### 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.

MFANSQ1d: Compare fractions and decimals to the thousandths place.

#### 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.

MFANSQ4d: Illustrate and explain calculations using models and line diagrams

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.

### 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.

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).

MFAAA1d: Add, subtract, and multiply algebraic expressions.

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

MFAAA1f: Evaluate formulas at specific values for variables.

#### MFAAA2: Students will interpret and use the properties of exponents

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

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

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

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

MFAPR2a: Relate proportionality to fraction equivalence and division.

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

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

### 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.

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

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

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

MFAEI1d: Represent and find solutions graphically.

#### 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.

#### MFAEI3: Students will create algebraic models in two variables.

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

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

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

#### MFAEI4: Students will solve literal equations.

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

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

### 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.

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

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

#### MFAQR2: Students will compare and graph functions.

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

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

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

MFAQR2d: Use technology to graph non-linear functions.

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

#### MFAQR3: Students will construct and interpret functions.

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

Correlation last revised: 9/24/2019

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.