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, in json format:
{
  "explanation": "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.


Your response, in json format:
{
  "explanation": "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.


Your response, in json format:
{
  "explanation": "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.

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.

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.

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.

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.

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.

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

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
problem_activity: Narrative
The purpose of this activity is for students to use the weights from the previous activity to support place value understanding, specifically to see the multiplicative relationships between different decimal place values (MP7). These relationships will be taken up in greater detail in the next unit but the weights provide a convenient way to see these relationships which complements the diagrams students used in earlier lessons.
Students first compare weights of two gold nuggets, one weighed using 0.1 ounce weights and the other using 0.01 ounce weights. The two nuggets have the same weight because ten 0.01 ounce weights are equivalent to one 0.1 ounce weight, as students saw in the warm-up. Students move from here to making multiplicative comparisons between place values. They can use the weights to help visualize or calculate or they might use a diagram like those in the previous lesson.
Representation: Internalize Comprehension.
Synthesis: Provide students with a partially completed graphic organizer, such as a two column table, to record the relationship between tenths and hundredths, hundredths and thousandths, and tenths and thousandths.
Supports accessibility for: Conceptual Processing, Memory
Launch
Groups of 2
Activity
2 minutes: independent work time
8 minutes: partner work time
Monitor for students who use different strategies to compare the values of the 6s in the gold nugget weights:
using the value of each place in the decimal
thinking about fractions or representing the decimals as fractions
using a diagram such as a hundredths grid
Student Facing
How many 0.01 ounce weights will balance one 0.1 ounce weight? Explain or show your reasoning.
How many 0.001 ounce weights will balance a 0.1 ounce weight? Explain or show your reasoning.
The table shows the weights of 3 of the gold nuggets Diego and his friends found panning for gold.
Fill in the blanks. Explain or show your reasoning.
|   gold   | weight                             (grams) |
|----------|--------------------------------------------|
| nugget A |                    0.6                     |
| nugget B |                    0.06                    |
| nugget C |                   0.006                    |
Nugget A weighs
\(\underline{\hspace{0.9cm}}\)
times as much as Nugget B.
Nugget A weighs
\(\underline{\hspace{0.9cm}}\)
times as much as Nugget C.
Nugget C weighs
\(\underline{\hspace{0.9cm}}\)
times as much as Nugget B.
Nugget C weighs
\(\underline{\hspace{0.9cm}}\)
times as much as Nugget A.
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
“How are the weights of the nuggets the same? How are they different?” (They all have a 6 in them. They each balance with 6 of one of the unit weights. The value of the 6 is different for each nugget.)
“How do hundredths, the weights for B, compare to tenths, the weights for A?” (There are 10 hundredths in each tenth or a tenth of a tenth is a hundredth.)
“Nugget B weighs how many times as much as Nugget A? How do you know?” (
\(\frac{1}{10}\)
because Nugget A is 6 tenths and a tenth of that is 6 hundredths since a tenth of a tenth is a hundredth.)
“How do thousandths, the weights for C, compare to tenths, the weights for A?” (There are 100 thousandths in a tenth and one hundredth of a tenth is a thousandth.)
“Nugget A weighs how many times as much as Nugget C?” (100, there are 100 thousandths in a tenth.)


correct_option_index: 4