Last updated: 4/28/2025

Algebra 1 (Next Gen)

17 days including 8 lessons and 2 tests (1st assessment after Lesson 4)

Unit 1: Building Blocks of Algebra
(3) AI.A.APR.1 Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.
(3) AI.A.SSE.1 Interpret expressions that represent a quantity in terms of its context. ★
(2) AI.A.SSE.1b Interpret expressions by viewing one or more of their parts as a single entity.
(3) AI.A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.
(1) AI.N.Q.1 Select quantities and use units as a way to:
  1. interpret and guide the solution of multi-step problems;
  2. choose and interpret units consistently in formulas; and
  3. choose and interpret the scale and the origin in graphs and data displays.
(1) AI.N.Q.3 Choose a level of accuracy appropriate to limitations on measurement and context when reporting quantities.
(1) AI.N.RN.3 Use properties and operations to understand the different forms of rational and irrational numbers.

How do I identify a number as rational or irrational?

 

How can we simplify a radical?

 

How do I perform all four arithmetical operations and apply properties to create equivalent forms of rational numbers and square roots?

 

How do I categorize the sum or product of rational or irrational numbers? 

 

How do I rationalize a denominator?

1. Identify a number as rational or irrational.

2.  Simplify a radical.

3.  Add and substract radicals.

4.  Multiply and divide radicals.

5.  Rationalize denominators.

 

 

Denominator

Irrational

Perfect Square

Radical

Rational

Rationalize

Simplify

Square Root

 

 

I can identify a rational and irrational number.

 

I can simplify a radical.

 

I can add, subtract, multiply and divide radicals.

 

I can categorize the sum or product of rational or irrational numbers.

 

I can rationalize a denomiator.

21 days including 10 lessons and 1 test (after Lesson 7, there is a Mixed Practice Graded Assignment)

Unit 2

Linear Equations and Inequalities
(6) AI.A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
(5) AI.A.CED.2 Create equations and linear inequalities in two variables to represent a real-world context.
(4) AI.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
(3) AI.A.CED.4 Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
(2) AI.A.REI.1a Explain each step when solving a linear or quadratic equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
(1) AI.A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
(2) AI.A.SSE.1a Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.

How can I create an equation/inequality in one variable in order to represent a real-world example?

 

How can we evaluate and verify solutions?

 

How can we solve multi-step equations and inequalities?

 

How can we solve a literal equation?

 

How can we translate, write and solve word problems?

 

How can we graph linear inequality solutions on a number line?

 

1.  CREATE equations/inequalities in oone variable to represent a real-world context. 

2.  Evaluate Expressions and Verify Solutions

3.  Solve multi-step equations and inequalities

4.  Solve literal equations

5.  Translate, write and solve word problems

6.  Graph linear inequality solutions on a number line

Consecutive Integers

Equation

Evaluate

Expression

Inequality

Infinite Solutions

Integers

Interval Notation

Inverse Operations

No Solution

Solve

Solution

Substitute

I can create equations/ inequalities in one variable to represent a real-world context.

 

I can evaluate expressions.

 

I can solve multi-step equations including combining like terms, distributive property, and variables on both sides.

 

I can identify an equation with no solutions or infinite solutions.

 

I can translate a word problem into symbols.

 

I can solve a consecutive number word problems.

 

I can solve a literal equation.

 

I can solve rational equations.

 

I can identify and use interval notation to represent an inequality.

 

I can solve and graph a linear inequality on a number line.

 

 

 

 

11 days including 8 lessons and 1 test

Unit 3

Functions

 
(5) AI.F.BF.1 Write a function that describes a relationship between two quantities. ★
(1) AI.F.BF.1a Determine a function from context. Define a sequence explicitly or steps for calculation from a context.
(3) AI.F.IF.1 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. 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 f is the graph of the equation y = f(x).
(3) AI.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
(4) AI.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities; and
  2. sketch graphs showing key features given a verbal description of the relationship.
(5) AI.F.IF.5 Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
(5) AI.F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.
(4) AI.F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.
(3) AI.F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

How can we identify and define a relation and a function?

 

How can we identify the domain and range of a function from a list, table, map and graph?

 

How can we use the vertical line test to etermine if a relation is a function?

