Dexter R-XI School District
Algebra 1 Unit Plans
School Board Approved 6/23/24
Unit 1
Solving Linear Equations
Grade
9-12
Length Of Unit
14 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
How can you use simple equations to solve real-world problems?
Seeing Structure in Expressions
How can you use multi-step equations to solve real-world problems?
Creating Equations
How can rearranging formulas help solve real-world problems?
Reasoning with Equations and Inequalities
Priority - Missouri Learning Standards
- A1.SSE.A Interpret and use structure.
- A1.CED.A Create equations that describe linear, quadratic and exponential relationships.
- A1.REI.A Understand solving equations as a process, and solve equations and inequalities in one variable.
- A1.LQE.A Construct and compare linear, quadratic and exponential models and solve problems.
Supporting - Missouri Learning Standards
- A1.REI.A.1 Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(Summative) as the original
- A1.CED.A.1 Create equations and inequalities in one variable and use them to model and/or solve problems
- A1.CED.A.4 Solve literal equations and formulas for a specified variable that highlights a quantity of interest
- A1.SSE.A.1 Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions.
Instructional Objectives And Learning Targets
A1.REI.A.1, A1.CED.A.1, A1.CED.A.4, A1.SSE.A.1
- I can explain how each step taken when solving an equation in one variable creates an equivalent equation that has the same solution(Summative) as the original.
- I can create linear equations with one variable and use them to model and/or solve problems.
- I can solve literal equations and formulas for a specified variable.
- I can interpret the meaning of individual terms or factors in a given problem and choose/use a formula that matches the situation.
Topics
- Lesson 1 - Solving Simple Equations
- Solving linear equations by adding or subtracting
- Solving linear equations by multiplying or dividing
- Solving real-life problems
- Lesson 2 - Solving Multi-Step Equations
- Solving two-step equations
- Combining like terms to solve an equation
- Using structure to solve multi-step equations
- Solving real-life problems
- Using unit analysis to model real-life problems
- Lesson 3 - Solving Equations with Variables on Both Sides
- Solving equations with variables on both sides
- Identifying special solutions of linear equations (infinitely many, no solution)
- Solving real-life problems
- Lesson 4 - Solving Absolute Value Equations
- Solving absolute value equations
- Writing absolute value equations
- Solving equations with two absolute values
- Identifying extraneous solutions
- Lesson 5 - Rewriting Equations and Formulas
- Rewriting literal equations
- Rewriting and using formulas for area
- Rewriting the formula for temperature
- Using the formula for simple interest
- Solving real-life problems
Teaching Activities
- Lesson 1 - One Step Equations:
- Lesson 2 - Multi-step Equations:
- Lesson 3 - Equations with Variables on Both Sides:
- Lesson 4 - Absolute Value Equations:
- Lesson 5 - Rearranging Literal Equations:
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked in “Materials and Additional Resources” document
Assessments With Missouri Learning Standards
1.1-1.2 Quiz (Formative)
A1.REI.A.1 A1.CED.A.1
1.3 Quiz (Formative)
A1.REI.A.1 A1.CED.A.1
1.4 Quiz (Formative)
A1.REI.A.1 A1.CED.A.1
Ch 1 Test - Big Ideas Math (Summative)
A1.REI.A.1 A1.CED.A.1, A1.SSE.A.1
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- Conjecture
- Rule
- Theorem
- Equation
- Linear Equation
- Inverse Operations
- Equivalent Equations
- Expression
- Identity
- Absolute Value Equation
- Extraneous Solution
- Literal Equation
- Formula
Materials And Additional Resources
Solving One Step Equations Video Lesson
Solving Multi-step Equations Video Lesson
Solving Equations with Variables on Both Sides Video Lesson
Solving Absolute Value Equations Video Lesson
Rearranging Literal Equations Video Lesson
Unit 2
Solving Linear Equations
Grade
9-12
Length Of Unit
14 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
How can you use an inequality to describe a real-life statement?
Seeing Structure in Expressions
How can you use inequalities to describe intervals on the real number line?
Creating Equations
Priority - Missouri Learning Standards
- A1.SSE.A Interpret and use structure.
- A1.CED.A Create equations that describe linear, quadratic and exponential relationships.
- A1.REI.A Understand solving equations as a process, and solve equations and inequalities in one variable.
- A1.LQE.A Construct and compare linear, quadratic and exponential models and solve problems
Supporting - Missouri Learning Standards
- A1.REI.A.1 Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(Summative) as the original
- A1.CED.A.1 Create equations and inequalities in one variable and use them to model and/or solve problems
Instructional Objectives And Learning Targets
A1.REI.A.1, A1.CED.A.1
- I can explain how each step taken when solving an equation in one variable creates an equivalent equation that has the same solution(Summative) as the original.
- I can create equations and inequalities in one variable and use them to model and/or solve problems.
- I can interpret data points as a solution or non-solution of an equation, inequality, or system of equations or inequalities.
