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

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Understand the relationship between zeros and factors of polynomials.

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

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

Work with addition and subtraction equations.

Analyze patterns and relationships.

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Write and interpret numerical expressions.

Use properties of operations to generate equivalent expressions.

Add and subtract within 20.

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.

Write expressions in equivalent forms to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

Interpret the structure of expressions.

Represent and solve equations and inequalities graphically.

Use the four operations with whole numbers to solve problems.

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

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

Solve systems of equations.

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

Represent and solve problems involving addition and subtraction.

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

Generate and analyze patterns.

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

Perform arithmetic operations on polynomials.
problem_activity: Problem 1
You and a friend are going for a run along a path. You both run at the same exact speed, but your friend starts 100 yards ahead of the starting point which is where you start.
The graph below is a sketch of your and your friend’s distance traveled from the starting point over time. When will you and your friend be the same distance from the starting point? Explain your answer using the graph.
[IMG]
Problem 2
Graph the system of equations below.
| $${y={1\over3}(x-6)}$$                        $${6y=2x-12}$$ | .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/09/23/slice-1-2022-09-23t114209772.png |
|--------------------------------------------------------------|------------------------------------------------------------------------------------------------------|
Anika was not sure how to interpret the graph of the system. She thought that since there was only one line visible in the graph then there were no solutions to the system of equations. Do you agree with Anika's reasoning? Explain why or why not.
Problem 3
Consider the equation
$$y = \frac{2}{5} x + 1$$
. Write a second linear equation to create a system of equations that has:
a.   Exactly one solution
b.   No solutions
c.   Infinite solutions


correct_option_index: 32