 

How can we determine the zeroes of a function?

 

How can we find the domain and range of a continuous graph?

 

How can we evaluate functions?

 

How can we identify the 9 families of functions?

 

1. Define and identify a relation and a function
2. Identify the domain and range of a function from a list, table,
map, and graph
3. Use the vertical line test to determine if a relation is a function
4. Determine the zeroes of a function
5. Find the domain and range of continuous graphs
6. Evaluate functions
7. Identify the 9 families of functions

Constant Graph

Continuous Graph

Coordinate Plane

Decreasing Graph

Domain

Increasing Graph

Input

Function

Function Notation

Mapping

Output

Ordered Pair

Origin

Quadrants

Range

Relation

Table of Values

Vertical Line Test

x-axis

x-coordinate

y-axis

y-coordinate

Zeros

 

Function Families:

Absolute Value

Cubic

Cube Root

Exponential

Linear

Piecewise

Quadratic

Square Root

Step

I can recall how to plot a point on a coordinate plane and identify a given coordinate on the plane.

 

I can identify a relation and a function from a roster, a map or a graph.

 

I can use the vertifcal line test to identify a function from a graph.

 

I can identify the domain and range of a graphed function.

 

I can identify the zeroes/solutions/roots/x-intercepts of a graphed function.

 

I can evaluate an expression presented in function notation.

 

I can use a function table to identify coordinates and graph a line.

 



26 days including 14 lessons, 1 quiz and 1 test (Graded Assignments after Lesson 4 and 12, Super Quiz after lesson 7)

Unit 4

Linear Functions

 

In regrads to AI-F.IF.3 (Sequences)
(6) AI.A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
(5) AI.A.CED.2 Create equations and linear inequalities in two variables to represent a real-world context.
(4) AI.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
(3) AI.A.CED.4 Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
(4) AI.A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
(3) AI.A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
(5) AI.F.BF.1 Write a function that describes a relationship between two quantities. ★
(2) AI.F.IF.3 Recognize that a sequence is a function whose domain is a subset of the integers.
(4) AI.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities; and
  2. sketch graphs showing key features given a verbal description of the relationship.
(5) AI.F.IF.5 Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
(5) AI.F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.
(3) AI.F.IF.7 Graph functions and show key features of the graph by hand and by using technology where appropriate. ★
(1) AI.F.IF.7a Graph linear, quadratic, and exponential functions and show key features.
(1) AI.F.IF.7b Graph square root, and piecewise-defined functions, including step functions and absolute value functions and show key features.
(4) AI.F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.
(3) AI.F.LE.2 Construct a linear or exponential function symbolically given:
  1. a graph;
  2. a description of the relationship;
  3. two input-output pairs (include reading these from a table).
(3) AI.F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
(1) AI.S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

How can we graph linear equations on a coordinate plane from a table.

 

How can we calculate the average rate of change?

 

How can we write a linear equation in slope-intercept form, standard form, and point-slope form?

 

How can we use the graphing calculator to generate a table of values in order to graph lines?

 

How can we graph linear equations with appropriate scales and lables?

 

How can we solve and graph linear word problems?

 

 

1. Graph linear equations on a coordinate plane from a table
2. Calculate the average rate of change
3. Write a linear equation in slope-intercept form, standard form, and point-slope form (from ordered pairs and a graph)
4. Use the graphing calculator to generate a table of values in order to graph lines
5. Graph linear equations with appropriate scales and labels
6. Solve and graph linear word problems

Average Rate of Change

Point-Slope Form

Slope

Slope-Intercept Form

Slope Formula

Standard Form

x-intercept

y-intercept

I can graph a linear function from a table of values.

 

I can identify the type of slope of a line from a graph and by using the slope formula.

 

I can find the average rate of change from a graph or a table of values (vertical/horizontal).

 

I can identify the slope and y-intercept of a line from an equation written in slope-intercept form.

 

I can graph a line using slope-intercept form.

 

I can write the equation of a line in slope-intercept form given a graph.

 

I can use the graphing calculator to generate a table of value and use that table to graph a line.

 

I can transpose any linear equation into slope-intercept form.