Topics
- Lesson 1 - Writing and Graphing Inequalities
- Write linear inequalities
- Sketch the graphs of linear inequalities
- Write linear inequalities from graphs
- Lesson 2 - Solving Inequalities Using Addition or Subtraction
- Solve inequalities using addition
- Solve inequalities using subtraction
- Use inequalities to solve real-life problems
- Lesson 3 - Solving Inequalities Using Multiplication or Division
- Solve inequalities by multiplying or dividing by positive numbers
- Solve inequalities by multiplying or dividing by negative numbers
- Use inequalities to solve real-life problems
- Lesson 4 - Solving Multi-step Inequalities
- Solve multi-step inequalities
- Solve inequalities with variables on both sides
- Solve inequalities with special solutions
- Lesson 5 - Solving Compound Inequalities
- Writing and graphing compound inequalities
- Solving compound inequalities with “and”
- Solving compound inequalities with “or”
- Lesson 6 - Solving Absolute Value Inequalities
- Solving absolute value inequalities
- Modeling real-life problems
Teaching Activities
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked in “Materials and Additional Resources”
Assessments With Missouri Learning Standards
2.1-2.4 Quiz (Formative)
A1.REI.A.1, A1.CED.A.1, A1.CED.A.1
Ch 2 Test (Summative)
A1.REI.A.1, A1.CED.A.1, A1.CED.A.1
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- Solution set
- Inequality
- Absolute value inequality
- Solution of an inequality
- Compound inequality
- Equivalent inequality
- Absolute deviation
Materials And Additional Resources
Lesson 1: Inequalities Quizlet #1, Inequalities Quizlet #2
Lesson 2: One Step Inequalities Matching
Lesson 3: Inequalities with Multiplication and Division Puzzle
Lesson 4: Multi-step Inequalities Escape Room, Multi-step Inequalities Mystery Design Worksheet
Lesson 5: Compound Inequalities Quizlet Compound Inequalities Would You Rather, Compound Inequalities Google Slide Practice
Lesson 6: Absolute Value Inequalities Escape Room
Unit 3
Graphing Linear Functions
Grade
9-12
Length Of Unit
20 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
How can functions help us see and analyze relationships between two different sets of data?
Interpreting Functions
How are equations and graphs related?
Building Functions
Priority - Missouri Learning Standards
- A1.IF.B Interpret linear, quadratic and exponential functions in terms of the context.
- A1.IF.B.3 Using tables, graphs and verbal descriptions,interpret key characteristics of a function that models the relationship between two quantities.
- A1.IF.C Analyze linear, quadratic and exponential functions using different representations.
- A1.IF.C.7 Graph functions expressed symbolically and identify and interpret key features of the graph.
- A1.BF.A Build new functions from existing functions (limited to linear, quadratic and exponential).
- A1.BF.A.1 Analyze the effect of translations and scale changes on functions.
Supporting - Missouri Learning Standards
- A1.IF.A Understand the concept of a function and use function notation.
- A1.IF.A1 Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range.
- A1.IF.A2 Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- A1.IF.B4 Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.
- A1.IF.B5 Determine the average rate of change of a function over a specified interval and interpret the meaning.
- A1.IF.C8 Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context.
- A1.IF.C9 Compare the properties of two functions given different representations.
- A1.BF.A.1 Analyze the effect of translations and scale changes on functions.
Instructional Objectives And Learning Targets
A1.IF.A1, A1.IF.A2, A1.IF.B.3, A1.IF.B4, A1.IF.B5, A1.IF.C.7, A1.IF.C8, A1.IF.C9, A1.BF.A.1
- I can represent a function using function notation f(x).
- I can understand that f(x) denotes the elements of the range of a function f that correspond to the elements of the domain.
- I can use function notation to evaluate functions.
- I can interpret statements involving the inputs and outputs of a function.
- I can use tables, graphs, and verbal descriptions to interpret key characteristics of a function that models the relationship between two quantities.
- I can determine the domain and range of a function from its graph.
- I can describe how the domain and range within the context of a situation affect the characteristics of the graph of the function.
- I can determine the average rate of change of a function over a specified interval and interpret its meaning.
- I can graph linear functions and identify and interpret key features of the graph by hand and by using technology.
- I can translate between different but equivalent forms of a function and interpret them in terms of a given context.
- I can compare the properties of two functions given different representations.
- I can analyze the effect of the scale change on the graph of f(x) by kf(x).
- I can analyze the effect of the translation on the graph of f(x) by f(x) + k.
- I can analyze the effect of the translation on the graph of f(x) by f(x+k).
- I can find the specific value of k given the graphs of f(x) and the graph after translations and scale changes has been performed.
