options: Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

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

Perform arithmetic operations on polynomials.

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

Represent and solve problems involving multiplication and division.

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

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Analyze patterns and relationships.

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

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Gain familiarity with factors and multiples.

Create equations that describe numbers or relationships

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

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

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

Add and subtract within 20.

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

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

Work with addition and subtraction equations.

Write expressions in equivalent forms to solve problems.

Use polynomial identities to solve problems.

Reason about and solve one-variable equations and inequalities.

Interpret the structure of expressions.

Solve equations and inequalities in one variable.

Understand the relationship between zeros and factors of polynomials.

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

Multiply and divide within 100.

Use the four operations with whole numbers to solve problems.
problem_activity: Problem 1
At the candy store, M&Ms and Skittles are sold for $0.50 per ounce. Kevita puts some M&Ms in a bag and then adds 8 ounces of Skittles. The total cost for her bag of candy is $6.50.
Kevita and Mary write the equation
$${0.5(x+8)=6.50}$$
to represent the situation, where
$$x$$
represents the number of ounces of M&Ms.
Kevita says that to solve this equation, you first distribute the
$$0.5$$
through the parentheses to get
$${0.5x+4=6.50}$$
.
Mary says that to solve this equation, you first divide by
$$0.5$$
on both sides to get
$${x+8=13}$$
.
Do you agree with either Kevita or Mary? Why? Finish solving the problem to find out how many ounces of M&Ms Kevita put in her bag of candy.
Problem 2
The taxi fare in Gotham City is $2.40 for the first
$${1 \over 2}$$
mile and additional mileage is charged at the rate of $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?
What are two different ways you can solve this problem?
Problem 3
The ages of three cousins are consecutive integers. The sum of their ages is 45. Calculate their ages.
a.   Draw a tape diagram to represent the ages of the cousins.
b.   Let the youngest cousin's age be represented as
$$x$$
years old. Write and solve an equation to find the ages of the cousins.


correct_option_index: 31