 

I can identify, graph and write the equation of a horizontal and vertical lines.

 

 

I can write the equation of a line given one point and the slope.

 

I can write the equation of a line given two points.

 

I can solve linear equation word problems.

 

 

 

5 days including 1 quiz

 

Graphing Linear Inequalities
(6) AI.A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
(3) AI.A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

How can we graph linear inequalities with and without a graphing calculator?

 

How can we interpret the graphs of inequalites?

 

How can we write the name of the inequality when given a graph?

 

How can we solve and graph linear inequality word problems?

1. Graph linear inequalities with and without a graphing calculator
2. Interpret the graphs of inequalities
3. Write the name of the inequality when given a graph
4. Solve and graph linear inequality word problems

Greater Than

Greater Than or Equal To

Less Than

Less Than or Equal To

Solution Set

Test - Point

I can use slope-intercept form and the graphing calculator to graph a linear inequality and identify a point in the solution set.

 

I can write the equation of a linear inequality given a graph.

 

I can solve inequality word problems.

 

 

 

 

 

 

3 days

Included in Unit 4

Arithmetic Sequences
(5) AI.F.BF.1 Write a function that describes a relationship between two quantities. ★
(2) AI.F.IF.3 Recognize that a sequence is a function whose domain is a subset of the integers.
(5) AI.F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.
(3) AI.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
(3) AI.F.LE.2 Construct a linear or exponential function symbolically given:
  1. a graph;
  2. a description of the relationship;
  3. two input-output pairs (include reading these from a table).

How can we find missing terms in an arithmetic sequence?


How can we use explicit and recursive formulas to determine an nth term?


How can we relate the equation of a sequence to that of a line?

1. Find missing terms in an arithmetic sequence
2. Use explicit and recursive formulas to determine an nth term
3. Relate the equation of a sequence to that of a line

Arithmetic Sequence

Common Difference

Explicit Formula

Recursive Formula

Term

nth term

 

I can find missing terms in an arithmetic sequence.


I can use explicit and recursive formulas to determine an nth term.


I can relate the equation of a sequence to that of a line.

16 days including 7 lessons and 1 test (Graded Assignment after Lesson 5)

Unit 5

Linear Systems
(5) AI.A.CED.2 Create equations and linear inequalities in two variables to represent a real-world context.
(4) AI.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
(3) AI.A.CED.4 Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
(4) AI.A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
(1) AI.A.REI.11 Given the equations y = f(x) and y = g(x):
  1. recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);
  2. find the solutions approximately using technology to graph the functions or make tables of values; and
  3. interpret the solution in context.★
(3) AI.A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
(1) AI.A.REI.6a Solve systems of linear equations in two variables both algebraically and graphically.
(1) AI.A.REI.7a Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.
(2) AI.A.SSE.1b Interpret expressions by viewing one or more of their parts as a single entity.

How can we graph and solve a system of linear and quadratic equations?

 

How can we solve a system of linear equations using the subsitution method?

 

How can we solve a system of linear equations using the elimination method?

 

How can we graph a system of linear inequalities?

 

How can we solve a system of linear equation and inequality word problems?

1. Graph and solve a system of linear and quadratic equations
2. Solve a system of linear equations using the substitution method
3. Solve a system of linear equations using the elimination method
4. Graph a system of linear inequalities
5. Solve a system of linear equation and inequality word problems

System of Equations

System of Inequalities

Substitution

Elimination

Solutions

I can solve a system of equations by graphing (linear/quadratic).

 

I can solve a system of equations by substituion.

 

I can solve a system of equations by elimination.

 

I can solve a system of equations word problem.

 

I can solve a system of inequalities by graphing and identify a solution in the solution set.

 

I can solve a systems of inequalities word problem.

 

 

15 days including 13 lessons and 1 test (Graded Assignment)

Unit 6

Exponential Functions
(6) AI.A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
(4) AI.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
(2) AI.A.REI.1a Explain each step when solving a linear or quadratic equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
(1) AI.A.SSE.3c Use the properties of exponents to rewrite exponential expressions.
(5) AI.F.IF.5 Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
(3) AI.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
(2) AI.F.LE.1a Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.
(2) AI.F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
(2) AI.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.
(3) AI.F.LE.2 Construct a linear or exponential function symbolically given:
  1. a graph;
  2. a description of the relationship;
  3. two input-output pairs (include reading these from a table).
(3) AI.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
(3) AI.F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

How can we evaluate exponential functions?


