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

Perform arithmetic operations on polynomials.

Interpret the structure of expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with radicals and integer exponents.

Rewrite rational expressions.

Write and interpret numerical expressions.

Generate and analyze patterns.

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

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

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

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

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

Solve systems of equations.

Represent and solve equations and inequalities graphically.

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

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

Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.

Represent and analyze quantitative relationships between dependent and independent variables.

Work with addition and subtraction equations.

Represent and solve problems involving multiplication and division.

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

Reason about and solve one-variable equations and inequalities.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

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

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

Analyze patterns and relationships.
problem_activity: Problem 1
Working together, it takes Sam, Jenna, and Francisco 2 hours to paint one room. When Sam is working alone, he can paint one room in 6 hours. When Jenna works alone, she can paint one room in 4 hours. Describe how long it would take Francisco to paint one room on his own.
Problem 2
Jamie and Ralph take a canoe trip up a river for 1 mile and then return. The current in the river is 1 mile per hour. The total trip time is 2 hours and 24 minutes. Assuming that they are paddling at a constant rate throughout the trip, find the speed that Jamie and Ralph are paddling. When Jamie and Ralph are paddling WITH the current (one way of their trip), their speed is
$${x+1}$$
. When Jamie and Ralph are paddling AGAINST the current (the other way of their trip), their speed is
$${x-1}$$
.


correct_option_index: 5

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