options: Analyze patterns and relationships.

Write expressions in equivalent forms to solve problems.

Create equations that describe numbers or relationships

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

Rewrite rational expressions.

Use polynomial identities to solve problems.

Solve systems of equations.

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

Represent and solve equations and inequalities graphically.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Use properties of operations to generate equivalent expressions.

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

Work with addition and subtraction equations.

Understand the relationship between zeros and factors of polynomials.

Perform arithmetic operations on polynomials.

Solve equations and inequalities in one variable.

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Generate and analyze patterns.

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

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

Represent and solve problems involving addition and subtraction.

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

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

Reason about and solve one-variable equations and inequalities.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Write and interpret numerical expressions.

Interpret the structure of expressions.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

Multiply and divide within 100.

Add and subtract within 20.
problem_activity: Problem 1
a.   Write two equivalent expressions to represent the total area of the rectangle shown. Justify that your two expressions are equivalent.
[IMG]
b.   Expand the expression below using a rectangular array.
$${\frac{1}{3}(9x-12y-18)}$$
Problem 2
a.   What could be the missing dimensions of the rectangular array? Which set of dimensions uses the greatest common factor of the two terms?
[IMG]
b.   Factor the expression below using a rectangular array. Use the greatest common factor as the representation of the width.
$${24d-8e+6}$$
Problem 3
The table below includes expressions that are written in expanded form and in factored form. Complete the table. Use rectangular arrays as needed.
|          **           Factored Form          **          | **           Expanded Form          ** |
|----------------------------------------------------------|----------------------------------------|
|                       $$3(x-14y)$$                       |                                        |
|                                                          |               $$2x+3x$$                |
|                 $$\frac{3}{4}(8a+16b)$$                  |                                        |
|                                                          |             $$24m+8n-12p$$             |
| $$\frac{1}{2}\left(\frac{1}{3}x-8y+\frac{2}{3}z\right)$$ |                                        |
|                                                          |              $$5xy+15y$$               |
|                       $$2x(-3+y)$$                       |                                        |


correct_option_index: 11