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

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

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

Represent and solve problems involving multiplication and division.

Work with radicals and integer exponents.

Perform arithmetic operations on polynomials.

Reason about and solve one-variable equations and inequalities.

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

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

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

Write and interpret numerical expressions.

Represent and solve problems involving addition and subtraction.

Work with addition and subtraction equations.

Create equations that describe numbers or relationships

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

Solve equations and inequalities in one variable.

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

Solve systems of equations.

Multiply and divide within 100.

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

Interpret the structure of expressions.

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

Add and subtract within 20.

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

Use properties of operations to generate equivalent expressions.

Analyze patterns and relationships.

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.
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: 14

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