Topics
- Lesson 1 - Identifying Functions
- Determine whether relations are functions
- Find the domain and range of a function
- Identify the independent and dependent variables of functions
- Lesson 2 - Linear Functions
- Identify linear functions using graphs, tables, and equations
- Graph linear functions using discrete and continuous data
- Write real-life problems to fit data
- Lesson 3 - Function Notation
- Use function notation to evaluate and interpret functions
- Use function notation to solve and graph functions
- Solve real-life problems using function notation
- Lesson 4 - Graphing Linear Equations in Standard Form
- Graph equations of horizontal and vertical lines
- Graph linear equations in standard form using intercepts
- Use linear equations in standard form to solve real-life problems
- Lesson 5 - Graphing Linear Equations in Slope-Intercept Form
- Find the slope of a line
- Use the slope-intercept form of a linear equation
- Use slopes and y-intercepts to solve real-life problems
- Lesson 6 - Transformations of Graphs of Linear Functions
- Translate and reflect graphs of linear functions
- Stretch and shrink graphs of linear functions
- Combine transformations of graphs of linear functions
- Lesson 7 - Graphing Absolute Value Functions
- Translate graphs of absolute value functions
- Stretch, shrink, and reflect graphs of absolute value functions
- Combine transformations of graphs of absolute value functions
Teaching Activities
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked in “Materials and Additional Resources”
Assessments With Missouri Learning Standards
3.1-3.3 Quiz (Formative)
A1.IF.A.1, A1.IF.A2, A1.IF.B.3, A1.IF.B4, A1.IF.B5
Ch 3 Test (Summative)
A1.IF.A1, A1.IF.A2, A1.IF.B.3, A1.IF.B4, A1.IF.B5, A1.IF.C.7, A1.IF.C8, A1.IF.C9, A1.BF.A.1
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- Relation
- Nonlinear function
- Rise
- Vertical stretch
- Function
- Discrete domain
- Run
- Vertical shrink
- Domain
- Continuous domain
- Constant function
- Absolute value function
- Range
- Function Notation
- Family of functions
- Vertex
- Independent Variable
- Standard form
- Parent function
- Vertex form
- Dependent Variable
- X-intercept
- Transformation
- Linear function
- Ordered Pair
- Y-intercept
- Translation
- Slope-intercept form
- Mapping Diagram
- Quadrant
- Reflection
- Horizontal stretch
- Linear equation in two variables
- Slope
- Horizontal shrink
Materials And Additional Resources
Lesson 1: Is it a Function Gimkit
Lesson 2: Discrete vs Continuous Data Blooket Identifying Linear Functions Practice
Lesson 3: Evaluating Linear Functions Partner Race
Lesson 4: Graph using intercepts google slide practice
Lesson 6: Linear Function Transformation Rules Translations Quizlet, Transformations Blooket Transformations Task Cards
Lesson 7: Absolute Value Functions Maze
Unit 4
Writing Linear Functions
Grade
9-12
Length Of Unit
15 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
How can linear functions help us see and analyze relationships between two different sets of quantitative data?
Interpreting Functions
Building Functions
How can creating scatter plots help us analyze data trends in real-world situations?
Data and Statistics
Priority - Missouri Learning Standards
- A1.LQE.A.3 Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.
- A1.LQE.B Use arithmetic and geometric sequences.
- A1.LQE.B.4 Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.
- A1.DS.A Summarize, represent and interpret data.
Supporting - Missouri Learning Standards
- A1.CED.A.2 Create and graph linear, quadratic and exponential equations in two variables.
- A1.LQE.A.1 Distinguish between situations that can be modeled with linear or exponential functions.
- A1.LQE.B.6 Find the terms of sequences given an explicit or recursive formula.
- A1.DS.A.5 Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.
- A1.DS.A.5a a. Construct a linear function to model bivariate data represented on a scatter plot that minimizes residuals.
- A1.DS.A.5b b.Construct an exponential function to model bivariate data represented on a scatter plot that minimizes residuals.
- A1.DS.A.6 Interpret the slope (rate of change) and the y-intercept (constant term) of a linear model in the context of the data.
- A1.DS.A.7 Determine and interpret the correlation coefficient for a linear association.
- A1.DS.A.8 Distinguish between correlation and causation.
Instructional Objectives And Learning Targets
A1.CED.A.2,A1.LQE.A.1,A1.LQE.A.3,A1.LQE.B.4,A1.LQE.B.6,A1.DS.A.5a,A1.DS.A.6, A1.DS.A.7,A1.DS.A.8
- I can create and graph linear equations in two variables on the Cartesian coordinate plane with labels and scales.
- I can recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
- I can construct linear equations given graphs, verbal descriptions, and tables.
- I can write arithmetic sequences in recursive and explicit forms given graphs, verbal descriptions, or tables.
- I can use arithmetic sequences to model situations.
- I can find the terms of a sequence give an explicit or recursive formula.
- I can construct a scatter plot of quantitative data in two variables and determine the type of function that models the relationship.
- I can construct a linear function to model the data on a scatter plot that minimizes residuals using calculation and/or technology.
- I can interpret the slope (rate of change) and y-intercept (constant term) of a linear model in the context of the data.
- I can determine and interpret the correlation coefficient for a linear association.
- I can distinguish between correlation and causation and understand and explain that a strong correlation does not imply causation.
