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: 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.

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

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

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.

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 & 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.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
problem_activity: Activity
In the previous unit, students studied scale drawings of real-world objects. In grade 8, they will study dilations and similarity. The purpose of this activity is to use students’ recent study of scale drawings as a transition to the study of proportional relationships. Initially, students may describe the difference between Moons A, B, C, and D in qualitative terms, e.g., “D is more squished than the others.” They may also use the term “scaled copies,” which appeared in the work of the previous unit, but struggle to identify measurements to use in these figures that consist only of curved sides. It is important to ask students to articulate what they mean by “squished” in quantitative terms, for example, by talking about the height relative to the width and helping students to define “height” and “width” of a moon in some appropriate way. Once students have that, they can note that the height of the enclosing rectangle is always one and a half times its width for Moons A, B, and C, but not D, or they might note that the distance tip to tip is three times the width of the widest part of the moon for Moons A, B, and C, but not so for D.
[IMG]
As students explore these transformations, ask questions with the goal of having students articulate that for two images to look like scaled copies of each other, the ratios of the side lengths need to be the same.
In the third question, students are asked to represent the situation with tables and double number line diagrams, providing students with an opportunity to recall these representations from their work in grade 6.
Digital
Launch
Give students 3 minutes of quiet think time and tell them to pause after the first two questions. After the quiet think time, ask students to discuss their answers with a partner to describe how Moon D is different. Use MLR 2 (Collect and Display) as students share. Record the explanations that students are using to describe the moons. Ensure that students see some ways to measure lengths associated with the moons, then complete the last question.
If using the digital activity, give students 3 minutes of quiet think time and tell them to pause after the first two questions. After the quiet think time, students can discuss answers with a partner. Based on student conversations, you may want to have a whole-group discussion to ensure they see a way to measure the lengths associated with the moons before they attempt to answer the last question.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2–3 minutes of work time. Check to make sure students have a method for comparing the measurements of each moon. For example, create a rectangle around each moon and compare the width-height ratios.
Supports accessibility for: Memory; Organization
Student Facing
Here are four different crescent moon shapes.
What do Moons A, B, and C all have in common that Moon D doesn’t?
Use numbers to describe how Moons A, B, and C are different from Moon D.
Use a table or a double number line to show how Moons A, B, and C are different from Moon D.
Student Response
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click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Can you make one moon cover another by changing its size? What does that tell you about its dimensions?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Print
Launch
Give students 3 minutes of quiet think time and tell them to pause after the first two questions. After the quiet think time, ask students to discuss their answers with a partner to describe how Moon D is different. Use MLR 2 (Collect and Display) as students share. Record the explanations that students are using to describe the moons. Ensure that students see some ways to measure lengths associated with the moons, then complete the last question.
If using the digital activity, give students 3 minutes of quiet think time and tell them to pause after the first two questions. After the quiet think time, students can discuss answers with a partner. Based on student conversations, you may want to have a whole-group discussion to ensure they see a way to measure the lengths associated with the moons before they attempt to answer the last question.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2–3 minutes of work time. Check to make sure students have a method for comparing the measurements of each moon. For example, create a rectangle around each moon and compare the width-height ratios.
Supports accessibility for: Memory; Organization
Student Facing
Here are four different crescent moon shapes.
[IMG]
What do Moons A, B, and C all have in common that Moon D doesn’t?
Use numbers to describe how Moons A, B, and C are different from Moon D.
Use a table or a double number line to show how Moons A, B, and C are different from Moon D.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
For question 2, students might attempt to find the area of each moon by counting individual square units. Suggest that they create a rectangle around each moon instead and compare the width-height ratios.
For question 3, if students are not sure how to set up these representations, providing a template may be helpful.
Activity Synthesis
As students suggest ways to characterize the difference between Moons A, B, and C and Moon D, ask questions that help them clarify and make their statements more precise. For example,
“What does it mean to be ‘smashed down?’ What measurements might you make to show that this is true?”
“Is there anything else about what A, B, and C have in common that you can identify?”
“What things might we measure about these moons to be able to talk about what makes them different in a more precise way?”
“How can you represent the ratios of the measurements you are comparing using a table and a double number line diagram?”
If some students are still struggling with the tables or diagrams, ask students who were successful to share their representations with the class.
Speaking: MLR8 Discussion Supports.
To aid students in producing statements about comparisons of proportional relationships. Provide sentence frames for students to use when they are comparing and contrasting such as: “All _____ have _____ except _____,” “What makes _____ different from the others is _____.” Ask students to further add to the statement to clarify the comparisons if they used descriptor words such as “wider, narrower, etc.” Improved statements should include mathematical language to describe the measurements (such as length, width, ratio, etc.). This will help students practice and develop language for comparisons.
Design Principle(s): Support sense-making


correct_option_index: 4