Grade 8 Honors Math

PA Core Mathematics Standards

• CC.2.1.8.E.1 Distinguish between rational and irrational numbers using their properties.
• CC.2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers.
• CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents.
• CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs and data displays.
• CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real world or mathematical problems.
• CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context.
• CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multi-step problems.
• CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
• CC.2.2.8.B.3 Analyze and solve linear equations and pairs of simultaneous linear equations.
• CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships.
• CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable.
• CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method.
• CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

• The distinction between rational numbers and irrational numbers.
• Operations with rational numbers.
• Properties of integer exponents.
• Square roots of small perfect squares and cube roots of small perfect cubes.
• Decimal rounding using place value.
• Simplification of numerical expressions using arithmetic properties.
• The additive inverse property.
• The multiplicative inverse property.
• The steps for solving a basic linear equation in one variable.
• The process for verifying that a solution to a basic linear equation is correct.

• Developing a deep understanding of the real number system, including its structure and properties, alongside mastering rational exponents and expressions, forms the foundation for effective mathematical reasoning.
• By writing, interpreting, and manipulating linear equations and inequalities, students learn to model and solve real-world situations.

• Review the structure of the real number system, including a Venn diagram of sets within the real number system and closure properties of rational numbers under addition and multiplication.
• Understand rational exponents and simplify expressions involving radicals and rational exponents.
• Explain the difference between precision and accuracy, and select an appropriate level of precision when reporting quantities.
• Write, interpret, and simplify linear expressions in one variable, and use linear expressions to model real-world situations.
• Solve linear equations with grouping symbols or with the variable on both sides, and use linear equations to model and solve real-world problems.
• Rewrite formulas to express a variable of interest in terms of the other variables, and solve literal equations to obtain a general solution for a class of equations.
• Write and solve linear inequalities in one variable, represent solutions of linear inequalities on a number line, and use linear inequalities to model and solve real-world problems.
• Write and solve compound linear inequalities in one variable using both and and or, represent solutions of compound inequalities on a number line, and use compound inequalities to model and solve real-world problems.

• How do the properties of the real number system, including closure properties and the relationships between different sets, influence our ability to perform mathematical operations and solve real-world problems?
• In what ways do rational exponents and linear expressions provide tools for simplifying complex mathematical concepts, and how can these tools be applied to model and solve practical situations?
• Why is it important to understand the concepts of precision and accuracy in mathematics, and how do they impact our ability to effectively communicate solutions and represent real-world scenarios using equations and inequalities?
   

• L1.1 How do closure properties of the real number system affect our ability to perform operations with real numbers effectively?
• L1.2 How do simplifying expressions involving radicals and rational exponents enhance our problem-solving skills in mathematics?
• L1.3 How does understanding the difference between accuracy and precision impact our ability to report quantities effectively in mathematical and real-world contexts?
• L2.1 How do we write and interpret algebraic expressions, and how does applying the distributive property help us simplify these expressions for better understanding and problem-solving?
• L2.2 How do the properties of equality and the distributive property enable us to solve equations with variables on both sides, and why is this skill important in algebra?
• L2.3 How do we solve both simple and complex literal equations for a given variable, and why is mastering this skill essential for understanding relationships between variables in mathematical contexts?
• L2.4 How can we write inequalities to model real-world problems, and in what ways do the properties of inequalities help us solve these challenges effectively?
• L2.5 How do we write, solve, and graph compound inequalities, and how can these inequalities be used to effectively model and analyze real-world situations?
   

• Into Algebra Modules 1-2
• Student textbook
• iXL
• Student workbook
   

• Equation
• Like terms
• Index
• Rational number
• Precision
• Equivalent equations
• Solution of an equation
• Irrational number
• Real number
• Significant digits
• Expression
• Compound inequality
• Radical expression
• Accuracy
• Inequality
• Literal equation
• Radicand
• Closure

• Module Test
• Unit Test
• iXL Quiz
   

PA Core Mathematics Standards

• CC.2.2.HS.C.3  Write functions or sequences that model relationships between two quantities.
• CC.2.2.HS.D.7  Create and graph equations or inequalities to describe numbers or relationships.
• CC.2.2.HS.D.8  Apply inverse operations to solve equations or formulas for a given variable.
• CC.2.2.HS.D.10  Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
• CC.2.2.8.C.1  Define, evaluate, and compare functions.
• CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context.
• CC.2.2.8.C.2  Use concepts of functions to model relationships between quantities.
• CC.2.2.HS.C.6  Interpret functions in terms of the situation they model.
• CC.2.2.HS.C.5  Construct and compare linear, quadratic and exponential models to solve problems.
• CC.2.2.HS.C.2  Graph and analyze functions and use their properties to make connections between the different representations.
• CC.2.2.HS.C.4  Interpret the effects transformations have on functions and find the inverses of functions.
• CC.2.2.8.B.2  Understand the connections between proportional relationships, lines, and linear equations.