Topics
- Lesson 1 - Writing Equations in Slope Intercept Form
- Using slopes and y-intercepts to write equations
- Using graphs to write equations
- Using points to write equations
- Writing a linear function
- Solving real-life problems
- Lesson 2 - Writing Equations in Point-Slope Form
- Using a slope and a point to write an equation
- Using two points to write an equation
- Writing a linear function
- Lesson 3 - Writing Equations of Parallel and Perpendicular Lines
- Identifying parallel lines
- Writing an equation of a parallel line
- Identifying perpendicular lines
- Writing an equation of a perpendicular line
- Lesson 4 - Scatter Plots and Lines of Fit
- Interpreting a scatter plot
- Identifying correlation
- Using lines of fit to model data
- Lesson 5 - Analyzing Lines of Fit
- Analyzing residuals
- Correlation coefficients
- Interpolating and extrapolating data
- Identifying correlation and causation
- Lesson 6 - Arithmetic Sequences
- Extending an arithmetic sequence
- Graphing an arithmetic sequence
- Writing arithmetic sequences as functions
- Finding the nth term of an arithmetic sequence
- Writing real life functions
- Lesson 7 - Piecewise Functions
- Evaluating a piecewise function
- Graphing and writing piecewise functions
- Graphing and writing step functions
- Writing absolute value functions
Teaching Activities
- Lesson 4.1: Writing equations in slope intercept form notes and examples
- Lesson 4.2: Writing equations in point-slope form notes and examples
- Lesson 4.3: Writing equations of parallel and perpendicular lines notes and examples
- Lesson 4.4: Intro to Scatter Plots and Correlation Guided Notes Writing Equations for Lines of Fit
- Lesson 4.5: Using residuals to analyze lines of fit notes and examples
- Lesson 4.6: Arithmetic sequences notes and examples
- Lesson 4.7: Piecewise functions notes and examples
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked in “Materials and Additional Resources”
Assessments With Missouri Learning Standards
4.1-4.3 Quiz (Formative)
A1.CED.A.2,A1.LQE.A.1,A1.LQE.A.3
Ch 4 Test (Summative)
A1.LQE.B.4,A1.LQE.B.6,A1.DS.A.5a,A1.DS.A.5b,A1.DS.A.6,A1.DS.A.7, A1.DS.A.8
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- Vertex
- Arithmetic sequence
- Linear model
- Slope-intercept form
- Term
- Common difference
- Function
- Rate
- Sequence
- Function notation
- Point-slope form
- Parallel line
- Correlation coefficient
- Piecewise function
- Perpendicular lines
- Reciprocal
- Extrapolation
- Step function
- Scatter plot
- Correlation
- Causation
- Absolute value function
- Line of fit
- Residual
- Interpolation
- Vertex form
- Linear regression
- Line of best fit
Materials And Additional Resources
4.1: Writing Equations from Two Points Digital Mystery Picture, Writing Equations from a graph digital practice
4.2: Writing equations in point slope form digital mystery picture, Writing equations in two forms math mystery - The Case of the Stolen Jewelry Writing Equations from Two Points Math Lib
4.3: Parallel, Perpendicular, or Neither Maze, Equations of Parallel and Perpendicular Lines Pixel Art
4.4: Interpreting Scatter Plots Practice, Build a Snowman Lines of Fit Practice, Flower Growth Scatter Plot and Lines of Fit Practice
4.5: Graphing Lines of fit using desmos demo video
Unit 5
Solving Systems of Linear Equations
Grade
9-12
Length Of Unit
15 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
How can you graph and solve a system of equations?
How can systems of equations be used to represent and solve real-world situations?
Reasoning with Equations and Inequalities
Priority - Missouri Learning Standards
- A1.REI.C Represent and solve linear and exponential equations and inequalities graphically.
- A1.REI.C.6 Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane.
- A1.REI.C.8 Solve problems involving a system of linear inequalities.
Supporting - Missouri Learning Standards
- A1.CED.A.2 Create and graph linear, quadratic and exponential equations in two variables.
- A1.REI.B Solve systems of equations
- A1.REI.B.3 Solve a system of linear equations algebraically and/or graphically.
- A1.REI.B.5 Justify that the technique of linear combination produces an equivalent system of equations.
- A1.REI.C.7 Graph the solution to a linear inequality in two variables.
Instructional Objectives And Learning Targets
A1.CED.A.2,A1.REI.B.3,A1.REI.B.5,A1.REI.C.6,A1.REI.C.7,A1.REI.C.8
- I can create and graph linear equations in two variables on the Cartesian coordinate plane with labels and scales.
- I can solve a system of linear equations graphically.
- I can solve a system to linear equations algebraically.
- I can justify that the technique of linear combination produces an equivalent system of equations.
- I can explain that the graph of a linear equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane and that a point not on the graph of a linear equation in the Cartesian coordinate plane is not a solution.
- I can graph the solution to a linear inequality in two variables.
