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

Multiply and divide within 100.

Generate and analyze patterns.

Perform arithmetic operations on polynomials.

Work with addition and subtraction equations.

Write and interpret numerical expressions.

Understand the relationship between zeros and factors of polynomials.

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

Rewrite rational expressions.

Use the four operations with whole numbers to solve problems.

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

Create equations that describe numbers or relationships

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Write expressions in equivalent forms to solve problems.

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

Solve systems of equations.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Use properties of operations to generate equivalent expressions.

Gain familiarity with factors and multiples.

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

Add and subtract within 20.

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

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

Use polynomial identities to solve problems.

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

Reason about and solve one-variable equations and inequalities.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Interpret the structure of expressions.

Represent and solve problems involving multiplication and division.

Solve equations and inequalities in one variable.
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: 21