• The development of algebraic expressions and the application of simplification strategies.
• The construction of equations to represent mathematical relationships and the application of strategies to solve them.
• The use of coordinate planes to graph solutions of linear equations and analyze their characteristics.
• The interpretation of the linear function y = mx + b as a representation of a straight line where m is the slope and b is the y-intercept. 
• Conceptual understanding of functions as input-output relationships with exactly one output for each input.
• Application of linear functions to real-world modeling.
• Determination of slope from representations such as tables, graphs, or equations.
• Interpretation of slope in real-world contexts.
• Analysis of relationships among graphical, algebraic, and verbal representations of functions.
• Development of linear models to represent mathematical and real-world relationships.
• Representation and analysis of linear functions through graphing and input-output evaluation.
• Identification of functions and corresponding input-output relationships.
• Evaluation of functions within defined domains.
• Application and interpretation of function notation.

• Linear functions model real-life situations like budgeting, speed, or trends over time. Learning how to read, write, and interpret these functions helps students understand patterns and solve everyday problems.
• Working with equations, graphs, and data helps students think logically and critically. These skills go beyond math—they're essential for science, technology, economics, and decision-making in life.
• Mastering linear functions lays the foundation for more complex math, including quadratic and exponential functions, systems of equations, and calculus. It's a key step in progressing through middle and high school math.
• Understanding multiple representations—graphical, algebraic, verbal—helps students become flexible thinkers and effective communicators, a skill that supports collaboration and success across disciplines.

• Connect linear equations in standard form to their graphs. 
• Identify intercepts for linear equations. 
• Model with linear equations. 
• Calculate and interpret slope. 
• Use slope to graph lines.  
• Determine if a relation is a function. 
• Write functions using function notation. 
• Write linear functions in slope-intercept form and point-slope form. 
• Recognize transformations as changes to the domain and range values. 
• Draw connections among transformations in graphs, equations, and verbal descriptions. 
• Apply transformations to functions and graphs from their verbal descriptions. 
• Create a new function from an existing one by adding a constant function to it. 
• Compare linear functions in different forms. 

• How can we represent real-world situations using linear equations and functions, and what do those representations tell us?
• What do different representations of a function—graphical, algebraic, numerical, and verbal—reveal about its behavior and meaning?
• How do changes in an equation affect the graph of a function, and how can we use transformations to build or analyze functions?
• What makes a relationship a function, and how do we use function notation to communicate and manipulate these relationships?
   

• L3.1 How can we connect solutions of equations to points on their graphs?
• L3.2 How do we describe and interpret the slope of a line?
• L4.1 How are functions and relations related?
• L4.2 How can we describe the graphs of linear functions?
• L4.3 What are the characteristics of linear functions?
• L4.4 How can we use linear functions to model real-world scenarios?
• L5.1 How do we determine how transformations to functions affect their graphs?
• L5.2 How can we relate all linear functions to the linear parent function f(x) = x?
• L5.3 How can we compare functions given in different forms?
   

• Into Algebra Modules 3-5
• Student textbook
• iXL
• Student workbook
• Desmos
   

• Linear Equations 
• Rate of Change
• Discrete Function
• Linear Function
• Transformation
• Standard Form 
• Slope
• Domain
• Range
• Function Family
• X-intercept
• Continuous Function 
• End Behavior
• Relation
• Parent Function
• Y-intercept
• Dependent Variable
• Function
• Zero
• Inverse Function

