few_shots: Example:
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:
Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

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

K
options: Write and interpret numerical expressions.

Analyze patterns and relationships.

Represent and solve equations and inequalities graphically.

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

Rewrite rational expressions.

Reason about and solve one-variable equations and inequalities.

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

Write expressions in equivalent forms to solve problems.

Use properties of operations to generate equivalent expressions.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Create equations that describe numbers or relationships

Work with addition and subtraction 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.

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

Solve equations and inequalities in one variable.

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

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Interpret the structure of expressions.

Solve systems of equations.

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

Add and subtract within 20.

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

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

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Generate and analyze patterns.

Represent and solve problems involving addition and subtraction.

Perform arithmetic operations on polynomials.

Use polynomial identities to solve problems.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Task
Lisa is working with the system of equations $x + 2y = 7$ and $2x - 5y = 5$. She multiplies the first equation by 2 and then subtracts the second equation to find $9y = 9$, telling her that $y = 1$. Lisa then finds that $x = 5$. Thinking about this procedure, Lisa wonders
There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by -2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?
What is the answer to Lisa's question? Explain.
Does the answer to (a) change if we have a system of two equations in two unknowns with no solutions? What if there are infinitely many solutions?


correct_option_index: 22