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.


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.
shot_info: im_task_001477

K

im_task_000157

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fl_problem_000674

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options: Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

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

Perform arithmetic operations on polynomials.

Work with radicals and integer exponents.

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

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Represent and solve problems involving addition and subtraction.

Understand the relationship between zeros and factors of polynomials.

Analyze patterns and relationships.

Solve systems of equations.

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

Represent and solve problems involving multiplication and division.

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

Add and subtract within 20.

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

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

Reason about and solve one-variable equations and inequalities.

Use the four operations with whole numbers to solve problems.

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

Write expressions in equivalent forms to solve problems.

Rewrite rational expressions.

Represent and solve equations and inequalities graphically.

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Multiply and divide within 100.

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

Create equations that describe numbers or relationships
problem_activity: Narrative
The purpose of this activity is for students to solve a variety of Add to and Take from Result or Change Unknown story problems. Students solve the story problems any way they choose and write an equation that matches the story and has a box around the answer to the question. During the activity synthesis, students consider the different ways to write equations for a story problem.
MLR8 Discussion Supports.
Synthesis: For each method that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Social-Emotional Functioning, Attention
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
"We are going to solve some more story problems about books other kids like to read."
Activity
Read the problems.
5 minutes: independent work time
5 minutes: partner discussion
Student Facing
Mai has read 3 books about dogs.
Diego gives her 4 more books to read.
How many books about dogs will Mai read all together?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Noah has 4 books of poetry.
His sister gives him some more books.
Now he has 10 books of poetry.
How many books did his sister give him?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Tyler has 7 books about spiders.
He gives 3 of his books to Kiran.
How many books does Tyler have left?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Lin has 5 books about outer space.
Her teacher gives her some more books.
Now she has 10 books about outer space.
How many books did Lin's teacher give her?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Student Response
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Activity Synthesis
Invite students to share the equation for each problem.
"Why is the answer in different places in our equations?" (Because in some stories we know the two numbers to add together and then the answer is the total. In other problems we know the starting number and the total and the answer is the other number we added.)


correct_option_index: 9