• Module Test
• Unit Test
• iXL Quiz

PA Core Mathematics Standards

• CC.2.2.7.B.3  Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
• CC.2.2.HS.C.6  Interpret functions in terms of the situation they model.
• CC.2.4.8.B.1  Analyze and/or interpret bivariate data displayed in multiple representations.
• CC.2.4.HS.B.3  Analyze linear models to make interpretations based on the data.
• CC.2.4.HS.B.5  Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.
• CC.2.2.HS.C.3  Write functions or sequences that model relationships between two quantities.
• CC.2.2.HS.D.7  Create and graph equations or inequalities to describe numbers or relationships.
• CC.2.2.HS.D.10  Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

• Construction of scatter plots using bivariate data and identification of associations between variables.
• Estimation of lines of best fit for scatter plot data and assessment of how well the line represents the data trend.
• Application of linear models to bivariate data and interpretation of slope and y-intercept to solve contextual problems.
• Generation of numerical patterns based on given rules.
• Identification of mathematical rules from observed number sequences.
• Application and interpretation of function notation.
• Construction of linear function models to represent real-life relationships.
• Representation of linear functions on the coordinate plane.
• Understanding of functions as a subset of relations characterized by one-to-one domain-to-range pairings.
• Development, representation, and application of linear functions to solve real-world problems.

• Recognizing and describing consistent patterns (like arithmetic sequences), evaluating data (through correlation and regression), and using those tools are needed to make predictions, solve problems, and communicate reasoning in real-world contexts.
• Whether analyzing trends with lines of best fit or solving absolute value equations, students learn to critically assess models, consider their accuracy (e.g., residuals, causation vs. correlation), and apply them meaningfully through graphing, evaluating, and interpreting various forms of functions.

• Estimate correlation coefficients.
• Use two points to write a line of best fit. 
• Consider whether there is a causation for the correlation of a data set.  
• Solve problems using a line of best fit by interpolation and extrapolation.  
• Assess the fit of a function using residuals.  
• Find the “nth” term in an arithmetic sequence using a recursive rule. 
• Model a real-world situation using an arithmetic sequence. 
• Write an arithmetic sequence using an explicit or recursive formula.
• Identify the domain and range of a sequence and determine whether the sequence is infinite or finite. 
• Convert between recursive and explicit forms for arithmetic sequences. 
• Evaluate piecewise-defined functions.
• Graph absolute value functions.
• Use absolute value functions to solve real-world problems.
• Solve absolute value equations and inequalities graphically and algebraically.

• How can we use functions and equations to model, represent, and solve real-world problems?
• What can patterns and data tell us about relationships between variables—and how can we use that information to make predictions?
• How do we determine if a mathematical model is a good fit for a situation, and how do we refine it when it's not?
   

• L6.1 How can we create a line fitted to data that shows a linear correlation and use it to make predictions?
• L6.2 How can we use the linear regression function on a graphing calculator to find the line of best fit for a bivariate data set?
• L7.1 How can we use arithmetic sequences defined recursively to solve real-world problems?
• L7.2 How can we use arithmetic sequences defined explicitly to solve real-world problems?
• L8.1 How can we write, graph, and use piecewise-defined functions to solve real-world problems?
• L8.2 How can we evaluate and graph absolute value functions?
• L8.3 How can we solve absolute value equations and inequalities both graphically and algebraically?

• Into Algebra Modules 6-8
• Student textbook
• iXL
• Student workbook
• Desmos
   

• Bivariate Data
• Interpolation
• Residual Plot
• Piecewise-Function
• Correlation
• Arithmetic Sequence
• Step Function
• Tolerance
• Correlation Coefficient
• Linear Regression
• Recursive Rule 
• Axis of Symmetry
• Extrapolation
• Residual
• Vertex

• Module Test
• Unit Test
• iXL Quiz
   

PA Core Mathematics Standards

• CC.2.2.7.B.3  Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
• CC.2.2.HS.D.9  Use reasoning to solve equations and justify the solution method.
• CC.2.2.8.B.3  Analyze and solve linear equations and pairs of simultaneous linear equations.
• CC.2.2.HS.D.10  Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
• CC.2.2.HS.D.7  Create and graph equations or inequalities to describe numbers or relationships.

• Development and solution of linear equations in two variables for modeling and solving real-world problems.
• Graphical representation of linear equations for real-world modeling and problem-solving.
• Graphical analysis of systems of equations to determine exact or approximate solutions.
• Development, solution, and graphical representation of linear inequalities in one variable.
• Modeling of real-world situations using linear inequalities in one variable.
• Development, solution, and graphing of systems of linear equations.
• Application of systems of equations to represent and solve contextual problems.

