few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


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


Your response:
Thought: This set of problems involves solving linear equations and pairs of linear equations.
Answer: L

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001392

8
options: Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Write expressions in equivalent forms to solve problems.

Perform arithmetic operations on polynomials.

Represent and solve problems involving addition and subtraction.

Rewrite rational expressions.

Solve equations and inequalities in one variable.

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

Use properties of operations to generate equivalent expressions.

Generate and analyze patterns.

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

Write and interpret numerical expressions.

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

Represent and solve equations and inequalities graphically.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Multiply and divide within 100.

Create equations that describe numbers or relationships

Use polynomial identities to solve problems.

Work with addition and subtraction equations.

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

Reason about and solve one-variable equations and inequalities.

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve systems of equations.

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

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

Represent and solve problems involving multiplication and division.

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

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

Interpret the structure of expressions.

Add and subtract within 20.
problem_activity: Narrative
The purpose of this activity is for students to find the value of sums within 10. Students may apply what they learned about the commutative property and counting on. They may count on for certain equations, such as
\(+1\)
or
\(+2\)
equations as they can keep track easily, but count all for others. In the lesson synthesis, students return to the addition expressions cards they created in a previous lesson.
Action and Expression: Internalize Executive Functions
. Invite students to plan a method, including the tools they will use, for finding the sum. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Organization, 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.
Activity
Read the task statement.
5 minutes: independent work time
3 minutes: partner discussion
Student Facing
Find the value of each sum.
\(7 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(3 + 5 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} = 8 + 2\)
\(3 + 6 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(5 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} = 4 + 4\)
\(2 + 6 = \boxed{\phantom{\frac{aaai}{aaai}}}\)
\(\boxed{\phantom{\frac{aaai}{aaai}}} = 1 + 9\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Display answers to problems.


correct_option_index: 21

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