Unit

Overarching Question

Essential Questions

Big Ideas

Full Objectives

Unit 0:

Math with a Growth Mindset

1. Math is about learning not performing.
2. Math is about making sense.
3. Math is filled with conjectures, creativity, and uncertainty.
4. Mistakes are beautiful things.

1. Students will understand the importance of a growth mindset (e.g., that math is not about talent or natural ability but is about thoughtful practice) and what it means to talk and listen. Students will also understand that class is where students practice thinking and doing math.
2. Students will learn the value of taking time to think about math and listen to how others make sense of their work to arrive at a common understanding.
3. Students will build the habits of using precise language, practicing, and sharing their thoughts. 

Unit 1:

Family of Functions

Timing

 ~5 weeks

Objectives

(Click on each objective for the objective analysis) 

Big Idea 1

A2.A.2.2 

(except rational) 

A2.F.2.1

Big Idea 2

A2.F.1.1

A2.F.1.3

(only identify characteristics)

A2.F.1.4

(only identify characteristics)

A2.F.1.5

(only identify characteristics)

A2.F.1.6

(only identify characteristics)

A2.F.1.7

(only identify characteristics)

Big Idea 3

A2.F.2.2

A2.F.2.3

Big Idea 4

A2.F.1.1

A2.F.1.2

(except parent graphs)

What makes each family of functions unique?

1. How can arithmetic operations on functions be represented by a graph and related to an algebraic process?

2. What are the similarities and differences between functions and within a family of functions?

3. What families of functions also have inverses that are functions?

4. How are functions used to represent real-world problems?

1. Big Idea 1: Operations on functions can be represented with both algebraic and graphical models.
2. Big Idea 2: Families of functions share similar behaviors, characteristics and properties.
3. Big Idea 3: Two functions are inverses if the function f maps x to y and the inverse of f maps y to x.
4. Big Idea 4: Functions within the same family are made by applying transformations onto the parent function. 

A2.A.2.2 Add, subtract, multiply, divide, and simplify polynomial expressions.

A2.F.1.1 Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain.

A2.F.1.2 Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [f(x +c), f(x)+ c, f(cx), and cf(x)] algebraically and graphically.

A2.F.1.3 Graph a quadratic function. Identify the domain, range, x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology

A2.F.1.4 Graph exponential and logarithmic functions. Identify the domain, range, asymptotes, and x- and y-intercepts using various methods and tools that may include calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically.

A2.F.1.5 Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease.

A2.F.1.6 Graph a rational function and identify the domain (including holes), range, x- and y-intercepts, vertical and horizontal asymptotes, using various methods and tools that may include a graphing calculator or other appropriate technology (excluding slant or oblique asymptotes).

A2.F.1.7 Graph a radical function (square root and cube root only). Identify the domain, range, and x- and y-intercepts using various methods and tools that may include a graphing calculator or other appropriate technology.

A2.F.2.1 Add, subtract, multiply, and divide functions using function notation and recognize domain restrictions.

A2.F.2.2 Combine functions by composition and recognize that g(x) = f^-1(x), the inverse function of f(x), if and only if f(g(x)) = g(f(x)) = x.

A2.F.2.3 Find and graph the inverse of a function, if it exists, in mathematical models. Know that the domain of a function f is the range of the inverse function f^-1 and the range of the function f is the domain of the inverse function f^-1

Unit 2:

Quadratics

Timing

~6 weeks

Objectives

(Click on each objective for the objective analysis)

Big Idea 1

A2.A.1.1

A2.A.2.1

(except cubes and grouping)

Big Idea 2

A2.A.1.1

A2.N.1.1

A2.N.1.2

Big Idea 3

A2.A.2.4

A2.F.1.1

A2.F.1.2

(only quadratic)

A2.F.1.3

A2.D.1.2 

(only quadratic) 

Where are quadratic functions used in the world?

1. What are the distinguishing characteristics of a quadratic?

2. How can we identify key features of a quadratic?

3. What mathematical and real world value do quadratic functions possess?

4. How are quadratic functions used to solve real world problems?

5. How are complex numbers related to real numbers?

1. Big Idea 1: A quadratic function has degree 2.
2. Big Idea 2: The graph and equation of a quadratic function can yield information about its roots.
3. Big Idea 3: Equivalent representations of a function highlights different properties.  

A2.N.1.1 Find the value of iⁿ for any whole number n.

A2.N.1.2 Simplify, add, subtract, multiply, and divide complex numbers.

A2.A.1.1 Use mathematical models to represent quadratic relationships and solve using factoring, completing the square, the quadratic formula, and various methods (including graphing calculator or other appropriate technology). Find non-real roots when they exist.

