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.


Thought: This task involves learning addition, which is a mathematical operation, using objects.
Answer: F

Example 2:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

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


Thought: In this problem, students learn to understand fractions as numbers by comparing their sizes.
Answer: G

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


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


Thought: This set of problems involves performing operations, specifically multiplication, on multi-digit whole numbers in base ten.
Answer: D

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

K

im_task_000157

3

fl_problem_000674

5
options: 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.

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

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.

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.

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.

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.

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

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.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
problem_activity: Narrative
The purpose of this activity is for students to write equations for multiplication situations and diagrams using a symbol for the unknown number. When students write an equation to represent a situation, including a symbol for the unknown number, they model a situation with mathematics (MP4).
Students find an unknown factor or unknown product in multiplication problems. In this task, the unknown factor diagrams and situations only include the “how many groups” problem type and the factors 2, 5, and 10. This sets students up to skip-count to find the unknown number.
This problem type will be revisited extensively in future lessons and will be related to division. It is not necessary to make the connection to division now. In the synthesis students explain how the equations they wrote represent the diagram or situation.
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were important or most useful to pay attention to. Display the sentence frame, “The next time I write an equation with an unknown number, I will . . . .“
Supports accessibility for: Visual-Spatial Processing
Launch
Groups of 2
Activity
“Now you will practice writing your own equations with a symbol for the unknown.”
2–3 minutes: independent work time
“Share your equations with your partner. Discuss how you know each equation matches the diagram or situation.”
2–3 minutes: partner discussion
Have a whole-class discussion focused on how the equations match the different representations.
Consider asking:
“How did you use the representations to write an equation with a symbol for the unknown?” (I looked for what was missing in the diagram. I thought about the situation to figure out if it was the number in each group, the number of groups, or the total that was missing.)
“Now find the missing number in each equation and write a new equation that includes the solution.”
3–5 minutes: partner work time
Student Facing
Write an equation to represent each diagram or situation. Use a symbol for the unknown. Be prepared to share your reasoning.
Find the number that makes each equation true. Rewrite the equation with the solution.
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 diagram or situation                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | equation with symbol | equation with solution |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------|------------------------|
| |https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275|  |https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275| image:: https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275 |                      |                        |
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Jada has some packs of sports cards. Each pack has 5 cards. If Jada has 45 cards, how many packs of cards does she have?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |                      |                        |
| |https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19|  |https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19| image:: https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19 |                      |                        |
| |https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408|  |https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408| image:: https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408 |                      |                        |
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         The school has 6 bags. Each bag has 10 basketballs in it. How many basketballs does the school have?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                      |                        |
Student Response
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Advancing Student Thinking
If students write an equation without a symbol for the unknown number, consider asking:
“How does your equation represent the diagram (or situation)?”
“How could you show the number that was unknown with a symbol?”
Activity Synthesis
“What strategies did you use to find the unknown numbers?” (I counted by 2 to get the total. I counted by different numbers until I found a number that gave me the product.)
“How did each equation change as you found the unknown number?” (The symbol was replaced with the number.)


correct_option_index: 1