8th Algebra I - standards per pg. 82+ federal HS - a appendix
FROM PG. 102
The fundamental purpose of 8th Grade Algebra I is to formalize and extend the mathematics that students learned through the end of seventh grade. The critical areas, called units, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. In addition, the units will introduce methods for analyzing and using quadratic functions, including manipulating expressions for them, and solving quadratic equations. Students understand and apply the Pythagorean theorem, and use quadratic functions to model and solve problems. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
This course differs from High School Algebra I in that it contains content from 8th grade. While coherence is retained, in that it logically builds from the Accelerated 7th Grade, the additional content when compared to the high school course demands a faster pace for instruction and learning.
Critical Area 1: Work with quantities and rates, including simple linear expressions and equations forms the foundation for this unit. Students use units to represent problems algebraically and graphically, and to guide the solution of problems. Student experience with quantity provides a foundation for the study of expressions, equations, and functions. This unit builds on earlier experiences with equations by asking students to analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations.
Critical Area 2: Building on earlier work with linear relationships, students learn function notation and language for describing characteristics of functions, including the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that depending upon the context, these representations
are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students explore systems of equations and inequalities, and they find and interpret their solutions. Students build on and informally extend their understanding of integral exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.
Critical Area 3: Students use regression techniques to describe relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.
Critical Area 4: In this unit, students build on their knowledge from unit 2, where they extended the laws of exponents to rational exponents. Students apply this new understanding of number and strengthen their ability to see structure in and create quadratic and exponential expressions. They create and solve equations, inequalities, and systems of equations involving quadratic expressions.
Critical Area 5: In preparation for work with quadratic relationships students explore distinctions between rational and irrational numbers. They consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students learn that when quadratic equations do not have real solutions the number system must be extended so that solutions exist, analogous to the way in which extending the whole numbers to the negative numbers allows x+1 = 0 to have a solution. Formal work with complex numbers comes in Algebra II. Students expand their experience with functions to include more specialized functions—absolute value, step, and those that are piecewise-defined.
FROM PG. 103
Unit 1 Relationships Between Quantities and Reasoning with Equations
• Reason quantitatively and use units to solve problems.
• Interpret the structure of expressions. • Create equations that describe numbers or relationships.
• Understand solving equations as a process of reasoning and explain the reasoning.
• Solve equations and inequalities in one variable.
Unit 2 Linear and Exponential Relationships
• Extend the properties of exponents to rational exponents.
• Analyze and solve linear equations and pairs of simultaneous linear equations.
• Solve systems of equations. • Represent and solve equations and inequalities graphically
• Define, evaluate, and compare functions.
• Understand the concept of a function and use function notation.
• Use functions to model relationships between quantities.
• Interpret functions that arise in applications in terms of a context.
• Analyze functions using different representations. • Build a function that models a relationship between two quantities.
• Build new functions from existing functions.
• Construct and compare linear, quadratic, and exponential models and solve problems.
• Interpret expressions for functions in terms of the situation they model.
Unit 3 Descriptive Statistics
• Summarize, represent, and interpret data on a single count or measurement variable.
• Investigate patterns of association in bivariate data.
• Summarize, represent, and interpret data on two categorical and quantitative variables.
• Interpret linear models.
Unit 4 Expressions and Equations
• Interpret the structure of expressions. • Write expressions in equivalent forms to solve problems.
• Perform arithmetic operations on polynomials.
• Create equations that describe numbers or relationships.
• Solve equations and inequalities in one variable. • Solve systems of equations.
Unit 5 Quadratics Funtions and Modeling
• Use properties of rational and irrational numbers.
• Understand and apply the Pythagorean theorem.
• Interpret functions that arise in applications in terms of a context.
• Analyze functions using different representations. • Build a function that models a relationship between two quantities.
• Build new functions from existing functions.
• Construct and compare linear, quadratic and exponential models and solve problems.
Mathematical Practice Standards
ACTUAL STANDARDS... PER PAGE 82+
Extend the properties of exponents to rational exponents.