A2.A.2.1 Factor polynomial expressions including but not limited to trinomials, differences of squares, sum and difference of cubes, and factoring by grouping using a variety of tools and strategies.

A2.A.2.4 Recognize that a quadratic function has different equivalent representations [f(x) = ax² + bx + c, f(x) = a(x − ℎ)² + k, and f(s) = a(x − p)(x − q)]. Identify and use the mathematical model that is most appropriate to solve problems.

A2.F.1.1 Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain.

A2.F.1.2 Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [f(x +c), f(x)+ c, f(cx), and cf(x)] algebraically and graphically.

A2.F.1.3 Graph a quadratic function. Identify the domain, range, x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology

A2.D.1.2 Collect data and use scatter plots to analyze patterns and describe linear, exponential, or quadratic relationships between two variable.   

Unit 3

Polynomials and Rational Functions

Note: This can be broken into Unit 3A Polynomials and 3B Rational and Radical Functions

Timing

~7 weeks

Objectives

Big Idea 1

A2.A.1.4

A2.A.2.1

A2.F.1.1

Big Idea 2

A2.N.1.2

A2.A.1.4

A2.A.2.1

Big Idea 3

A2.A.2.2

A2.A.2.3

A2.F.1.5

Big Idea 4

A2.A.1.3

A2.A.2.2

A2.A.2.3

A2.F.1.6

Big Idea 5

A2.N.1.3

A2.A.1.5

A2.A.2.5

How are real situations modeled with polynomial functions?

1. What are the characteristics of polynomial functions?

2. When change occurs in a polynomial equation, how is the graph affected?

3. How do polynomials, rational and radical functions represent real-world scenarios?

4. How are complex numbers related to real numbers?

5. Why are solutions considered “extraneous”?

1. Big Idea 1: The behavior, properties, and characteristics of a polynomial function can be determined by its degree.
2. Big Idea 2: The graph and equation of a polynomial function yields information about its roots.
3. Big Idea 3: Basic arithmetic operations can be performed on polynomials similar to the way they are performed on numbers.
4. Big Idea 4: Rational functions can be described by the division of two polynomial functions.
5. Big Idea 5: Radical expressions can be written as expressions with rational exponents, and both are inverse operations of integral exponents. 

A2.N.1.2 Simplify, add, subtract, multiply, and divide complex numbers. 

A2.N.1.3 Understand and apply the relationship between rational exponents to integer exponents and radicals to solve problems. 

A2.A.1.3 Solve one-variable rational equations and check for extraneous solutions.

A2.A.1.4 Solve polynomial equations with real roots using various methods (e.g., polynomial division, synthetic division, using graphing calculators or other appropriate technology).

A2.A.1.5 Solve square and cube root equations with one variable, and check for extraneous solutions. 

A2.A.2.1  Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies. 

A2.A.2.2 Add, subtract, multiply, divide, and simplify polynomial expressions.

A2.A.2.3 Add, subtract, multiply, divide, and simplify rational expressions.
A2.A.2.5 Rewrite algebraic expressions involving radicals and rational exponents using the properties of exponents..

A2.F.1.1 Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain.

A2.F.1.5 Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease.

A2.F.1.6 Graph a rational function and identify the domain (including holes), range, x- and y-intercepts, vertical and horizontal asymptotes, using various methods and tools that may include a graphing calculator or other appropriate technology (excluding slant or oblique asymptotes).

A2.F.1.7 Graph a radical function (square root and cube root only). Identify the domain, range, and x- and y-intercepts using various methods and tools that may include a graphing calculator or other appropriate technology.

Unit 4: Exponential and Logarithmic Functions

Timing

~ 6 weeks

Objectives

Big Idea 1

A2.A.1.2

A2.F.1.4

A2.D.1.2

Big Idea 2

A2.A.3.4

A2.F.1.4

A2.F.2.4

Big Idea 3

A2.A.1.2

A2.A.1.6

A2.A.1.8

A2.F.2.4

Big Idea 4

A2.A.1.6

A2.A.1.7

A2.D.1.2

Big Idea 5 

A2.A.3.3

A2.A.3.4

A2.D.1.2

How can exponential and logarithmic functions be used to represent real world scenarios?

1. What are the distinguishing characteristics of an exponential function and logarithmic function?

2. How can we identify key features of exponential and logarithmic functions?

3. What mathematical and real-world value do exponential and logarithmic functions possess?

4. How are exponential and logarithmic functions used to solve real-world problems?

5. How are sequences and series related to functions?

1. Big Idea 1: Exponential functions are defined as f(x)=a^x.
2. Big Idea 2: Exponential functions share similar characteristics with power functions.
3. Big Idea 3: Logarithms and exponents can be used to solve mathematical and real-world problems.
4. Big Idea 4: Sequences  can be described as functions.
5. Big Idea 5: Sums of series can be represented by exponential and logarithmic functions. 

