Glastonbury Public Schools Mathematics Curriculum

Grade 8 Algebra

What are functions and why are they important?

Mathematics is learned through questions that arise while solving well-constructed problems. Our students begin with problems, they use strategies to solve the problems, and they learn the necessary mathematics along the way. Many classroom investigations are designed so that students will collaboratively or individually discover the mathematical properties. The properties are then discussed in class, summarized, and become part of the students’ mathematical knowledge to be applied to future problems.

The discovery of the mathematics is an essential part of the development of each student’s confidence as a mathematician. Knowledge that is gained through inquiry is more likely to be remembered for the long term. Teachers and parents work together to promote this discovery of math through investigation, problem solving, and reasoning. Our goal is for students to understand that mathematics makes sense.

Unit 1: Patterns, Sequences and Functions

Students will analyze sequences, discover patterns, model with functions, and make predictions. The students will model these sequences using explicit rules and recursive processes. Students will learn that arithmetic sequences have a common difference and geometric sequences have a common ratio. Students will understand that in a function, the value of one variable is uniquely determined by the value of another variable. They will discover the similarities and differences of linear, quadratic, exponential, and absolute value functions. Through inquiry and exploration, students will connect arithmetic and geometric sequences to linear and exponential functions.

Common Core State Standards: 8-FA.1, 8-FA.2, 8-FA.3, 8-FB.4, F-IF.1, F-IF.3, F-IF.5, F-BF.1.a, F-BF.2, F-LE.1.a, F-LE.1.b, F-LE.1.c, F-LE.2, A-CED.2

Unit 2: Linear Functions

Students will tackle a variety of problems leading them through the variety of processes available to use algebra to solve problems. The will formally describe the process used to solve equations and inequalities in one variable and two variables using deductive reasoning and properties of equality. Two variable equations will be represented in function notation as well as graphically. Functions will be related to real life situations. Throughout the unit real life situations will be modeled using equations, tables, and graphs.

Common Core State Standards: 8-FB.4, 8-FB.5, 8-SP.A1, 8-SP.A.2, 8-SP.A.3.N-Q.1b, N-Q.1c, N-Q.2, N-Q.3, S.ID.6.a, S-ID.6.c, S.ID.7, S.ID.8, S.ID.9, F-IF.2, F-IF.6, F-IF.7.a, F-IF.9, F-LE.1.a, F-LE.1.b, F-LE.12, F-LE.15, A-SSE.1.a, A-CED.1, A-CED.2, A-CED.4, A-REI.1, A-REI.3, 8-EE.C.8, 8-EE.c8a, 8-EE.Cb, 8-EE.C8c, A-REI.5, A-REI.6 A-REI.10, A-REI.11, A-REI.12, 8-G.B.6, 8-G.B.7, 8-G.B.8

Unit 3: Exponential Functions

Conceptual Lens: End Behavior

The unit on exponential functions builds on the concepts of functions and patterns. This unit is an introductory unit which concentrates on exponential growth and decay. Real world data is used show that some data patterns may be modeled with non-linear functions. Rules of exponents are reviewed, while simple rational exponents are introduced. Instructional activities underscore the role of exponential functions. Students will explore the role of the initial value and growth/decay factor and how they impact the graph. Students will develop an understanding of the parameters of an exponential function. Students will explore the relationship between percentage rate of change and exponential growth or decay. Comparisons will be made between linear and exponential functions, including examples involving interest calculations.

Common Core State Standards: N-RN.1; N-RN.2, N-Q.2; N-Q.3; S.ID.6, F-IF.1.a, F-IF.2,F-IF.3,F-IF.4, F-IF.5, F-IF.7e, F-IF.8b, F-IF.9, F-BF.1a, F-BF.2, F-LE.1a, F-LE.1.c, F-LE.2, F-LE.4, F-LE.5, A-SSE.1.a; A-SSE.1.b; A-SSE.2; A-CED.1, A-REI.10; A-REI.11, 8.EE.A.1, 8.EE.A.3, 8.EE.A.4

Unit 4: Quadratic Functions

Students will use real life situations to discover the properties and shape of a quadratic function through the use of tables and graphs. Students will learn to sketch parabolas from factored and later, standard form. Through the use of factored form, the symmetry of the graph will be revealed. Students will find the axis of symmetry by formula or symmetry. Students will learn to use arithmetic operations on polynomials. Several methods of factoring will be used to find solutions of the quadratic. Other methods of solving quadratics will also be explored including solving by square roots and solving using the quadratic formula. Technology will be used at different times throughout this unit to support the understanding of the concepts and allow for efficient approximations of solutions.

Common Core State Standards: F-IF.4, F-IF.5, F.IF.7, F.IF.8.a, F.IF.9,A-SSE.1a; A-SSE.2; A-SSE.3a; A-SSE.3b, A-APR.1,A-CED.1, A-REI.1; A-REI.4a; A-REI.4b; A-REI.7

Unit 5: One-Variable Data

Students will analyze one-variable quantitative and categorical data. Students will learn to construct appropriate graphs (dot plots, histograms and boxplots) and summary statistics (mean, median, range, IQR) for the given data, as well as interpret the shape, center, spread and outliers. Students will analyze categorical data by determining the joint, marginal and conditional distributions.

Common Core State Standards: S.ID.1, S.ID.2, S.ID.3, S.ID.5

Unit 6: Pulling it all together,

Students will use real life situations to discover absolute value and piecewise functions. They will discover similarities and differences between quadratic and absolute value functions. They will discover similarities between linear and absolute value functions. Piecewise functions are introduced as a necessary compilation of functions to describe real life situations. Students will discover transformations and the similarities in graphing lines, parabolas and absolute value functions from the similar forms of the equations (f(x) = a(x – h) + k, g(x) = a(x – h)2 + k and h(x) = a|x – h| + k). Although function families are different, there are many similarities in the behaviors that allow us to learn each new function family with a deeper understanding by connecting to previous knowledge about the behaviors of functions.

Common Core State Standards: 8-F.B.5, N-Q.3, F-IF.1, F-IF.2, F.IF.5, F.IF.7b, A-REI.7; A-REI.10; A-REI.11, F.LE.3