• Algebraic expressions, equations, and inequalities can model constraints, relationships, and solutions to problems in real life. Whether it's budgeting, comparing plans, or analyzing scenarios, these tools help students make informed decisions.
• Graphing linear equations and systems, helps students to visualize relationships and interpret intersection points, regions, and boundaries. This helps them analyze multiple constraints and identify solutions that make sense in context.

• Solve systems of linear equations graphically, using the substitution method, using the elimination method, and by multiplying.
• Use systems of linear equations to represent and solve real-world problems.
• Identify when a system of linear equations has one solution, no solution, or infinitely many solutions.
• Write, solve, and graph linear inequalities in two variables.
• Write and graph a linear inequality to model and solve a real-world problem.
• Write, graph, and solve systems of linear inequalities.
• Model real-world problems with systems of linear inequalities.

• How can systems of linear equations be used to model and solve real-world problems?
• What are the different methods for solving systems of equations, and how do we determine the most efficient method to use?
• What does the solution to a system of equations or inequalities represent, and how can we interpret it graphically and algebraically?
• How do linear inequalities model constraints in real-life situations, and how can their solutions be represented and interpreted on a graph?
   

• L9.1 How can I write linear systems to model real-world problems and solve them by graphing?
• L9.2 How can I write systems of linear equations to model real-world situations and solve them by substitution?
• L9.3 How can I write linear systems to model real-world situations and solve the systems by adding or subtracting?
• L9.4 How can I write linear systems to model real-world problems and solve them by multiplying first?
• L10.1 How can I write and graph linear inequalities in two variables to model and solve real-world problems?
• L10.2 How can I write and graph systems of linear inequalities to model and solve real-world problems?
   

• Into Algebra Modules 9-10
• Student textbook
• iXL
• Student workbook
• Desmos
   

• Consistent System
• Solution to a System
• Boundary Line
• Dependent System
• System of Equations
• Half-Plane
• Inconsistent System
• Substitution
• Linear Inequality 
• Independent System
• Elimination

• Module Test
• Unit Test
• iXL Quiz
   

PA Core Mathematics Standards

• CC.2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions.
• CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.
• CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials.
• CC.2.2.HS.D.5 Use polynomial identities to solve problems.
• CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms.

• Application of the Distributive Property to simplify and manipulate algebraic expressions.
• Use of properties of exponents in the simplification and evaluation of expressions.
• Development and simplification of algebraic expressions.
• Development of linear equations and application of methods to find solutions.
• Application of monomial multiplication to solve real-world problems.
• Identification and understanding of polynomial structure, including binomials, trinomials, degree, and leading coefficient.
• Application of algebraic methods to multiply polynomials.
• Calculation of area using polynomial expressions to represent dimensions.
   

• Understanding monomials, binomials, and trinomials helps students recognize and describe patterns in numbers and shapes, laying a foundation for more advanced math and real-world problem solving.
• Using polynomial multiplication to find area and volume connects algebraic expressions to spatial reasoning, helping students see how math describes the physical world.
• Recognizing special products and patterns promotes strategic thinking and efficiency, encouraging students to spot shortcuts and underlying structures in math.
• Using polynomials to represent numbers and scenarios helps students make sense of and solve practical problems, linking abstract math to everyday life and careers.

• Recognize characteristics of monomials.
• Multiply monomials by other monomials.
• Recognize characteristics of polynomial expressions, including monomials, binomials, and trinomials.
• Multiply polynomial expressions.
• Model area and volume with polynomial multiplication.
• Solve problems using patterns in special products of binomials.
• Distinguish between like and unlike terms.
• Apply the Distributive Property to subtract polynomials.
• Add and subtract polynomials.
• Use polynomials to represent numbers. 
• Model real-world situations with polynomials.

• How can understanding the structure of polynomials help us simplify expressions and solve problems?
• What role do the properties of exponents and the Distributive Property play in simplifying and multiplying polynomial expressions?
• How can polynomial expressions be used to model and solve real-world problems, such as calculating area?
• Why is it important to recognize patterns and relationships when working with algebraic expressions and polynomial operations?

• L15.1 How can I multiply monomials and raise monomials to powers to solve real-world problems?
• L15.2 How can I write monomials, binomials, and trinomials in standard form and multiply them?
• L15.3 How can I find special products of binomials?
• L16.1 How can I add and subtract polynomials?
• L16.2 How can I model mathematical and real-world problems with polynomials?
   