How can we interpret the parts of an exponential function and rewrite it?


How can we graph exponential functions?


How can we construct geometric sequences given a graph or table?


How can we solve growth and decay word problems?

 

How can we differentiate between linear and exponential functions?

1. Evaluate exponential functions
2. Interpret the parts of an exponential function and rewrite it
3. Graph exponential functions
4. Construct geometric sequences given a graph or table
5. Solve growth and decay word problems

6.  Differentiate between linear and exponential functions.

 

Asymptote

Common Ratio

Exponential Functions

Geometric Sequences

Growth

Half- life

Interest

Compound interest

Decay

I can evaluate exponential functions.


I can interpret the parts of an exponential function and rewrite it.


I can graph exponential functions.


I can construct geometric sequences given a graph or table.


I can solve growth and decay word problems.

15 days including 10 lessons, 1 quiz and 1 test

Unit 7

Polynomials
(3) AI.A.APR.1 Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.
(3) AI.A.SSE.1 Interpret expressions that represent a quantity in terms of its context. ★
(2) AI.A.SSE.1a Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.
(3) AI.A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.
(3) AI.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (Shared standard with Algebra II)

How can we identify types of polynomials?

 

How can we add polynomials?

 

How can we subtract polynomials?

 

How can we multiply monomials by polynomials?

 

How can we mutliply binomials?

 

How can we multiply binomials by polynomials?

 

How can we solve word problems involving polynomials?

 

How can I apply the polynomial vocabulary to put a polynomial in standard form?

 

How can I use the properties of exponents to rewrite an exponential expression?

 

 

 

1. Identify types of polynomials by number of terms and degree and put them in standard form
2. Add polynomials
3. Subtract polynomials
4. Multiply polynomials
5. Solve word problems involving polynomials

6. Standard form of a given polynomial.

7. Identify all parts of a given polynomial.

8. Use the properties of exponents to rewrite an exponential expression.

Base

Binomial

Coefficient

Constant

Degree of a Monomial

Degree of a Polynomial

Exponent

Exponent Rules

Leading Coefficient

Like Terms

Monomial

Polynomial

Power

Standard Form

Term

Trinomial

Variable

I can identify types of polynomials by number of terms and degree and put them in standard form.

 

I can add polynomials.

 

I can subtract polynomials.

 

I can multiply monomials by polynomials.

 

I can mutliply binomials.

 

I can multiply binomials by polynomials.

 

I can solve word problems involving polynomials.

 

I can use the properties of exponents to rewrite exponential expressions.

 

 

 

 

 

 

11 days including 1 quiz, 1 test

Included in Unit 7

Factoring
(3) AI.A.APR.1 Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.
(3) AI.A.SSE.1 Interpret expressions that represent a quantity in terms of its context. ★
(3) AI.A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.
(3) AI.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (Shared standard with Algebra II)

How can we factor polynomials using greatest common factors?

 

How can we factor a binomial using the difference of perfect squares?

 

How can we factor a trinomial with a leading coefficient equal to one?

 

How can we factor a trinomial with a leading coefficient greater than one?

 

How do we factor completely?

 

How can I interpret an expression as a product and a factor?

 

How can I use the structure of an expression to identify ways to rewrite it?

 

1. Factor polynomials using Greatest Common Factors
2. Factor a binomial using the Difference of Perfect Squares
3. Factor a trinomial with a coefficient equal to one.
4. Factor a trinomial with a coefficient greater than one
5. Factor completely

6. Identify an expression as a product and a factor.

7. Recognize and use the structure of an expression to rewtie it into equivalent expressions.

Binomial

Difference of Perfect Squares

Equivalent Expressions

Expression

Factor

Greatest Common Factor

Monomial

Polynomial

Product

Trinomial

 

I can identify the greatest common factor of an expression and then factor that expression using the GCF.

 

I can factor the difference of two perfect squares.

 

I can factor trinomials with a leading coefficient of one.