A2.A.1.2 Represent real-world or mathematical problems using exponential equations, such as compound interest, depreciation, and population growth, and solve these equations graphically (including graphing calculator or other appropriate technology) or algebraically.

A2.A.1.6 Solve common and natural logarithmic equations using the properties of logarithms.

A2.A.1.7 Solve real-world and mathematical problems that can be modeled using arithmetic or finite geometric sequences or series given the nth terms and sum formulas. Graphing calculators or other appropriate technology may be used.

A2.A.1.8 Represent real-world or mathematical problems using systems of linear equations with a maximum of three variables and solve using various methods that may include substitution, elimination, and graphing (may include graphing calculators or other appropriate technology).

A2.A.3.3 Solve problems that can be modeled using arithmetic sequences or series given the n^th terms and sum formulas. Graphing calculators or other appropriate technology may be used.

A2.A.3.4 Solve problems that can be modeled using finite geometric sequences and series given the n^th terms and sum formulas. Graphing calculators or other appropriate technology may be used.

A2.F.1.4 Graph exponential and logarithmic functions. Identify asymptotes and x- and y-intercepts using various methods and tools that may include graphing calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically.

A2.F.2.4 Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.

A2.D.1.2 Collect data and use scatter plots to analyze patterns and describe linear, exponential or quadratic relationships between two variables. Using graphing calculators or other appropriate technology, determine regression equation and correlation coefficients; use regression equations to make predictions and correlation coefficients to assess the reliability of those predictions. 

Unit 5:

Statistics and Data

Timing

1 week

Objectives 

Big Idea 1:

A2.D.1.1

A2.D.2.1

A2.D.2.2

A2.D.2.3

How can data and statistics be used to describe and interpret real-world situations?

1. How can data be used to display information?

2. How can data be used to skew information?

3. How are the mean and standard deviation related to a normal distribution?

A2.D.1.1 Use the mean and standard deviation of a data set to create a normal distribution (bell-shaped curve).

A2.D.2.1 Evaluate reports by making inferences, justifying conclusions, and determining appropriateness of data collection methods. Show how graphs and data can be distorted to support different points of view.

A2.D.2.2 Identify and explain misleading conclusions and graphical representations of data sets.

A2.D.2.3 Differentiate between correlation and causation when describing the relationship between two variables.

Unit 6:

Systems of Equations

Timing

~4 weeks

Objectives

Big Idea 1

A2.A.1.7

A2.A.1.8

A2.A.1.9

Big Idea 2 

A2.N.2.1

A2.N.2.2

A2.F.1.8

A2.D.1.2

Big Idea 3

A2.A.1.7 

Big Idea 4

A2.F.1.8 

How can real-world situations be modeled and solved by systems of equations?

1. How can we apply our knowledge to model real-world situations?

2. How can we represent and analyze our solutions to problems?

3. How can we represent the same thing in multiple different ways?

1. Big Idea 1: Two-variable systems can be solved using various methods.
2. Big Idea 2: Real world data can be represented, organized and solved using systems of equations.
3. Big Idea 3: Methods for solving real-world or mathematical two variable systems of equations can be extended to three variable systems of equations.
4. Big Idea 4: Piecewise functions can be used to model mathematical and real-world situations. 

A2.N.2.1 Use matrices to organize and represent data. Identify the order (dimension) of a matrix.

A2.N.2.2 Use addition, subtraction, and scalar multiplication of matrices to solve problems. 

A2.A.1.7 Represent and evaluate mathematical models using systems of linear equations with a maximum of three variables. Graphing calculators or other appropriate technology may be used. 

A2.A.1.8 Use tools to solve systems of equations containing one linear equation and one quadratic equation. Graphing calculators or other appropriate technology may be used.

A2.A.1.9 Solve systems of linear inequalities in two variables, with a maximum of three inequalities; graph and interpret the solutions on a coordinate plane. Graphing calculators or other appropriate technology may be used.

A2.F.1.8 Graph piecewise functions with no more than three branches (linear, quadratic, or exponential). Analyze the function by identifying the domain, range, intercepts, and intervals for which it is increasing, decreasing, and constant using various methods and tools (e.g., graphing calculator, other appropriate technology).

A2.D.1.2 Collect data and use scatter plots to analyze patterns and describe linear, exponential, or quadratic relationships between two variables.

Culminating Unit

Timing

~2 weeks

Algebra 2 Showcase:

Shark Tank: Sink or Swim