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:
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:
{
  "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:
{
  "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: 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.

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

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.

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.

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.

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.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
problem_activity: Activity
The purpose of this activity is to give students practice using the language of percent error. The problems here are similar in structure to percent increase or decrease problems, but the language is different. Students may need some help interpreting the language used for percent error and drawing parallels to the language used for percentage increase and decrease. Students should use similar strategies they used to calculate percentage increase or decrease. This activity includes one of each type of problem:
finding the erroneous amount given the correct amount and the percent error
finding the correct amount given the erroneous amount and the percent error
finding the percent error given the erroneous amount and the correct amount
Students may need help understanding that a different approach is needed for each question. As students work, monitor for those who use strategies similar to those used for percentage increase and decrease, and ask them to share during the whole-class discussion.
Launch
Before students begin working, read the first question aloud. It is helpful to tie the language used in the task to the phrase "percentage increase." Ask several students to explain in their own words what information is given in the problem, and what it is asking them to find. The plant is supposed to get
\(\frac34\)
cup of water, but it is getting 25% more than that. We can think of this as
\(\frac34\)
cup increased by 25%.
Arrange students in groups of 2. Give students 3–5 minutes of quiet work time. Partner then by whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Represent the same information through different modalities. If students are unsure where to begin, suggest that they draw a double number line to help organize the information provided.
Supports accessibility for: Conceptual processing; Visual-spatial processing
Student Facing
Instructions to care for a plant say to water it with
\(\frac34\)
cup of water every day. The plant has been getting 25% too much water. How much water has the plant been getting?
The pressure on a bicycle tire is 63 psi. This is 5% higher than what the manual says is the correct pressure. What is the correct pressure?
The crowd at a sporting event is estimated to be 3,000 people. The exact attendance is 2,486 people. What is the
percent error
?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
A micrometer is an instrument that can measure lengths to the nearest micron (a micron is a millionth of a meter). Would this instrument be useful for measuring any of the following things? If so, what would the largest percent error be?
The thickness of an eyelash, which is typically about 0.1 millimeters.
The diameter of a red blood cell, which is typically about 8 microns.
The diameter of a hydrogen atom, which is about 100 picometers (a picometer is a trillionth of a meter).
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Students might struggle with figuring out how to calculate how much water the plant has been getting. Ask students, "How much more water has the plant been getting? How do you calculate that total?"
Activity Synthesis
Select students who used these strategies for each problem to share:
Calculate a quarter of
\(\frac34\)
and add it to
\(\frac34\)
.
Use 1.05 to divide into 63.
Calculate percent error using
\(\frac{514}{2,486}\)
.
After each student has shared, ask the class if they agree or disagree or if they had a different way to calculate the solution. If students use strategies similar to ones they did calculating percentage increase or decrease, ask students if they see a connection. If no student brings it up, ask students how the solution strategies here are similar to the ones used with percentage increase and decrease.
Speaking: MLR8 Discussion Supports.
As students describe their strategies for calculating the erroneous amount, correct amount, and percent error, revoice student ideas to demonstrate mathematical language use. Press for details in students’ explanations by requesting that students challenge an idea, elaborate on an idea, or give an example. This will help students to produce and make sense of of the language needed to communicate their own ideas.
Design Principle(s): Support sense-making; Optimize output (for explanation)


correct_option_index: 2