- I can solve problems involving a system of inequalities by graphing and interpret the solution in the context provided.
Topics
- Lesson 5.1 - Solving Systems of Linear Equations by Graphing
- Check solutions to systems
- Solve systems by graphing
- Lesson 5.2 - Solving Systems of Linear Equations by Substitution
- Lesson 5.3 - Solving Systems of Linear Equations by Elimination
- Elimination with addition and subtraction
- Elimination that requires multiplication
- Lesson 5.4 Solving Special Systems of Linear Equation
- Systems with no solution
- Systems with infinitely many solutions
- Lesson 5.5 - Solving Equations by Graphing
- Solving Linear equations with variables on both sides by graphing
- Solving absolute value equations by graphing
- Lesson 5.6 - Graphing Linear Inequalities in Two Variables
- Checking solutions
- Graphing a linear inequality in one variable
- Graphing a linear inequality in two variables
- Lesson 5.7 - Systems of Linear Inequalities
- Checking solutions
- Graphing a system of linear inequalities
- Graphing systems with no solution
- Writing a system of linear inequalities given a graph
Teaching Activities
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked in “Materials and Additional Resources”
Assessments With Missouri Learning Standards
5.1-5.4 Quiz (Formative)
A1.CED.A.2 A1.REI.B, A1.REI.B.3, A1.REI.B.5, A1.REI.C, A1.REI.C.6
Ch 5 Test (Summative)
A1.CED.A.2, A1.REI.B, A1.REI.B.3, A1.REI.B.5, A1.REI.C, A1.REI.C.6, A1.REI.C.7, A1.REI.C.8
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- System of linear equations
- Solution of a linear inequality in two variables
- Parallel
- Solution of a system of linear equations
- Graph of a linear inequality
- Absolute value equation
- Linear equation
- Half-planes
- Linear inequality in two variables
- Ordered pair
- System of linear inequalities
- Graph of a system of linear inequalities
- Coefficient
- Solution of a system of linear inequalities
Materials And Additional Resources
Lesson 5.1: Graphing in slope intercept form review / warm-up, Solve Systems by Graphing Riddle Practice
Lesson 5.3: Solve Systems with Elimination Mystery Picture #1 (add/subtact), Solve Systems with Elimination Mystery Picture #2 (multiply)
Lesson 5.6: Graphing Linear Inequalities Escape Room
Unit 6
Exponential Functions and Sequences
Grade
9-12
Length Of Unit
15 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
How can you simplify expressions involving exponents?
Number and Quantity
How can we differentiate an exponential model from a linear model given a real world set of data?
Interpreting Functions
What are real world models of exponential growth and decay?
Linear, quadratic, and exponential models
Priority - Missouri Learning Standards
- A1.IF.B Interpret linear, quadratic and exponential functions in terms of the context.
- A1.IF.B.3 Using tables, graphs and verbal descriptions,interpret key characteristics of a function that models the relationship between two quantities.
- A1.IF.C Analyze linear, quadratic and exponential functions using different representations.
- A1.IF.C.7 Graph functions expressed symbolically and identify and interpret key features of the graph.
- A1.LQE.A Construct and compare linear, quadratic and exponential models and solve problems.
- A1.LQE.A.3 Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.
- A1.LQE.B Use arithmetic and geometric sequences.
- A1.LQE.B.4 Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.
Supporting - Missouri Learning Standards
- A1.NQ.A Extend and use properties of rational exponents.
- A1.NQ.A.1 Explain how the meaning of rational exponents extends from the properties of integer exponents.
- A1.NQ.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1
- A1.LQE.A.1b Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.
- A1.LQE.A.2 Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.
- A1.LQE.B.5 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers.
- A1.LQE.B.6 Find the terms of sequences given an explicit or recursive formula.
Instructional Objectives And Learning Targets
A1.NQ.A.1, A1.NQ.A.2, A1.IF.B.3, A1.IF.C.7, A1.LQE.A.1b, A1.LQE.A.2, A1.LQE.A.3, A1.LQE.B.4, A1.LQE.B.6
- I can explain the properties of exponents, including rational exponents.
- I can rewrite expressions with rational exponents as equivalent radical expressions.
- I can rewrite radical expressions as equivalent expressions with rational exponents.
- I can interpret key characteristics of a function that models the relationship between two quantities using tables, graphs, and verbal descriptions.
- I can graph exponential functions and identify and interpret key features of the graph by hand and by using technology.
- I can recognize exponential situations in which a quantity grows or decays by a constant percent rate and show that exponential functions change by equal factors over equal intervals.
- I can describe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.
- I can construct exponential equations given graphs, verbal descriptions, or tables.
- I can write geometric sequences in recursive and explicit forms given graphs, verbal descriptions, or tables.
- I can translate between explicit and recursive forms of geometric sequences.
- I can model situations with geometric sequences.
- I can find terms of sequences given an explicit or recursive formula.
