Glastonbury Public Schools Mathematics Curriculum

Algebra I

(Algebra IB1 and Algebra 1B2 learn this curriculum as well.)

Functions: What is a function and how can understanding function families help us to solve problems?

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 be problem solvers and understand that mathematics makes sense.

I. Patterns, Sequences and Functions

Conceptual Lens: Patterns

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 compare those to other sequences that do not have a common difference. Students will understand that in a function, the value of one variable is uniquely determined by the value of another variable. They will be able to determine why a function is useful and how to describe functions through function notation. Through inquiry and exploration, students will connect arithmetic sequences to linear functions. Students will build the understanding that functions represent, model, and predict underlying patterns.

Common Core State Standards: F-IF1, F-IF3, F-IF5, F-BF1a, F-BF2, F-LE1b, F-LE1c, F-LE2

II. Linear Functions

Conceptual Lens: Continuous vs. Discrete Domain

Students will tackle a variety of problems leading them through the variety of processes available to use algebra to solve problems. They 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. Students will build the understanding of when a continuous or discrete domain better represents a situation and be able to represent both domains using the correct notation. Throughout the unit real life situations will be modeled using equations, tables, and graphs and students will build the understanding that multiple representations of real life situations facilitate the finding and modeling of solutions.

Common Core State Standards: N-Q.1.b, N-Q.1.c, N-Q.2, N-Q.3, S.IDs.i.6.a, S-ID.6.c, S.ID.7, S.ID.8, S.ID.9, F-IfF.2, F-IF.6,F-IF.7.a, F-IF.9, F-LE.1.a, F-LE1.b, F-LE2, A-SSE.1.a, A-CED.1, A-CED.2, A-CED.4, A-REI.1, A-REI.3, A-REI.10,

III. Systems of Linear Equations/ Inequalities

Conceptual Lens: Simultaneous Equations

Students will extend their knowledge of linear functions to understand what it means when two or more linear equations are working together. Systems of linear equations are a powerful mathematical tool that is used to model, represent and solve problems. They can be represented in many different forms, and students will use critical thinking to determine which representation would be best for each given situation. Students will then explore the system of linear equations and inequalities to determine the number and type of solution and provide meaning beyond calculations to understanding what each type of solution means. Students will work with discrete and continuous situations to enhance their understanding of the meaning of the solutions of a system of linear equations and inequalities to realize that real world situations often involve multiple mathematical expressions.

Common Core State Standards: N-Q.1.b, N-Q.1.c, N-Q.2, N-Q.3, F-IF.2, F-IF.7.a,, A-SSE.1.a,, A-CED.2, A-REI.5, A-REI.6, A-REI.10, A-REI.11, A-REI.12

IV. Quadratic Functions

Conceptual Lens: Zeros

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 discover what happens when you multiply two linear functions together and how that affects the shape of the graph. 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 help produce the graph of a quadratic function as well as 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 when a quadratic equation can not be factored. Technology will be used at different times throughout this unit to support the understanding of the concepts and allow for efficient approximations of solutions involving zeros and maximum/ minimum of the graph. Students will build the understanding that the graph of a function reveals solutions to related equations.

Common Core State Standards: F-IF.4, F-IF.5, F.IF.7, F.IF.8a, 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

V. Pulling it all together

Conceptual Lens: Modeling

Students will gather and analyze data by looking at patterns in tables and graphing points to recognize the curve and choose the appropriate model for the data. Students will also make sense of the context of the problem to ensure that the model chosen is an appropriate fit. Once they justify which model to use from a previously studied function (linear, quadratic, or other, students will create a best-fit curve using technology and predict future outcomes (extrapolation) as well as predict within the given set of data (interpolation). Students will also justify what domain is appropriate given the model they created and the context of the problem. Students will compare models for given sets of data and see the intersection points of non-linear systems of equations using technology. Once students have carefully examined each set of data and the context of the problem, they will have a deeper understanding of how analyzing the patterns found in the data helps us to pick the appropriate model for the data to make predictions.

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

VI. Statistics

Conceptual Lens: Interpretation of Data

Students will analyze one-variable quantitative and categorical data. Students will learn to construct appropriate graphs (dot plots, histograms and box-plots) 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. Students will build understanding that the process of statistics reveals a story from data that can be used to make informed decisions.

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