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

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.

Write and interpret numerical expressions.

Represent and solve problems involving multiplication and division.

Solve systems of equations.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

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

Perform arithmetic operations on polynomials.

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

Solve equations and inequalities in one variable.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Analyze patterns and relationships.

Generate and analyze patterns.

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

Reason about and solve one-variable equations and inequalities.

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Work with addition and subtraction equations.

Create equations that describe numbers or relationships

Rewrite rational expressions.

Work with radicals and integer exponents.

Use polynomial identities to solve problems.

Add and subtract within 20.

Use the four operations with whole numbers to solve problems.

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

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

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

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

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.
problem_activity: Problem 1
For Simon’s birthday, he and his family go out to eat at a restaurant.
a.   The amount of tax is $3.40, which is 5% of the food bill. How much was the food bill not including the tax?
b.   If Simon wants to leave a 20% tip on the amount of the food bill before tax, how much should he leave for a tip?
c.   What is Simon’s total bill including tax and tip? What percent of the food bill is this?
Problem 2
Emily has a coupon for 20 percent off of her purchase at the store. She finds a backpack that she likes on the discount rack. Its original price is $60, but everything on the rack comes with a 30 percent discount.
Emily says, “
Thirty percent and twenty percent make fifty percent, so it will cost $30.
”
Is Emily correct? Explain your reasoning. In your explanation, if you disagree with Emily, find the price she will pay for the backpack.
Problem 3
In order to make money, a store marks up its prices by 25% from the warehouse prices. Let
$$p$$
represent the price at which the store gets its merchandise from the warehouse, and let
$$s$$
represent the price the store sells the merchandise for after the markup.
a.   Write an equation to determine the selling price,
$$s$$
, based on the warehouse purchase price,
$$p$$
.
b.   Create a table showing possible pairs of solutions to the equation.
| **                Warehouse price (                                 $$p$$                                )               ** | **                Selling price (                                 $$s$$                                )               ** |
|-----------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------|
|                                                                                                                             |                                                                                                                           |
|                                                                                                                             |                                                                                                                           |
|                                                                                                                             |                                                                                                                           |
|                                                                                                                             |                                                                                                                           |
c.   Create and label a graph for your table.
d.   Interpret the points
$$(0, 0)$$
and
$$(1, r) $$
from the graph in context of the situation.


correct_option_index: 28