Alegebraic R. I H

In Algebra I, the content is organized around families of functions, with special emphasis on linear and quadratic functions. As students learn about each family of functions, they will learn to represent them in multiple ways - as verbal descriptions, equations, tables, and graphs. They will also learn to model real-world situations using functions in order to solve problems arising from those situations. In addition to its algebra content, Algebra I includes lessons on probability and data analysis as well as numerous examples and exercises involving geometry. These math topics often appear on standardized tests, so maintaining students’ familiarity with them is important. This course is an important part of CAPT and SAT preparation, therefore, instruction, practice and assessments will be presented in a variety of formats – multiple choice, short answer, grid-in and open ended that students will encounter on standardized testing. There will also be extensive use of technology including the graphing calculator throughout the year.

1. Enduring Understandings (broad ideas, usually grounded in the discipline):

These strands of thought are integrated throughout the text and developed throughout the course of study.

Equations in One Variable

First Semester Material to be Covered Prior to the Mid-Term Exam

1. Expressions, Equations, and Functions – students write and evaluate expressions, equations and inequalities. They learn to apply the order of operations and to use a problem solving plan to solve real-world problems. Students represent functions as rules and as tables. They also graph functions given a rule or table of values.

2. Properties of Real Numbers – students will learn about the real number system. They will classify real numbers, compare and order integers and rational numbers, perform basic operations, find square roots, apply properties to evaluate and simplify expressions, and use the Distributive Property to write equivalent expressions. Students will use conditional statements and logical reasoning to reason with real numbers.

3. Solving Linear Equations – students use properties of equality to solve one-step, two-step, and multi-step equations in one variable. They also use properties of equality and the distributive property to solve equations with variable on both sides. Students write ratios and proportions, solve proportions using cross products, and solve percent problems, such as finding the percent of a number, a base, and part of a base. Finally, students rewrite equations in function form and solve formulas and literal equations for a given variable.

Equations in Two Variables

1. Graphing Linear Equations and Functions – students learn how to plot points in a coordinate plane and use tables, x- and y- intercepts, and the slope and y- intercept to graph linear equations and functions. They interpret slope as a rate of change in real-world situations and explore how changing the slope and y- intercept changes the graph. They use slope to identify parallel and perpendicular lines. They write and graph direct variation equations and use them to solve real-world problems. They learn how to use function notation and they compare families of graphs.

2. Writing Linear Equations – students write equations of lines in slope-intercept form given three situations: the slope and y- intercept; the slope and a point; or two points. Also, they write and graph equations using point slope form, using a graph of the line, or using real-world data. They write equations of lines in standard form, and use their equations to solve real-world problems. They write and find equations of lines parallel or perpendicular to a given line. They make scatter plots of data and use a line of fit to model and interpret the data. They perform linear regression to find the best-fitting line for data, and make predictions using the graph and the equation.

3. Solving and Graphing Linear Inequalities – students write, solve, and graph one-step and multi-step inequalities using addition, subtraction, multiplication, and division. They learn to reverse an inequality sign when multiplying or dividing by a negative number. Students solve and graph compound inequalities using and and or. They solve absolute value equations using or and they solve and graph absolute value inequalities using and and or. Finally, students graph linear inequalities in two variables.

4. Systems of Equations – students use graphing, substitution, and elimination to solve systems of linear equations. When solving by the elimination method, they either add or subtract, or they multiply first and then add or subtract. Students identify linear systems as having one solution, no solution, or infinitely many solutions.

Second Semester material to be covered prior to the final exam.

Statistics and Probability

Probability and Data Analysis – students use sample spaces to calculate probabilities and odds. They identify and use the number of permutations or the number of combinations in a set of objects to calculate the probability of an event. They find the probability of compound events by identifying whether the events are dependent or independent. Students analyze data by identifying sampling methods and potentially biased samples and questions. They compare measures of central tendency: the mean, median, and mode; and they compare measures of dispersion: the range and mean absolute deviation and look for outliers. They analyze and display data in circle graphs, stem-and-leaf plots, histograms, and box-and-whisker plots.

Unit 4 – Exponential and Quadratic Functions

1. Exponents and Exponential Functions - students learn and use properties of

exponents involving products and quotients. They learn how to apply the product of powers property, the power of a power property, the power of a product property, the quotient of powers property, and the power of a quotient property. Students also use zero and negative exponents. Students learn how to read, write, and compute with numbers in scientific notation. Students also learn how to graph and write rules for exponential functions, including exponential growth and exponential decay functions.

2. Polynomials and Factoring – students identify, classify, add, subtract and multiply polynomials. They use vertical and horizontal formats to find sums and differences. To find products, they use the distributive property, tables of products, and patterns (including the FOIL pattern, the square of a binomial pattern, and the sum and difference patterns). They write polynomials to describe and solve real-world problems and solve polynomial equations. Students factor polynomials and use factoring to solve equations, to find the zeros of functions, and to find the roots of equations. Finally, they factor polynomials completely using a variety of techniques.

3. Quadratic Equations and Functions – students graph quadratic functions and compare them to the parent graph. They find the axis of symmetry, the vertex, and minimum or maximum values. They solve quadratic equations by factoring, graphing, using square roots, completing the square, and using the quadratic formula. Students use the discriminate to determine the number and type of solutions of a quadratic equation. Finally, students determine whether a linear, exponential, or quadratic function best models a set of data.

Exponential and Quadratic Functions - Radical and Rational Functions

Unit 5 – Radical and Rational Functions

4. Radicals and Geometry Connections – students graph square root functions. They use properties to simplify radical expressions, including rationalizing the denominator. They add, subtract, and multiply radicals. They solve radical equations, including equations with extraneous solutions. They apply the Pythagorean theorem and its converse to find missing lengths and to determine whether triangles are right triangles. They apply the distance and midpoint formulas to find the distance between two points and to find missing coordinates.

5. Rational equations and Functions – students model inverse variation by writing and graphing inverse equations. Students simplify rational expressions, stating any excluded values. They multiply, divide, add, and subtract rational expressions and then use these operations to solve rational equations.