doing the measuring. A few important issues which may come up include:
Making sure that the measuring device stays in a straight line.
It is hard to be accurate when the measuring device needs to be used
multiple
times in order to find the length of something long, such as a wall.
Taking turns with other groups that are trying to measure the same thing.
The measurements are not exact and need to be rounded.
Speaking: MLR8 Discussion Supports.
As students describe their process for measuring features of the room, press for details in students’ explanations by requesting that students challenge an idea, elaborate on an idea, or give an example of their measuring process. Provide a sentence frame such as: “It was challenging to measure ______ because . . . .” This will help students to produce and make sense of the language needed to communicate their own ideas.
Design Principle(s): Support sense-making; Optimize output (for explanation)


correct_option_index: 3