N.RN.1, 2
• Use properties of rational and irrational numbers.
N.RN.3.
• Reason quantitatively and use units to solve problems.
Foundation for work with expressions, equations and functions
N.Q.1, 2, 3
Domain - A-SSE: Seeing Structure in Expressions
Cluster - Interpret the structure of expressions
Standard - A-SSE.1:
Interpret expressions that represent a quantity in terms of its context.*
Standard - A-SSE.2:
Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
Cluster - Write expressions in equivalent forms to solve problems
Standard - A-SSE.3:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Domain - A-APR: Arithmetic with Polynomials and Rational Expressions
Cluster - Perform arithmetic operations on polynomials
Standard - A-APR.1:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Domain - A-CED: Creating Equations*
Cluster - Create equations that describe numbers or relationships
Standard - A-CED.1:
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential unctions.
Standard - A-CED.2:
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Standard - A-CED.3:
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Standard - A-CED.4:
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
Domain - A-REI: Reasoning with Equations and Inequalities A
Cluster - Understand solving equations as a process of reasoning and explain the reasoning
Standard - A-REI.1:
Explain each step in solving a simple 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.
Cluster - Solve equations and inequalities in one variable
Standard - A-REI.3:
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Standard - A-REI.4:
Solve quadratic equations in one variable.
8.EE.8a, 8b, 8c • Analyze and solve linear equations and pairs of simultaneous linear equations.
Cluster - Solve systems of equations
Standard - A-REI.5:
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Standard - A-REI.6:Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Standard - A-REI.7:
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2 + y2 = 3.
Cluster - Represent and solve equations and inequalities graphically
Standard - 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, often forming a curve (which could be a line).
Standard - A-REI.11:
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★
Standard - A-REI.12:
Graph the solutions to a linear inequality in two variables as a halfplane (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.
8.F.1, 2, 3• Define, evaluate, and compare functions.
Conceptual Category - F: Functions
Domain - F-IF: Interpreting Functions
Cluster - Understand the concept of a function and use function notation
Standard - 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).
Standard - 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.
Standard - F-IF.3:
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
8.F.4, 5• Use functions to model relationships between quantities.
AND SO ON INTEGRATING 8TH W/ HS STANDARDS
Cluster - Interpret functions that arise in applications in terms of the context
Standard - F-IF.4:
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★
Standard - F-IF.5:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★
Standard - F-IF.6:
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
Cluster - Analyze functions using different representations
Standard - F-IF.7:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
Standard - F-IF.8:
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Standard - F-IF.9:
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Domain - F-BF: Building Functions
Cluster - Build a function that models a relationship between two quantities
Standard - F-BF.1:
Write a function that describes a relationship between two quantities.*
Standard - F-BF.2:
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
Cluster - Build new functions from existing functions
Standard - F-BF.3:
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Standard - F-BF.4:
Find inverse functions.
Domain - F-LE: Linear, Quadratic, and Exponential Models*
Cluster - Construct and compare linear, quadratic, and exponential models and solve problems
Standard - F-LE.1:
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Standard - F-LE.2:
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Standard - 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.
Cluster - Interpret expressions for functions in terms of the situation they model
Standard - F-LE.5:
Interpret the parameters in a linear or exponential function in terms of a context.
Conceptual Category - S: Statistics and Probability*
Domain - S-ID: Interpreting Categorical and Quantitative Data
Cluster - Summarize, represent, and interpret data on a single count or measurement variable
Standard - S-ID.1:
Represent data with plots on the real number line (dot plots, histograms, and box plots).
Standard - S-ID.2:
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Standard - 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).
Cluster - Summarize, represent, and interpret data on two categorical and quantitative variables
Standard - 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.
Standard - S-ID.6:
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Cluster - Interpret linear models
Standard - S-ID.7:
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Standard - S-ID.8:
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Standard - S-ID.9:
Distinguish between correlation and causation.
