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.


Topic options: 
A. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
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 - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
D. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
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. 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. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
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. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
J. 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.
K. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.


Your response:
{
  "explanation": "This task involves learning addition, which is a mathematical operation, using objects.",
  "answer": "F"
}

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
$$-\frac{1}{4}$$


Topic options: 
A. 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.
B. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
C. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
D. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
E. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
F. 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.
G. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
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. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
J. 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.
K. 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.


Your response:
{
  "explanation": "This problem teaches students different ways of writing numbers that express the same value. This helps students better understand the complex number system, which includes rational numbers.",
  "answer": "I"
}

Example 3:
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.


Your response:
{
  "explanation": "This problem pertains to functions because it asks students to find the general solution to a trigonometric function.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: im_task_001477

K

fl_problem_001097

7

fl_problem_001894

HS_0
options: Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

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

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.

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

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

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.

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.

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.

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.
problem_activity: Narrative
The purpose of this activity is for students to learn about
prime numbers
and
composite numbers
. Students are given a set of cards with rectangles on them. They sort the rectangles by area and then attempt to draw an additional rectangle for each category. They notice that some areas can be represented by more than one rectangle and some areas can only be represented by one rectangle.
During the synthesis, highlight that the side lengths of each rectangle represent one factor pair (each pair of side lengths should be used only once), and that the area of each rectangle represents a multiple of each side length. Students learn that a number with only one factor pair—1 and the number itself—is a prime number, and a number with more than one factor pair is a composite number.
Here is an image of the cards for reference.
[IMG]
MLR8 Discussion Supports
. Invite students to take turns selecting a rectangle, and explaining how they should sort it to their partner. Display the following sentence frames: “This rectangle belongs with _____ , because . . .” Encourage students to challenge each other when they disagree.
Advances: Conversing, Representing
Engagement: Develop Effort and Persistence.
Chunk this task into manageable parts to support organizational skills in problem solving. Some students may benefit from explicit guidance for how to begin. For example, before sorting, students can find the area of each rectangle.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Organization
Required Materials
Materials to Gather
Grid paper
Inch tiles
Materials to Copy
Card Sort: Area
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Give each group a set of cards from the blackline master.
“Sort the cards into categories in any way that makes sense to you.”
2 minutes: partner work time
Ask students to share ways in which they sorted.
Activity
“If you did not already, sort the rectangles by their area.”
3–5 minutes: partner work time
Ask students to check their work with another group to make sure the cards in each category match.
“Now, create at least one rectangle to add to each category in your card sort.”
3–5 minutes: partner work time
Observe the rectangles students add to each category. Monitor for students who notice that no new rectangles could be drawn for the area of 7 square units.
Student Facing
Your teacher will give you a set of cards to sort.
Sort the cards by area. Record your sorting results. Be prepared to explain your choices.
For each group of sorted cards, think of at least one more rectangle. Name its length and width. Be prepared to explain your reasoning.
[IMG]
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
Select 2–3 students to share the rectangles they added to each category.
“Why were you able to create more rectangles for some areas and not others?” (Some of the numbers had more factor pairs. For some numbers, there was only one possible factor pair.)
Revoice student reasoning. “Only one rectangle can be made for the area of 7. Numbers like this are called
prime numbers
. Prime numbers have only one factor pair: 1 and itself.”
“Numbers like 15 that have more than one factor pair are called
composite numbers
.”
“What other composite numbers did you work with? How do you know they are composite?” (Twenty-four is a composite number because I can make 2 rows of 12 or 4 rows of 6. Eighteen is composite because it has factor pairs of 2 and 9 and 3 and 6.)


correct_option_index: 7