options: Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

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

Create equations that describe numbers or relationships

Write expressions in equivalent forms to solve problems.

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

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

Multiply and divide within 100.

Use the four operations with whole numbers to solve problems.

Reason about and solve one-variable equations and inequalities.

Generate and analyze patterns.

Solve systems of equations.

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

Rewrite rational expressions.

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve equations and inequalities in one variable.

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

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

Analyze patterns and relationships.

Gain familiarity with factors and multiples.

Perform arithmetic operations on polynomials.

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

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.

Represent and solve equations and inequalities graphically.

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

Solve problems involving the four operations, and identify and explain patterns in arithmetic.
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: 4

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