 

I can factor trinomials with a leading coefficient greater than one.

 

I can identify an expression that can be factored using the difference of perfect squares vs. a perfect square trinomial.

 

I can interpret an expression as a product and a factor.

 

I can use the structure of an expression and rewrite it as an equivalent expression.

 

 

 

 

 

 

25 Days including 14 lessons and 1 test (Graded Assignment after lesson 4, Graded Assignment after lesson 11)

Unit 8

Quadratic Functions
(2) AI.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(6) AI.A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
(5) AI.A.CED.2 Create equations and linear inequalities in two variables to represent a real-world context.
(4) AI.A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
(1) AI.A.REI.4 Solve quadratic equations in one variable.
(1) AI.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x -p)2 = q that has the same solutions. Understand that the quadratic formula is a derivative of this process.
(1) AI.A.REI.4b Solve quadratic equations by:
  1. inspection,
  2. taking square roots,
  3. factoring,
  4. completing the square,
  5. the quadratic formula, and
  6. graphing.


Recognize when the process yields no real solutions.
(3) AI.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (Shared standard with Algebra II)
(5) AI.F.BF.1 Write a function that describes a relationship between two quantities. ★
(3) AI.F.IF.1 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. 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 f is the graph of the equation y = f(x).
(3) AI.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
(4) AI.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities; and
  2. sketch graphs showing key features given a verbal description of the relationship.
(5) AI.F.IF.5 Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
(5) AI.F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.
(3) AI.F.IF.7 Graph functions and show key features of the graph by hand and by using technology where appropriate. ★
(4) AI.F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.
(3) AI.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(3) AI.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

 

How can we solve a quadratic equation by factoring?

 

How can we solve a quadratic equation by completing the square?

 

How can we solve quadratic equations using the quadratic formula?

 

How can we choose an appropriate method to solve a quadratic equation?

1. Explain when a product or sum is Rational or Irrational
2. Simplify radical expressions
3. Solve quadratic equations by Factoring, Quadratic Formula, and Completing the Square
4. Recognize real and non-real solutions
5. Write the equation of a quadratic given the solutions

Discriminant

Irrational

No Real Solution

Quadratic Formula

Radical

Rational

Real Solution

Standard Form of a Quadratic

I can write a quadratic equation in Vertex Form.

 

I can complete the square.

 

I can factor and solve a quadratic equation.

 

I can find the discriminant.

 

I can solve Quadratic Application Problems.

 

I can identify Key Features of a Quadratic Function.


I can add, subtract, mutiply irrationals and rationals.


I can use the Quadratic Formula to solve a quadratic equation.

12 days including 1 quiz, 1 review, 1 test

Included in Unit 8

Graphs of Quadratic Equations & Solving Word Problems
(2) AI.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(6) AI.A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
(5) AI.A.CED.2 Create equations and linear inequalities in two variables to represent a real-world context.
(4) AI.A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
(5) AI.F.BF.1 Write a function that describes a relationship between two quantities. ★
(3) AI.F.IF.1 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. 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 f is the graph of the equation y = f(x).
(3) AI.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
(4) AI.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities; and
  2. sketch graphs showing key features given a verbal description of the relationship.
(5) AI.F.IF.5 Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
(5) AI.F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.
(3) AI.F.IF.7 Graph functions and show key features of the graph by hand and by using technology where appropriate. ★
(4) AI.F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.
(3) AI.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(3) AI.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

How can we graph a quadratic equation when it is presented in multiple forms?

 

How can we identify the axis of symmetry, vertex, manimum/minimum, domain, range and zeroes (solutions/roots/x-intercepts) of a parabola?

 

How can we determine the average rate of change of a parabola along a given interval?

 

How can we solve a word problem and interpret quadratic graphs?

 

How can we change vertex form equations into standard form and vice versa?

 

How can we graph piecewise functions (linear/quadratic)?

