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

Multiply and divide within 100.

Write expressions in equivalent forms to solve problems.

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.

Generate and analyze patterns.

Perform arithmetic operations on polynomials.

Work with radicals and integer exponents.

Interpret the structure of expressions.

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

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Solve systems of equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Write and interpret numerical expressions.

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

Rewrite rational expressions.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

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

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

Use polynomial identities to solve problems.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

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

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

Work with addition and subtraction equations.

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

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving addition and subtraction.
problem_activity: Problem 1
Sarita has a fish tank in the shape of a rectangular prism. The bottom of the fish tank measures
$${10}$$
inches by
$$8$$
inches. Sarita wants to add some sand to cover the bottom of the tank, and she uses the formula
$${ V=l × w × h}$$
to determine the volume of sand she needs.
a.   If the height of the sand measures
$$2$$
inches, what is the volume of sand needed?
b.   If the height of the sand measures
$${3.5}$$
inches, what is the volume of sand needed?
c.   Sarita cannot decide how high she wants the sand to be in the tank. What expression can she use to represent the volume of sand needed for
any
height of sand?
Problem 2
In each example, write an expression to represent the quantity.
a.   Thomas is
$$x$$
years old.
His sister is
$$5$$
years older. How old is his sister?
His dog is
$$3$$
years younger. How old is his dog?
His cousin is
$${3\over4}$$
his age. How old is his cousin?
His friend is
$$y$$
years younger. How old is his friend?
b.   Reina has
$$5$$
more quarters than dimes.
She has
$$8$$
dimes. How many quarters does she have?
She has
$$15$$
quarters. How many dimes does she have?
She has
$$d$$
dimes. How many quarters does she have?
She has
$$q$$
quarters. How many dimes does she have?
Problem 3
a.   A numeric expression like
$${5+(8+2)^2}$$
has one and only one value. What is it?
b.   Consider the expression
$${ {5+(x+2)^2}}$$
. What are some values it can have? Make sure you organize your work so anyone can tell which value for the expression goes with which
$$x$$
value.
c.   How many different values can an algebraic expression like
$${5+(x+2)^2}$$
have?


correct_option_index: 19

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