• Into Algebra Modules 15-16
• Student textbook
• iXL
• Student workbook
   

• Degree of a Monomial
• Leading Coefficient
• Perfect Square
• Monomial
• Polynomial
• Figurate Numbers
• Binomial
• Standard Form
• Degree of Polynomials
• Trinomial

• Module Test
• Unit Test
• iXL Quiz
   

PA Core Mathematics Standards

• CC.2.1.6.E.3 Develop and/or apply number theory concepts to find common factors and multiples.
• CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems.
• CC.2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions.
• CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems
• CC.2.2.HS.D.5 Use polynomial identities to solve problems.
• CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms.

• Graphical representation of linear equations.
• Development of linear equations and application of algebraic methods to determine solutions.
• Application of equation-solving strategies to determine solutions of linear equations.
• Use of graphs to identify the roots of quadratic equations.
• Application of factoring techniques to solve quadratic equations.

• Learning to graph and analyze quadratics helps students understand phenomena like projectile motion, area optimization, and patterns of growth or decay.
• Factoring reveals the zeros of a function, helping students interpret where the graph crosses the x-axis and understand solution sets in real terms.
• Creating and solving quadratic equations from word problems trains students to translate real-life situations into math, analyze outcomes, and make informed decisions.
• These methods enhance algebraic fluency and demonstrate structured approaches to solving complex problems, building confidence for future math courses.
• Developing judgment about when to use factoring versus the Quadratic Formula nurtures strategic thinking and adaptability in problem solving.

• Graph quadratic equations and identify characteristics of the graphs.
• Solve quadratic equations graphically, by factoring, and by using the Zero Product Property.
• Factor a quadratic expression to reveal the zeros of the function it defines.
• Create quadratic equations in one variable and use them to solve problems.
• Solve quadratic equations by using square roots.
• Solve equations by completing the square.
• Solve quadratic equations using the Quadratic Formula.
• Choose an appropriate method to solve a quadratic equation.

• How do the key features of a quadratic function, such as vertex, axis of symmetry, and intercepts, relate to its graph?
• What strategies and methods can be used to solve quadratic equations, and how do you determine which method is most appropriate in different situations?
• In what ways can understanding the process of factoring help in solving quadratic equations and analyzing their solutions?
• How can quadratic equations be applied to real-world problems, and how does solving them algebraically and graphically provide different insights into the solutions?
   

• L17.1 How can I understand the key features of the graph of a quadratic function and solve quadratic equations approximately by graphing?
• L17.2 How can I use the Zero Product Property to solve quadratic equations in standard form with a leading coefficient of 1?
• L17.3 How can I use the Zero Product Property to solve quadratic equations in standard form when the leading coefficient is not 1?
• L17.4 How can I use special factoring patterns to solve quadratic equations?
• L18.1 How can I  solve quadratic equations of the form ax2 = c by using square roots and determine whether there are one, two, or no real solutions?
• L18.2  How can I  solve quadratic equations of the form ax2 + bx + c = 0 by completing the square?
• L18.3 How can I use the method of completing the square to derive the Quadratic Formula and solve equations by using the Quadratic Formula?
• L18.4 How can I solve quadratic equations using a variety of methods and choose an appropriate method based on the initial form of the equation?
   

• Into Algebra Modules 17-18
• Student textbook
• iXL
• Student workbook
• Desmos
• Graph Paper
   

• Parabola
• Standard Form
• Quadratic function
• Completing the Square
• Vertex of a Parabola
• Discriminant 
• Zero
• Quadratic Formula

• Module Test
• Unit Test
• iXL Quiz

PA Core Mathematics Standards

• CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents.
• CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
• CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems
• CC.2.2.HS.D.5 Use polynomial identities to solve problems.
• CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms.

• Expression of quadratic equations in standard form.
• Identification of the value needed to complete the square in a quadratic expression.
• Determination of x-intercepts or solutions where the function equals zero.
• Analysis of the number of real solutions to a quadratic equation.
• Use of quadratic function graphs to identify equation solutions.
• Application of completing-the-square technique to solve quadratic equations.
   

