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

Work with addition and subtraction equations.

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

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

Rewrite rational expressions.

Perform arithmetic operations on polynomials.

Multiply and divide within 100.

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

Create equations that describe numbers or relationships

Solve equations and inequalities in one variable.

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

Use polynomial identities to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

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

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

Generate and analyze patterns.

Use the four operations with whole numbers to solve problems.

Analyze patterns and relationships.

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

Use properties of operations to generate equivalent expressions.

Reason about and solve one-variable equations and inequalities.

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

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving addition and subtraction.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.

Interpret the structure of expressions.

Solve systems of equations.
problem_activity: Problem 1
At a market, long-grain rice can be purchased in any weight, measured in pounds. The cost and weight are proportional, for example, 5 pounds of rice costs $4.
a.   Write an equation to represent the cost,
$$y$$
, to purchase
$$x$$
pounds of long-grain rice.
b.   Determine the cost of 1, 10, and 15 pounds of rice.
c.   Graph the relationship between cost and weight of rice in the coordinate plane.
d.   What is the slope of the graph? What does it mean as a unit rate?
Problem 2
Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water.
Nia mixed 1 teaspoon salt with 3 cups water.
Trey mixed
$${1\over 2}$$
teaspoon salt with 1
$${{1\over2}}$$
cups of water.
Nia tasted Trey’s salt water. She said,
“I added more salt so I expected that mine would be more salty, but they taste the same.”
a.   Explain why the salt water mixtures taste the same.
b.   Find an equation that relates
$$s$$
, the number of teaspoons of salt, with
$$w$$
, the number of cups of water, for both of these mixtures.
c.   Draw the graph of your equation from part (b).
d.   Your graph in part (c) should be a line. Interpret the slope as a unit rate.


correct_option_index: 15