Topics
- Lesson 6.1 - Properties of Exponents
- Use zero and negative exponents
- USe the properties of exponents
- Lesson 6.2 - Radicals and Rational Exponents
- Find nth roots
- Evaluate expressions with rational exponents
- Lesson 6.3 - Exponential Functions
- Identify and evaluate exponential functions
- Graph exponential functions
- Lesson 6.4 - Exponential Growth and Decay
- Use and identify exponential growth and decay functions
- Interpret and rewrite exponential growth and decay functions
- Calculate compound interest
- Lesson 6.5 - Solving Exponential Equations
- Solve exponential equations with the same base
- Solve exponential equations with unlike bases
- Solve exponential equations by graphing
- Lesson 6.6 - Geometric Sequences
- Identify geometric Sequences
- Extend and graph geometric sequences
- Write geometric sequences as functions
- Lesson 6.7 - Recursively Defined Sequences
- Write terms of recursively defined sequences
- Write recursive rules for sequences
- Translate between recursive rules and explicit rules Write recursive rules for special sequences
Teaching Activities
- Lesson 6.1 - Properties of Exponents
- Lesson 6.2 - Radicals and Rational Exponents
- Lesson 6.3 - Exponential Functions
- Intro to exponential functions notes
- Transformations of exponential functions notes
- Lesson 6.4 - Exponential Growth and Decay
- Lesson 6.6 - Geometric Sequences
- 6.7 notes: find terms given recursive rule, write recursive rule given terms, translate between explicit and recursive rules
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked under “Materials and Additional Resources”
Assessments With Missouri Learning Standards
6.1-6.4 Quiz (Formative)
A1.NQ.A.1, A1.NQ.A.2, A1.IF.B.3, A1.IF.C.7, A1.LQE.A.1b, A1.LQE.A.2, A1.LQE.A.3
Ch 6 Test (Summative)
A1.NQ.A.1, A1.NQ.A.2, A1.IF.B.3, A1.IF.C.7, A1.LQE.A.1b, A1.LQE.A.2, A1.LQE.A.3, A1.LQE.B.4, A1.LQE.B.5, A1.LQE.B.6
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- power
- Dependent variable
- Arithmetic sequence
- Exponential decay
- exponent
- Parent function
- Common difference
- Exponential decay function
- base
- Exponential growth
- Explicit rule
- Compound interest
- Scientific notation
- Exponential growth function
- Recursive rule
- Exponential equation
- nth root
- Index of a radical
- Exponential function
- Geometric sequence
- radical
- Square root
- Independent variable
- Common ratio
Materials And Additional Resources
6.1: Exponent rules practice Knockout game, Exponent rules Blooket
6.3: Graphing exponential functions google slide practice, Transformations of Exponential Functions Blooket
6.4: Compound Interest MathLib
Unit 7
Polynomial Equations and Factoring
Grade
9-12
Length Of Unit
24 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
Can two algebraic expressions that appear to be different be equivalent?
Seeing Structure in Expressions
How can polynomials be simplified and applied to solve problems?
Big Reasoning with Equations and Inequalities
How are the properties of real numbers related to polynomials?
Arithmetic with Polynomials and Rational Expressions
Priority - Missouri Learning Standards
- A1.SSE.A.2 Analyze the structure of polynomials to create equivalent expressions or equations.
- A1.REI.A.2 Solve problems involving quadratic equations.
- A1.REI.A.2c Analyze different methods of solving quadratic equations.
Supporting - Missouri Learning Standards
- A1.SSE.A.3 Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.
- A1.APR.A Perform operations on polynomials.
- A1.APR.A.1 Add, subtract and multiply polynomials,and understand that polynomials follow the same general rules of arithmetic and are closed under these operations
Instructional Objectives And Learning Targets
A1.SSE.A.2,A1.SSE.A.3,A1.REI.A.2c,A1.APR.A.1
- I can factor polynomial expressions.
- I can analyze the structure of polynomials to determine an appropriate method for decomposing and composing to create equivalent equations.
- I can find the zeros of a quadratic function by rewriting it in factored form.
- I can solve quadratic equations using different methods.
- I can add, subtract, and multiply polynomials and understand that polynomials follow the same general rules of arithmetic and are closed under addition, subtract, and multiplication.
