few_shots: Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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.


Thought: 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.


Thought: 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.


Thought: 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.
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K

im_task_000157

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fl_problem_000674

5
options: Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Work with radicals and integer exponents.

Understand and apply properties of operations and the relationship between addition and subtraction.

Understand solving equations as a process of reasoning and explain the reasoning.

Work with equal groups of objects to gain foundations for multiplication.

Solve equations and inequalities in one variable.

Multiply and divide within 100.

Solve systems of equations.

Use the four operations with whole numbers to solve problems.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Work with addition and subtraction equations.

Use properties of operations to generate equivalent expressions.

Write and interpret numerical expressions.

Add and subtract within 20.

Generate and analyze patterns.

Understand the connections between proportional relationships, lines, and linear equations.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Write expressions in equivalent forms to solve problems.

Interpret the structure of expressions.

Use polynomial identities to solve problems.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand properties of multiplication and the relationship between multiplication and division.

Represent and solve equations and inequalities graphically.

Perform arithmetic operations on polynomials.
problem_activity: Narrative
The purpose of this activity is for students to compare a Put Together, Total Unknown story problem and a Put Together/Take Apart, Both Addends Unknown story problem with a similar context. This is the first time that students have worked with a Put Together/Take Apart, Both Addends Unknown story problem.
Representation: Access for Perception.
Synthesis: Create a visual display to represent each story. For Mai, draw 7 circles and ask, “how many should I color in yellow?” and “how many should I color in red?” (5 yellow and 2 red). For Lin, draw 8 unshaded circles, and ask, “do we know which colors to use for Lin’s apples?” (no, we do not know how many of each color she picked).
Supports accessibility for: Visual-Spatial Processing, Organization
Launch
Groups of 2
Read both stories.
“What do you notice? What do you wonder?” (There are 2 stories. They are both about picking apples. There are red apples and yellow apples in both. I wonder how many red apples Lin picked.)
Activity
Read the first story problem.
“What do you know about Mai’s apples in this story? What do you not know?” (We know that she picked red and yellow apples. We know that she picked 5 yellow apples and 2 red apples. We do not know how many apples she picked altogether.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Read the second story problem.
“What do you know about Lin’s apples in this story? What do you not know?” (We know that she picked 8 apples. We know that some of them were red and some of them were yellow. We don’t know how many red ones or how many yellow ones she picked.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Student Facing
Mai was picking apples at the orchard.
Mai picked 5 yellow apples and 2 red apples.
Lin picked 8 apples at the orchard.
Some of the apples were yellow.
The rest of the apples were red.
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Activity Synthesis
“What is the same about these stories?” (They are both about picking apples. They both have red and yellow apples.)
“What is different about the stories?” (The first story is about Mai and the next story is about Lin. In the first story we knew how many yellow apples and how many red apples. In the second story we know that there are 8 apples altogether.)
“In the next activity, we will work on showing what happened in the second story.”


correct_option_index: 27