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.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Your response, in json format:
{
  "explanation": "This task teaches students to understand addition as putting together counters, or adding to already placed counters.",
  "answer": "AB"
}

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} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response, in json format:
{
  "explanation": "This problem involves understanding fractions as numbers by comparing their quantities.",
  "answer": "F"
}

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?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Your response, in json format:
{
  "explanation": "This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.",
  "answer": "G"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Extend the properties of exponents to rational exponents.

Use properties of rational and irrational numbers.

Perform operations on matrices and use matrices in applications.

Represent and model with vector quantities.

Reason quantitatively and use units to solve problems.

Apply and extend previous understandings of numbers to the system of rational numbers.

Represent complex numbers and their operations on the complex plane.

Perform operations on vectors.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Compute fluently with multi-digit numbers and find common factors and multiples.

Use complex numbers in polynomial identities and equations.

Perform arithmetic operations with complex numbers.
problem_activity: Activity
The purpose of this task is for students to develop their understanding of the
\(|x|\)
notation in familiar contexts. They should build their understanding that
\(|x|\)
represents the distance from zero to
\(x\)
and that
\(|\text-x|\)
and
\(|x|\)
are equal.
Launch
Allow students 10 minutes quiet work time followed by whole-class discussion.
Student Facing
A part of the city of New Orleans is 6 feet below sea level. We can use “-6 feet” to describe its elevation, and “
\(|\text-6|\)
feet” to describe its vertical distance from sea level. In the context of elevation, what would each of the following numbers describe?
25 feet
\(|25|\)
feet
-8 feet
\(|\text-8|\)
feet
The elevation of a city is different from sea level by 10 feet. Name the two elevations that the city could have.
We write “
\(\text-5^\circ \text{C}\)
” to describe a temperature that is 5 degrees Celsius below freezing point and “
\(5^\circ \text{C}\)
” for a temperature that is 5 degrees above freezing. In this context, what do each of the following numbers describe?
\(1^\circ \text{C}\)
\(\text-4^\circ \text{C}\)
\(|12|^\circ \text{C}\)
\(|\text-7|^\circ \text{C}\)
Which temperature is colder:
\(\text-6^\circ \text{C}\)
or
\(3^\circ \text{C}\)
?
Which temperature is closer to freezing temperature:
\(\text-6^\circ \text{C}\)
or
\(3^\circ \text{C}\)
?
Which temperature has a smaller absolute value? Explain how you know.
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
At a certain time, the difference between the temperature in New York City and in Boston was 7 degrees Celsius. The difference between the temperature in Boston and in Chicago was also 7 degrees Celsius. Was the temperature in New York City the same as the temperature in Chicago? Explain your answer.
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
To summarize students’ work, consider displaying the following diagram and these four expressions. Give students a minute to study the diagram and match each letter on the diagram to an appropriate expression.
-4 feet
\(|{15}|\)
feet
\(|{\text -4}|\)
feet
15 feet
[IMG]
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. Invite students to suggest language or diagrams to include that will support their understanding of: absolute value of a number, elevation, sea level, less than, greater than.
Supports accessibility for: Conceptual processing; Language; Memory
Representing, Speaking: MLR7 Compare and Connect
. To help students connect the numerical values with the diagram in the activity synthesis, provide students phrases that also connect to the situation (e.g., “4 feet below sea level,” “15 feet from sea level,” “4 feet from sea level,” and “15 feet above sea level”). Emphasize the language needed to say what the numerical values mean and how those values connect to the diagram and the phrases.
Design Principle(s): Maximize meta-awareness


correct_option_index: 5