Topics
- 7.1 - Adding and Subtracting Polynomials
- Find the degrees of monomials
- Classify polynomials
- Add and subtract polynomials
- 7.2 - Multiply Polynomials
- Multiply binomials
- Use the foil method
- Multiply binomials and trinomials
- 7.3 - Special Products of Polynomials
- Use the square of a binomial pattern
- Use the sum and difference pattern
- 7.4 - Solving Polynomial Equations in Factored Form
- Use the zero-product property
- Factor polynomials using the GCF
- 7.5 - Factoring x^2+bx+c
- 7.6 - Factoring ax^2+bx+c
- 7.7 - Factoring Special Products
- Factor the difference of two squares
- Factor perfect square trinomials
- 7.8 - Factor Polynomials Completely
- Factor polynomials by grouping
Teaching Activities
- 7.1 - Adding and Subtracting Polynomials
- 7.2 - Multiply Polynomials
- Multiplying 3 ways notes - Distributive property, table, FOIL method
- 7.3 - Special Products of Polynomials
- Notes - square of binomials, sum and difference
- 7.4 - Solving Polynomial Equations in Factored Form
- 7.6 - Factoring ax^2+bx+c
- 7.7 - Factoring Special Products
- Notes - factoring a difference of two squares
- 7.8 - Factor Polynomials Completely
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked under “Materials and Additional Resources”
Assessments With Missouri Learning Standards
7.1-7.4 Quiz (Formative)
A1.REI.A.2c ,A1.APR.A.1
Ch 7 Test (Summative)
A1.SSE.A.2, A1.SSE.A.3, A1.REI.A.2c, A1.APR.A.1
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- Monomial
- Zero-product property
- Degree of a polynomial
- FOIL method
- Degree of a monomial
- roots
- Standard form
- Factored form
- polynomial
- Repeated roots
- Leading coefficient
- Factor by grouping
- binomial
- trinomial
- Factored completely
Materials And Additional Resources
7.2: Multiply polynomials puzzle
7.4 Factor out GCFs Mystery Picture
7.5: Factor trinomials pixel art level 1, Factor trinomials pixel art level 2, Factoring Connect 4 Partner Game
7.6: Factoring out a GCF Task Cards, Factoring a>1 Mystery Picture, Factor trinomials task cards
7.8: Factor by grouping mystery picture, Factor completely google sheet practice
Unit 8
Graphing Quadratic Functions
Grade
9-12
Length Of Unit
20 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
How do quadratic equations model real world problems and situations?
Interpreting Functions
How can we determine which type of model would best represent a give situation?
Linear, Quadratic, and Exponential Models
Priority - Missouri Learning Standards
- A1.IF.C.7 Graph functions expressed symbolically and identify and interpret key features of the graph.
- A1.BF.A.1 Analyze the effect of translations and scale changes on functions.
- A1.LQE.A Construct and compare linear, quadratic and exponential models and solve problems.
Supporting - Missouri Learning Standards
- A1.SSE.A.3 Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.
- A1.SSE.A.3a Find the zeros of a quadratic function by rewriting it in factored form.
- A1.SSE.A.3b .Find the maximum or minimum value of a quadratic function by completing the square
- A1.CED.A.2 Create and graph linear, quadratic and exponential equations in two variables.
Instructional Objectives And Learning Targets
A1.SSE.A.3a,A1.SSE.A.3b,A1.CED.A.2,A1.IF.C.7,A1.BF.A.1
- I can find the zeros of a quadratic function by rewriting it in factored form.
- I can find the maximum and minimum value of a quadratic.
- I can find vertex of an equation in the form f(x) = a (x - h)^2 + k.
- I can create and graph exponential equations in two variables on the Cartesian coordinate plane with labels and scales.
- I can graph quadratic functions and identify and interpret key features of the graph by hand and by using technology.
- I can analyze the effect of scale changes on the graph of f(x) by kf(x) for specific values of k.
- I can analyze the effect of the translation on the graph f(x) by f(x)
- +k and f(x+k) for specific values of k.
Topics
- Lesson 8.1 - Graphing f(x) = ax^2
- Identify characteristics of quadratic functions
- Graph and use quadratic functions of the form f(x)=ax^2
- Lesson 8.2 - Graphing f(x) = ax^2 + c
- Graph quadratic function of the form f(x) = ax^2 + c
- Lesson 8.3 - Graphing f(x) = ax^2 + bx + c
- Graph quadratic functions of the form f(x) = ax^2 + bx + c
- Find maximum and minimum values of quadratic functions
- Lesson 8.4 - Graphing f(x) = a (x - h)^2 + k
- Identify even and odd functions
- Graph quadratic functions in vertex form f(x) = a (x - h)^2 + kLesson
- Lesson 8.5 - Using Intercept Form
- Graph quadratic functions in the form f(x) = a (x - p) (x - q)
- Use intercept form to find zeros of functions
- Use characteristics to graph and write quadratic functions
- Use characteristics to graph and write cubic functions
- Lesson 8.6 - Comparing Linear, Exponential, and Quadratic Functions
- Choose functions to model data
- Write functions to model data
- Compare functions using average rate of change
Teaching Activities
- 8.1 - Graphing f(x) = ax^2
- 8.2 - Graphing f(x) = ax^2 + c
- Notes/practice: vertical stretch/shrink, vertical shifts, y-intercept
- 8.3 - Graphing f(x) = ax^2 + bx + c
- 8.4 - Graphing f(x) = a (x - h)^2 + k
- 8.5 - Using Intercept Form
- Notes: Finding zeros in intercept form, converting from standard form by factoring
- 8.6 - Comparing Linear, Exponential, and Quadratic Functions
- Notes: using graphs to identify functions
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked under “Materials and Additional Resources”
Assessments With Missouri Learning Standards
8.1-8.3 Quiz (Formative)
A1.CED.A.2,A1.IF.C.7, A1.BF.A.1
Ch 8 Test (Summative)
A1.SSE.A.3a, A1.SSE.A.3b, A1.CED.A.2, A1.IF.C.7, A1.BF.A.1
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- Quadratic function
- Maximum value
- Vertical stretch
- domain
- parabola
- Minimum value
- Vertical shrink
- range
- vertex
- Even function
- reflection
- Vertex form
- Axis of symmetry
- Odd function
- translation
- Intercept form
Materials And Additional Resources
8.1: Attributes of quadratics functions practice, Attributes of quadratic functions slides
8.3: Finding vertex and axis of symmetry self-checking google sheet practice
8.4: Transformations in vertex form gimkit
8.5: Intercept form extra practice
Unit 9
Solving Quadratic Equations
Grade
9-12
Length Of Unit
20 Days
Unit Description
Description
Essential Questions With Corresponding Big Ideas
How do quadratic equations model real world problems and situations?