• By graphing and transforming quadratic functions, students see how equations describe patterns of change, helping them predict and analyze real-world phenomena.
• Being fluent in interpreting and moving between forms allows students to analyze problems from multiple perspectives, improving problem-solving and reasoning.
• Whether by hand or using regression, matching curves to data teaches students how math models complex situations, supporting critical thinking and data literacy.
• Understanding transformations encourages insight into how changes in equations affect graphs which empowers students to predict outcomes, optimize solutions, and deepen conceptual understanding beyond simple calculation.

• Graph a quadratic function using transformations.
• Identify the vertex, maximum, minimum, reflection, and stretch for a parabola from the graph or from the equation.
• Convert between standard, vertex, and intercept forms.
• Compare quadratic functions represented in different ways.
• Compute second differences to determine if data is quadratic.
• Fit quadratic curves to data by hand and using regression.

• How can transformations be used to graph and analyze the key features of a quadratic function?
• How do the different forms of a quadratic equation—standard, vertex, and intercept—reveal unique information about the function’s graph and behavior?
• How can you determine whether a data set represents a quadratic relationship, and how can you model that relationship using equations and graphs?
   

• L19.1 How can I write and graph quadratic functions in vertex form?
• L19.2 How can I graph quadratic functions in standard form and convert between standard and vertex forms of quadratic functions?
• L19.3 How can I write and graph quadratic functions in intercept form?
• L19.4  How can I compare quadratic functions represented in different forms?
• L19.5 How can I fit quadratic functions to data by hand and by quadratic regression?

• Into Algebra Module 19
• Student textbook
• IXL 
• Student workbook
• Desmos

• Vertex Form
• Quadratic Regression
• Intercept Form
• Second Differences
• Coefficient of Determination
• First Difference

• Module Test
• Unit Test
• iXL Quiz

PA Core Mathematics Standards

• CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
• CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability models.
• CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model.
• CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable.
• CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables.
• CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data.
• CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments.
• CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.

• Construction and interpretation of frequency tables and two-way relative frequency tables.
• Calculation and interpretation of measures of center and variability, including mean, median, and range.
• Development and analysis of two-way and relative frequency tables to summarize categorical data.

• Summarizing and interpreting data using two-way tables, relative frequencies, and graphs enables students to extract meaningful patterns from real-world situations.
• Recognizing possible associations between categorical variables encourages students to question, analyze, and interpret connections beyond surface-level observations.
• Creating and interpreting graphs supports clearer communication of data insights and guides the selection of appropriate summary statistics.
• Recognizing quadratic patterns through second differences or fitting curves to data links data analysis to algebra, showing how math models inform real-world understanding.
• The ability to critically analyze data supports lifelong skills in interpreting information, making decisions, and solving problems across diverse fields.

• Summarize categorical data for two categories in two-way frequency tables.
• Interpret relative frequencies in context.
• Recognize possible associations between categorical variables.  
• Understand and analyze measures of center and spread.
• Understand and identify outliers. 
• Create dot plots and histograms to classify distribution shapes and choose appropriate measures of center and spread. 
• Compare data sets using statistics.  
• Apply rules of probability to compute probabilities of compound events.

• How can we effectively summarize categorical data using two-way frequency tables, and what insights can we gain from these summaries?
• In what ways do relative frequencies help us interpret data contextually, and how do they contribute to our understanding of data patterns?
• What methods can we employ to identify associations between categorical variables, and how do these associations impact our analysis of data sets?
• Why is it important to use measures of center and spread when analyzing data, and how do outliers influence these measures?
   

• L21.1 How can I read, create, and interpret two-way frequency tables and relative frequency tables?
• L21.2 How can I calculate conditional relative frequencies and use them to identify possible associations between categorical variables?
• L22.1 How can I identify distribution shapes and outliers and use them to choose appropriate measures of center and spread?
• L22.2 How can I compare data distributions using box plots and histograms?
   

• Into Algebra Modules 21-22
• Student textbook
• iXL
• Student workbook
• TI-30 Multiview Calculator
   

• Categorical Data
• Marginal Relative
• Dot Plot
• Statistic
• Quantitative Data
• Relative Frequency
• Interquartile Range
• Box Plot
• Frequency
• Two-Way Table
• Outlier
• Histogram
• Joint-Relative
• Conditional Frequency
• Standard Deviation

• Module Test
• Unit Test
• iXL Quiz