options: Reason about and solve one-variable equations and inequalities.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

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

Multiply and divide within 100.

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

Add and subtract within 20.

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

Use polynomial identities to solve problems.

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

Interpret the structure of expressions.

Represent and solve problems involving multiplication and division.

Solve systems of equations.

Represent and solve problems involving addition and subtraction.

Write expressions in equivalent forms to solve problems.

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

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.

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

Perform arithmetic operations on polynomials.

Represent and solve equations and inequalities graphically.

Generate and analyze patterns.

Analyze patterns and relationships.

Work with radicals and integer exponents.

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

Write and interpret numerical expressions.

Use properties of operations to generate equivalent expressions.

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

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.
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: 19

21