**Links to standards will be added when you ask Gordon to ;-)
Pre-Kindergarten
Kindergarten
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th Grade
7th Grade
8th Grade
The fundamental purpose of 8th Grade Algebra I is to formalize and extend the mathematics that students learned through the end of seventh grade. The critical areas, called units, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. In addition, the units will introduce methods for analyzing and using quadratic functions, including manipulating expressions for them, and solving quadratic equations. Students understand and apply the Pythagorean theorem, and use quadratic functions to model and solve problems. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
This course differs from High School Algebra I in that it contains content from 8th grade. While coherence is retained, in that it logically builds from the Accelerated 7th Grade, the additional content when compared to the high school course demands a faster pace for instruction and learning.
Critical Area 1: Work with quantities and rates, including simple linear expressions and equations forms the foundation for this unit. Students use units to represent problems algebraically and graphically, and to guide the solution of problems. Student experience with quantity provides a foundation for the study of expressions, equations, and functions. This unit builds on earlier experiences with equations by asking students to analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations.
Critical Area 2: Building on earlier work with linear relationships, students learn function notation and language for describing characteristics of functions, including the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that depending upon the context, these representations
are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students explore systems of equations and inequalities, and they find and interpret their solutions. Students build on and informally extend their understanding of integral exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.
Critical Area 3: Students use regression techniques to describe relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.
Critical Area 4: In this unit, students build on their knowledge from unit 2, where they extended the laws of exponents to rational exponents. Students apply this new understanding of number and strengthen their ability to see structure in and create quadratic and exponential expressions. They create and solve equations, inequalities, and systems of equations involving quadratic expressions.
Critical Area 5: In preparation for work with quadratic relationships students explore distinctions between rational and irrational numbers. They consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students learn that when quadratic equations do not have real solutions the number system must be extended so that solutions exist, analogous to the way in which extending the whole numbers to the negative numbers allows x+1 = 0 to have a solution. Formal work with complex numbers comes in Algebra II. Students expand their experience with functions to include more specialized functions—absolute value, step, and those that are piecewise-defined.
FROM PG. 103
Unit 1 Relationships Between Quantities and Reasoning with Equations
• Reason quantitatively and use units to solve problems.
• Interpret the structure of expressions. • Create equations that describe numbers or relationships.
• Understand solving equations as a process of reasoning and explain the reasoning.
• Solve equations and inequalities in one variable.
Unit 2 Linear and Exponential Relationships
• Extend the properties of exponents to rational exponents.
• Analyze and solve linear equations and pairs of simultaneous linear equations.
• Solve systems of equations. • Represent and solve equations and inequalities graphically
• Define, evaluate, and compare functions.
• Understand the concept of a function and use function notation.
• Use functions to model relationships between quantities.
• Interpret functions that arise in applications in terms of a context.
• Analyze functions using different representations. • Build a function that models a relationship between two quantities.
• Build new functions from existing functions.
• Construct and compare linear, quadratic, and exponential models and solve problems.
• Interpret expressions for functions in terms of the situation they model.
Unit 3 Descriptive Statistics
• Summarize, represent, and interpret data on a single count or measurement variable.
• Investigate patterns of association in bivariate data.
• Summarize, represent, and interpret data on two categorical and quantitative variables.
• Interpret linear models.
Unit 4 Expressions and Equations
• Interpret the structure of expressions. • Write expressions in equivalent forms to solve problems.
• Perform arithmetic operations on polynomials.
• Create equations that describe numbers or relationships.
• Solve equations and inequalities in one variable. • Solve systems of equations.
Unit 5 Quadratics Funtions and Modeling
• Use properties of rational and irrational numbers.
• Understand and apply the Pythagorean theorem.
• Interpret functions that arise in applications in terms of a context.
• Analyze functions using different representations. • Build a function that models a relationship between two quantities.
• Build new functions from existing functions.
• Construct and compare linear, quadratic and exponential models and solve problems.
Mathematical Practice Standards
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
ACTUAL STANDARDS... PER PAGE 82+
Extend the properties of exponents to rational exponents.
