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

Gain familiarity with factors and multiples.

Represent and solve problems involving addition and subtraction.

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

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

Write expressions in equivalent forms to solve problems.

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

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Add and subtract within 20.

Represent and solve equations and inequalities graphically.

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

Represent and solve problems involving multiplication and division.

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

Generate and analyze patterns.

Use polynomial identities to solve problems.

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

Solve equations and inequalities in one variable.

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

Analyze patterns and relationships.

Work with radicals and integer exponents.

Interpret the structure of expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Use the four operations with whole numbers to solve problems.

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

Work with addition and subtraction equations.

Create equations that describe numbers or relationships

Rewrite rational expressions.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Write and interpret numerical expressions.
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: 3