Unit 1: Introduction to Functions and Equations

a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given

equation into simpler forms, until an equivalent equation of the form

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

- if
*f*is a function and*x*is an element of its domain, then 𝑓(𝑥) denotes the output of*f*corresponding to the input*x.* - the graph of 𝑓is the graph of the equation 𝑦 = 𝑓(𝑥).

a. Identify and interpret parts of a

b) Interpret a

a) Build

b) Build a function that models a relationship between two quantities by combining

a) Fit a least squares regression line to linear data using technology. Use the fitted function to solve problems.

b) Assess the fit of a linear function by analyzing residuals.

Unit 3: Systems of Equations and Inequalities

a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

c. Solve real-world and mathematical problems leading to two linear equations in two variables.

- Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
- Use coordinates to verify algebraically that a given set of points produces a particular type of triangle or quadrilateral.

- Determine if two lines are parallel, perpendicular, or neither.
- Find the equation of a line parallel or perpendicular to a given line that passes through a given point.

Instructional Guide Unit 4: Exponential Functions

NC.1.N-RN.2

NC.M1.A-CED.2

a) Identify and interpret parts of a linear,

b) Interpret a linear,

a) Build linear and

b) Build a function that models a relationship between two quantities by combining

NC.M1.F-BF.2

NC.M1.F-IF.2

NC.M1.F-IF.4

NC.M1.F-IF.8b

b) Interpret and explain growth and decay rates for an exponential function.

NC.M1.F-IF.9

NC.M1.F-LE.1

NC.M1.S-ID.6c

c) Fit a function to exponential data using technology. Use the fitted function to solve problems.

NC.M1.A-APR.3

NC.M1.A-CED.2

NC.M1.A-REI.1

NC.M1.A-REI.11

NC.M1.A-REI.4

NC.M1.A-SSE.1a

a) Identify and interpret parts of a linear, exponential, or

NC.M1.A-SSE.1b

b) Interpret a linear, exponential, or

NC.M1.A-SSE.3

NC.M1.F-BF.1b

b) Build a function that models a relationship between two quantities by combining linear, exponential, or quadratic functions with addition and subtraction or two linear functions with multiplication.

NC.M1.F-IF.4

NC.M1.F-IF.5

NC.M1.F-IF.6

NC.M1.F-IF.8a

a) Rewrite a quadratic function to reveal and explain different key features of the function

NC.M1.F-IF.9

NC.M1.F-LE.3

Unit 6: One-Variable Statistics

NC.M1.S-ID.1

NC.M1.S-ID.2

NC.M1.S-ID.3