N.RN.1, 2
• Use properties of rational and irrational numbers.
N.RN.3.
• Reason quantitatively and use units to solve problems.
Foundation for work with expressions, equations and functions
N.Q.1, 2, 3
Domain - A-SSE: Seeing Structure in Expressions
Cluster - Interpret the structure of expressions
Standard - A-SSE.1:
Interpret expressions that represent a quantity in terms of its context.*
Standard - A-SSE.2:
Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
Cluster - Write expressions in equivalent forms to solve problems
Standard - A-SSE.3:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Domain - A-APR: Arithmetic with Polynomials and Rational Expressions
Cluster - Perform arithmetic operations on polynomials
Standard - A-APR.1:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Domain - A-CED: Creating Equations*
Cluster - Create equations that describe numbers or relationships
Standard - A-CED.1:
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential unctions.
Standard - A-CED.2:
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Standard - A-CED.3:
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Standard - A-CED.4:
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
Domain - A-REI: Reasoning with Equations and Inequalities A
Cluster - Understand solving equations as a process of reasoning and explain the reasoning
Standard - A-REI.1:
Explain each step in solving a simple 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.
Cluster - Solve equations and inequalities in one variable
Standard - A-REI.3:
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Standard - A-REI.4:
Solve quadratic equations in one variable.
8.EE.8a, 8b, 8c • Analyze and solve linear equations and pairs of simultaneous linear equations.
Cluster - Solve systems of equations
Standard - A-REI.5:
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Standard - A-REI.6:Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Standard - A-REI.7:
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2 + y2 = 3.
Cluster - Represent and solve equations and inequalities graphically
Standard - 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, often forming a curve (which could be a line).
Standard - A-REI.11:
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★
Standard - A-REI.12:
Graph the solutions to a linear inequality in two variables as a halfplane (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.
8.F.1, 2, 3• Define, evaluate, and compare functions.
Conceptual Category - F: Functions
Domain - F-IF: Interpreting Functions
Cluster - Understand the concept of a function and use function notation
Standard - 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).
Standard - 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.
Standard - F-IF.3:
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
8.F.4, 5• Use functions to model relationships between quantities.
AND SO ON INTEGRATING 8TH W/ HS STANDARDS
Cluster - Interpret functions that arise in applications in terms of the context
Standard - F-IF.4:
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★
Standard - F-IF.5:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★
Standard - F-IF.6:
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
Cluster - Analyze functions using different representations
Standard - F-IF.7:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
Standard - F-IF.8:
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Standard - F-IF.9:
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Domain - F-BF: Building Functions
Cluster - Build a function that models a relationship between two quantities
Standard - F-BF.1:
Write a function that describes a relationship between two quantities.*
Standard - F-BF.2:
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
Cluster - Build new functions from existing functions
Standard - F-BF.3:
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Standard - F-BF.4:
Find inverse functions.
Domain - F-LE: Linear, Quadratic, and Exponential Models*
Cluster - Construct and compare linear, quadratic, and exponential models and solve problems
Standard - F-LE.1:
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Standard - F-LE.2:
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Standard - 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.
Cluster - Interpret expressions for functions in terms of the situation they model
Standard - F-LE.5:
Interpret the parameters in a linear or exponential function in terms of a context.
Conceptual Category - S: Statistics and Probability*
Domain - S-ID: Interpreting Categorical and Quantitative Data
Cluster - Summarize, represent, and interpret data on a single count or measurement variable
Standard - S-ID.1:
Represent data with plots on the real number line (dot plots, histograms, and box plots).
Standard - S-ID.2:
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Standard - 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).
Cluster - Summarize, represent, and interpret data on two categorical and quantitative variables
Standard - 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.
Standard - S-ID.6:
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Cluster - Interpret linear models
Standard - S-ID.7:
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Standard - S-ID.8:
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Standard - S-ID.9:
Distinguish between correlation and causation.
**Links to standards will be added when you ask Gordon to ;-)
Pre-Kindergarten
Kindergarten
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th Grade
7th Grade
8th Grade