MFANSQ: Students will compare different representations of numbers (i.e. fractions, decimals, radicals, etc.) and perform basic operations using these different representations.

MFANSQ1: Students will analyze number relationships.

MFANSQ1a: Solve multi-step real world problems, analyzing the relationships between all four operations.

Determining a Spring Constant
Estimating Population Size

MFANSQ1d: Compare fractions and decimals to the thousandths place.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

MFANSQ2: Students will conceptualize positive and negative numbers (including decimals and fractions).

MFANSQ2b: Represent numbers on a number line.

Rational Numbers, Opposites, and Absolute Values

MFANSQ4: Students will apply and extend previous understanding of addition, subtraction, multiplication, and division.

MFANSQ4a: Find sums, differences, products, and quotients of multi-digit decimals using strategies based on place value, the properties of operations, and/or relationships between operations.

Square Roots

MFANSQ4b: Find sums, differences, products, and quotients of all forms of rational numbers, stressing the conceptual understanding of these operations.

Equivalent Algebraic Expressions I
Fractions with Unlike Denominators

MFANSQ4d: Illustrate and explain calculations using models and line diagrams

Fractions with Unlike Denominators

MFANSQ4e: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using estimation strategies and graphing technology.

Estimating Population Size
Fractions with Unlike Denominators

MFAAA: Students will extend arithmetic operations to algebraic modeling.

MFAAA1: Students will generate and interpret equivalent numeric and algebraic expressions.

MFAAA1a: Apply properties of operations emphasizing when the commutative property applies.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Using Algebraic Equations

MFAAA1b: Use area models to represent the distributive property and develop understandings of addition and multiplication (all positive rational numbers should be included in the models).

Square Roots

MFAAA1d: Add, subtract, and multiply algebraic expressions.

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Equations

MFAAA1e: Generate equivalent expressions using properties of operations and understand various representations within context.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Using Algebraic Equations
Using Algebraic Expressions

MFAAA1f: Evaluate formulas at specific values for variables.

Area of Triangles
Solving Formulas for any Variable

MFAAA2: Students will interpret and use the properties of exponents

MFAAA2b: Use properties of integer exponents to find equivalent numerical expressions.

Dividing Exponential Expressions

MFAAA2c: Evaluate square roots of perfect squares and cube roots of perfect cubes

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

MFAAA2e: Use the Pythagorean Theorem to solve triangles based on real-world contexts

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

MFAPR: Students will use ratios to solve real-world and mathematical problems

MFAPR1: Students will explain equivalent ratios by using a variety of models.

Part-to-part and Part-to-whole Ratios

MFAPR2: Students will recognize and represent proportional relationships between quantities.

MFAPR2a: Relate proportionality to fraction equivalence and division.

Direct and Inverse Variation
Part-to-part and Part-to-whole Ratios

MFAPR2b: Understand real-world rate/ratio/percent problems by finding the whole given a part and find a part given the whole.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Real-Time Histogram

MFAPR2c: Use proportional relationships to solve multistep ratio and percent problems.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percent of Change

MFAEI: Students will solve, interpret, and create linear models using equations and inequalities.

MFAEI1: Students will create and solve equations and inequalities in one variable.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

MFAEI1a: Use variables to represent an unknown number in a specified set.

Solving Algebraic Equations I
Using Algebraic Expressions

MFAEI1b: Explain each step in solving simple equations and inequalities using the equality properties of numbers.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Two-Step Equations

MFAEI1c: Construct viable arguments to justify the solutions and methods of solving equations and inequalities.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Two-Step Equations

MFAEI1d: Represent and find solutions graphically.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Circles
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Standard Form of a Line

MFAEI2: Students will use units as a way to understand problems and guide the solutions of multi-step problems.

MFAEI2c: Graph points in all four quadrants of the coordinate plane.

Linear Functions
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

MFAEI3: Students will create algebraic models in two variables.

MFAEI3a: Create an algebraic model from a context using two-variable equations.

Circles
Point-Slope Form of a Line
Standard Form of a Line
Using Algebraic Expressions

MFAEI3b: Find approximate solutions using technology to graph, construct tables of values, and find successive approximations.

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

MFAEI3c: Represent solutions to systems of equations graphically or by using a table of values.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

MFAEI3d: Analyze the reasonableness of the solutions of systems of equations within a given context.

Solving Linear Systems (Standard Form)

MFAEI4: Students will solve literal equations.

MFAEI4a: Solve for any variable in a multi-variable equation.

Area of Triangles
Solving Formulas for any Variable

MFAEI4b: Rearrange formulas to highlight a particular variable using the same reasoning as in solving equations.

Area of Triangles
Solving Formulas for any Variable

MFAQR: Students will create function statements and analyze relationships among pairs of variables using graphs, table, and equations.

MFAQR1: Students will understand characteristics of functions.

MFAQR1a: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.

Introduction to Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Radical Functions

MFAQR1b: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Radical Functions
Rational Functions

MFAQR1c: Graph functions using sets of ordered pairs consisting of an input and the corresponding output.

Introduction to Exponential Functions
Linear Functions
Points, Lines, and Equations

MFAQR2: Students will compare and graph functions.

MFAQR2a: Calculate rates of change of functions, comparing when rates increase, decrease, or stay constant.

Cat and Mouse (Modeling with Linear Systems)
Points, Lines, and Equations
Slope
Translating and Scaling Functions
Zap It! Game

MFAQR2b: Graph by hand simple functions expressed symbolically (use all four quadrants).

Radical Functions

MFAQR2c: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

MFAQR2d: Use technology to graph non-linear functions.

Absolute Value with Linear Functions
Quadratics in Vertex Form

MFAQR2e: Analyze graphs of functions for key features (intercepts, intervals of increase/decrease, maximums/minimums, symmetries, and end behavior) based on context.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Rational Functions
Slope-Intercept Form of a Line

MFAQR3: Students will construct and interpret functions.

MFAQR3a: Write a function that describes a relationship between two quantities.

Points, Lines, and Equations

MFAQR3c: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of context.

Absolute Value with Linear Functions
Translating and Scaling Functions