1. Graph quadratic equations in any form
2. Identify axis of symmetry, vertex, maximum/minimum, domain, range, and zeros of a parabola
3. Determine the average rate of change of a parabola along a given interval
4. Solve word problems and interpret quadratic graphs
5. Change vertex form equations into standard form and vice versa
6. Graph piecewise functions (linear/quadratic)

Axis of Symmetry

Domain

Maximum

Minimum

Parabola

Piecewise Function

Range

Roots/Solutions/x-intercepts/Zeros

Vertex (Turning Point)

Vertex Form

I can identify the parts of the graph of a quadratic (axis of symmetry, vertex, minimum/maximum, solutions/roots/zeroes/x-inercepts).

 

I can use the formula x=-b/2a to identify the axis of symmetry and vertex of a quadratic equation.

 

I can find the average rate of change given the graph of a parabola.

 

I can graph a quadratic equation using the graphing calculator to generate a table of values.

 

I can identify the zeroes/solutions/roots/x-intercepts of a quadratic equation given a table or a graph.

 

I can graph a quadratic equation using the vertx form.

 

I can convert the standard form of an equation into vertex form.

 

I can solve a projectile motion problem.

 

I can graph linear/quadratic piecewise functions.

 

 

10 days including 1 review, 1 test

Unit 9

Functions and Their Transformations
(3) AI.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(3) AI.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
(2) AI.F.LE.1a Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.
(2) AI.F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
(2) AI.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.

How can we graph a set of functions (families) with restricted and unrestrited domains?

 

How can we identify the type of function from a graph, an equation and a table?

 

How can we identify and perform transformations on all given functions?

 

How can we graph piecewise functions?

1. Graph a set of functions (families) with restricted and unrestricted domains
2. Identify the type of function from a graph, an equation and table
3. Identify and perform transformations on all given functions
4. Graph piecewise functions

Absolute Value Function

Cube Root Function

Cubic Function

Exponential Function

Family of Functions

Linear Function

Parent Functions

Piecewise Functions

Quadratic Function

Transformations

Shifts

Square Root Function

I can identify each function family by characteristics, equation, table of values and graph.

 

I can identify the type of function from a table using the differences of the y-values (linear/quadratic/exponential).

 

I can apply transformations to parent functions.

 

I can graph piecewise functions with focus on domain/range.

13 days including 1 quiz, 1 review, 1 test day

Unit 10

Statistics
(1) AI.S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
(1) AI.S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (inter-quartile range, sample standard deviation) of two or more different data sets.
(1) AI.S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
(1) AI.S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
(1) AI.S.ID.6 Represent bivariate data on a scatter plot, and describe how the variables’ values are related.
(1) AI.S.ID.6a Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
(1) AI.S.ID.8 Calculate (using technology) and interpret the correlation coefficient of a linear fit.
(1) AI.S.ID.9 Distinguish between correlation and causation.

How can we analyze data to determine bivariate vs. univariate data?

 

How can we analyze data to determine causation vs. correlation?

 

How can we analyze data to determine if it is qualitative vs quantitative?

 

How can we find appropriate measures of central tendency?

 

How can we create and answer questions about dot plots, frequency histograms, two-way frequency tables, scatter plots and box plots?

 

How can we calculate and apply standard deviation, correlation coefficients, residuals and lines of best fit for data?

 

 

 

1. Identify the difference between quantitative/qualitative data and univariate/bivariate data

2. Find the measures of central tendency for data

3. Create and answer questions about dot plots, frequency histograms, two-way frequency tables, scatter plots and box plots

4. Calculate and apply standard deviation, correlation coefficients, residuals and lines of best fit for data

Bivariate

Box Plots

Causality

Central Tendency

Correlation

Correlation Coefficient

Distribution

Dot Plots

Histograms

Interquartile Range

Line of Best Fit

Mean

Median

Mode

Outlier

Percentiles

Population

Qualitative Data

Quantitative Data

Quartiles

Range

Residual Plot

Residuals

Sample

Scatter Plots

Standard Deviation

Two-Way Frequency Tables

Univariate

I can analyze data to determine bivariate vs. univariate data.

 

I can analyze data to determine causation vs. correlation.

 

I can analyze data to determine if it is qualitative vs quantitative.

 

I can  find appropriate measures of central tendency.

 

I can create and answer questions about dot plots, frequency histograms, two-way frequency tables, scatter plots and box plots.

 

I can calculate and apply standard deviation, correlation coefficients, residuals and lines of best fit for data.

 

 
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