Reasoning with Equations and Inequalities
What do quadratic solutions mean in terms of the problem?
Seeing Structure in Expressions
Priority - Missouri Learning Standards
- A1.REI.A.2 Solve problems involving quadratic equations.
- A1.REI.A.2c Analyze different methods of solving quadratic equations.
Supporting - Missouri Learning Standards
- A1.SSE.A.3 Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.
- A1.SSE.A.3a Find the zeros of a quadratic function by rewriting it in factored form.
- A1.SSE.A.3b Find the maximum or minimum value of a quadratic function by completing the square
- A1.REI.A.2a a.Use the method of completing the square to create an equivalent quadratic equation..
- A1.REI.A.2b Derive the quadratic formula
Instructional Objectives And Learning Targets
A1.SSE.A.3a,A1.SSE.A.3b,A1.REI.A.2c,A1.REI.A.2a,A1.REI.A.2b
- I can find zeros of a quadratic function by rewriting it in factored form.
- I can find the maximum and minimum value of a quadratic by completing the square.
- I can solve quadratic equations using different methods.. (e.g., inspection, the square root property, completing the square, using the quadratic formula, factoring)
- I can use the method of completing the square to create an equivalent quadratic equation in the form (x-p)^2 , for the purpose of solving the quadratic equation for a certain value.
- I can understand/explain the relationship between the quadratic formula and the quadratic equation ax^2 + bx + c=0.
Topics
- Lesson 9.1 - Properties of Radicals
- Use properties of radicals to simplify expressions
- Simplify expressions by rationalizing the denominator
- Perform operations with radicals
- Lesson 9.2 - Solving Quadratic Equations by Graphing
- Use graphs to find and approximate the zeros of a function
- Lesson 9.3 - Solving Quadratic Equations using Square Roots
- Solve using square roots
- Approximate the solutions of quadratic equations
- Lesson 9.4 - Solving Quadratic Equations by Completing the Square
- Complete the square for expression of the form x^2+bx
- Solve quadratic equations by completing the square
- Find and use maximum and minimum values
- Lesson 9.5 - Solve Quadratic Equations using the Quadratic Formula
- Solve quadratics using the quadratic formula
- Interpret the discriminant
- Choose efficient methods for solving quadratic equations
- Lesson 9.6 - Solving Nonlinear Systems of Equations
- Solve systems of nonlinear equations by graphing
- Solve systems of nonlinear equations algebraically
- Approximate solutions of nonlinear systems and equations
Teaching Activities
- Lesson 9.3 - Solving Quadratic Equations using Square Roots
- Lesson 9.4 - Solving Quadratic Equations by Completing the Square
- Lesson 9.5 - Solve Quadratic Equations using the Quadratic Formula
- Lesson 9.6 - Solving Nonlinear Systems of Equations
- Solve systems of nonlinear equations by graphing
- Solve systems of nonlinear equations algebraically
- Approximate solutions of nonlinear systems and equations
Differentiation
Big Ideas Reteach / Extra Practice pages as needed
Additional practice assignments linked under “Materials and Additional Resources”
Assessments With Missouri Learning Standards
9.1-9.3 Quiz (Formative)
A1.SSE.A.3 A1.SSE.A.3a A1.REI.A.2
Ch 9 Test (Summative)
A1.SSE.A.3 A1.SSE.A.3a A1.REI.A.2 A1.REI.A.2a A1.REI.A.2b A1.SSE.A.3b A1.REI.A.2c
Academic Vocabulary
Tier 1
Tier 2
Tier 3
- counterexample
- Simplest form of a radical
- conjugates
- radicand
- Radical expression
- Rationalizing the denominator
- Like radicals
- Perfect cube
- Quadratic equation
- root
Materials And Additional Resources
9.4: Completing the Square Puzzle, Solve by completing the square task cards Completing the square pixel art
9.5: Quadratic Formula Tic Tac Toe