options: Solve equations and inequalities in one variable.

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

Work with addition and subtraction equations.

Represent and solve problems involving addition and subtraction.

Use the four operations with whole numbers to solve problems.

Analyze patterns and relationships.

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

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

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

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

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

Write and interpret numerical expressions.

Add and subtract within 20.

Generate and analyze patterns.

Use polynomial identities to solve problems.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Create equations that describe numbers or relationships

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Interpret the structure of expressions.

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

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Work with radicals and integer exponents.

Perform arithmetic operations on polynomials.

Multiply and divide within 100.

Use properties of operations to generate equivalent expressions.

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

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

Write expressions in equivalent forms to solve problems.

Solve systems of equations.
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.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Factored Form"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Expanded Form"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$3(x-14y)$$"}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$2x+3x$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{3}{4}(8a+16b)$$"}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$24m+8n-12p$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{2}\\left(\\frac{1}{3}x-8y+\\frac{2}{3}z\\right)$$"}]}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$5xy+15y$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$2x(-3+y)$$"}]}, {"_attributes": {"style": "text-align:center"}}]}]}]}]}


correct_option_index: 29