Unit 1 Title: Expressions, Order of Operations, and Scientific Notation
Major: A.SSE.1, 8.EE.4
In this unit, students will understand how to represent quantities, patterns, and relationships using the language of algebra. Students will understand how mathematical expressions can represent real-world relationships using symbols and operations. Understand how the properties are used to simplify expressions and perform operations with numbers expressed in scientific notation.
Unit 2 Title: Expressions and Equations
Major: A.SSE.1, N.Q.1, 3, A.CED.1-4, A.REI.1
In this unit, students will understand that quantities are used to form expressions, equations, and inequalities that represent real-world situations. Students analyze and explain the process of solving an equation. Students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems.
Unit 3 Title: Functions and their Graphs Part I
Major: A.REI.10, F.BF.1-2, and F.IF.1-7a (linear only), F.IF.9, F.LE.1-3, 5, G.GPE.5 Supporting:F.BF.3
In this unit, students will understand that functions describe situations where one quantity determines another. Students will learn function notation and develop the concepts of domain and range. They explore many examples of linear functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations.
Unit 4 Title: Descriptive Statistics
Major: S.ID.1-3, 5-6 Supporting: 8.SP.4, S.ID.7-9
In this unit, students will build upon students’ prior experiences with data, providing students with more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear 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. Students will also understand that there are various representations to organize, model and analyze data to best fit real world situations based upon its characteristics.
Unit 5 Title: Systems of Linear Equations and Inequalities
Major: A.CED.3, A.REI.11-12 Supporting: A.REI.5-6
In this unit students explore systems of equations and inequalities, and find and interpret their solutions. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution.) Students will understand that systems of equations and inequalities can be used to model, analyze and solve real world situations.
Unit 6 Title: Polynomials
Major: 8.EE.1, A.CED.1-2, 4, A.REI.4, N.RN.2, and A.SSE.2 Supporting: A.APR.1
In this unit, students will understand that manipulation of polynomials will enable them to model and analyze real-world non-linear situations. They will extend 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/equations.
Unit 7 Title: Functions and Their Graphs Part II
Major: F.BF.1-2, F.IF.4-5, F.IF.7a, F.IF.8a-b, F.IF.9, F.LE.3, A.SSE.3a
Supporting: F.BF.3
In this unit, students 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 expand their experience with functions to include more specialized functions such as absolute value.
Unit 8 Title: Connecting Algebra & Geometry
Pythagorean Theorem, Distance & Midpoint Formulas Major: 8.EE.2, 8.G.6-8, G.GPE.4, G.GPE.6-7
Supporting: 8.NS.1-2, G.GPE.5
In the first part of this unit, students will understand that the Pythagorean Theorem connects square roots, coordinates, slope, distance, area, and distances in a plane. They will also explain geometric formulas and use them to solve problems.
Transformations, Similar Figures, Angles and Geometric Formulas (Use 8th Grade Geometry Unit) Major: 8.G.1-4
Supporting: 8.G.9, G.CO.1, G.GMD.1-2
In the second part of this unit, students will experiment transformations in the coordinate plane. They will solve mathematical problems two and three dimensional figures involving area, volume and surface area. Students will also explain geometric formulas and use them to solve problems.
Major: A.SSE.1, 8.EE.4
In this unit, students will understand how to represent quantities, patterns, and relationships using the language of algebra. Students will understand how mathematical expressions can represent real-world relationships using symbols and operations. Understand how the properties are used to simplify expressions and perform operations with numbers expressed in scientific notation.
Unit 2 Title: Expressions and Equations
Major: A.SSE.1, N.Q.1, 3, A.CED.1-4, A.REI.1
In this unit, students will understand that quantities are used to form expressions, equations, and inequalities that represent real-world situations. Students analyze and explain the process of solving an equation. Students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems.
Unit 3 Title: Functions and their Graphs Part I
Major: A.REI.10, F.BF.1-2, and F.IF.1-7a (linear only), F.IF.9, F.LE.1-3, 5, G.GPE.5 Supporting:F.BF.3
In this unit, students will understand that functions describe situations where one quantity determines another. Students will learn function notation and develop the concepts of domain and range. They explore many examples of linear functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations.
Unit 4 Title: Descriptive Statistics
Major: S.ID.1-3, 5-6 Supporting: 8.SP.4, S.ID.7-9
In this unit, students will build upon students’ prior experiences with data, providing students with more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear 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. Students will also understand that there are various representations to organize, model and analyze data to best fit real world situations based upon its characteristics.
Unit 5 Title: Systems of Linear Equations and Inequalities
Major: A.CED.3, A.REI.11-12 Supporting: A.REI.5-6
In this unit students explore systems of equations and inequalities, and find and interpret their solutions. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution.) Students will understand that systems of equations and inequalities can be used to model, analyze and solve real world situations.
Unit 6 Title: Polynomials
Major: 8.EE.1, A.CED.1-2, 4, A.REI.4, N.RN.2, and A.SSE.2 Supporting: A.APR.1
In this unit, students will understand that manipulation of polynomials will enable them to model and analyze real-world non-linear situations. They will extend 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/equations.
Unit 7 Title: Functions and Their Graphs Part II
Major: F.BF.1-2, F.IF.4-5, F.IF.7a, F.IF.8a-b, F.IF.9, F.LE.3, A.SSE.3a
Supporting: F.BF.3
In this unit, students 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 expand their experience with functions to include more specialized functions such as absolute value.
Unit 8 Title: Connecting Algebra & Geometry
Pythagorean Theorem, Distance & Midpoint Formulas Major: 8.EE.2, 8.G.6-8, G.GPE.4, G.GPE.6-7
Supporting: 8.NS.1-2, G.GPE.5
In the first part of this unit, students will understand that the Pythagorean Theorem connects square roots, coordinates, slope, distance, area, and distances in a plane. They will also explain geometric formulas and use them to solve problems.
Transformations, Similar Figures, Angles and Geometric Formulas (Use 8th Grade Geometry Unit) Major: 8.G.1-4
Supporting: 8.G.9, G.CO.1, G.GMD.1-2
In the second part of this unit, students will experiment transformations in the coordinate plane. They will solve mathematical problems two and three dimensional figures involving area, volume and surface area. Students will also explain geometric formulas and use them to solve problems.