radnor high school · 2012. 9. 3. · mcdougal littell algebra i power presentations dvd rom...

Grade 8 Intro to Algebra Last Modified

April 24, 2012

Radnor Middle School Course Overview

Math

Introduction to Algebra 1

General Information Credits: N/A Length: Full Year Weighted: N/A Format: Meets Daily Prerequisite: Pre-Algebra, Course 3 Grade: 8

I. Course Description The goal of this course is to provide students with a foundation in the algebraic strand of mathematics through experiences with:

understanding patterns, relations, and functions;

representing and analyzing mathematical situations and structures using algebraic symbols;

using mathematical models to represent and understand quantitative relationships;

analyzing change in various contexts. Mathematics itself will be looked at not just as calculation but also as a modeling language, as a process for logical thought, and as a field of study. This approach to Algebra 1 is organized around families of functions, with special emphasis on linear 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.


April 24, 2012

MARKING PERIOD: 1 Unit: Chapter 1 – Expressions, Equations, and Functions

Common Core Standards

Interpret parts of an expression, such as terms, factors, and coefficients.

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Keystone Connections: A1.1.1.4 Use estimation strategies in problem solving situations. A1.1.2.1 Write, solve, and/or graph linear equations using various methods. A1.1.3.1 Write, solve, and/or graph linear inequalities using various methods. A1.2.1.1 Analyze and/or use patterns or relations. A1.2.1.2 Interpret and/or use linear functions and their equations, graphs, or tables.

PA State Standards 2.8.A1.D. Demonstrate an understanding and apply properties of functions (domain, range) and characteristics of linear functions.

Student Objectives:

Writing and evaluating algebraic expressions

Using expressions to write equations and inequalities

Representing functions as verbal rules, equations, tables and graphs

Materials &Texts Algebra 1‐ Larson series –McDougal, Littell & Co.‐ 2007 ed.

Lesson Practice Sheets B

MAJOR UNITS OF STUDY


April 24, 2012

Study Guides (optional)

Lesson Note Taking Guides (optional) Activities, Assignments, & Assessments ACTIVITIES

Evaluate Expressions

Apply Order of Operations

Write Expressions

Write Equations and Inequalities

Use a Problem Solving Plan

Represent Functions as Rules and Tables

Represent Functions as Graphs ASSIGNMENTS


Associated Chapter exercises

ASSESSMENTS Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. Additionally, teachers may use homework, group activities, and/or projects for grading purposes. The Radnor Middle School grading system and scale will be used to determine letter grades.

Lesson Assessment/Quizzes

Chapter Tests

Terminology

Variable Algebraic expression Evaluate and algebraic expression Power Exponent Base Order of operations Verbal model Rate Unit rate Equation

Open sentence Solution of an equation or inequality Formula Function Input Output Domain Range Independent variable Dependant variable

Media, Technology, Web Resources

McDougal Littell Algebra I Easy Planner DVD ROM

McDougal Littell Algebra I Power Presentations DVD ROM

McDougal Littell Classzone.com resources


April 24, 2012

Teacher developed smart-board documents

Scientific Calculator

www.learningupgrade.com


April 24, 2012

MARKING PERIOD: 1/2 Unit: Chapter 2 – Properties of Real Numbers


Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram

Keystone Connections: A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).

PA State Standards

Student Objectives:

Performing operations with real numbers

Applying properties of real numbers

Classifying and reasoning with real numbers




Lesson Note Taking Guides (optional)

Activities, Assignments, & Assessments ACTIVITIES

Use Integers and Rational Numbers

Add Real Numbers

Subtract Real Numbers

Multiply Real Numbers

Apply the Distributive Property

Divide Real Numbers


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Find Square Roots and Compare Real Numbers ASSIGNMENTS





Chapter Tests

Terminology

Whole numbers Integers Positive Integer Negative integer Rational number Opposites Absolute value Conditional statement If-then statement Counter example

Additive identity Additive inverse Multiplicative identity

Equivalent expressions Distributive property Term Coefficient Constant term Like terms

Multiplicative inverse Square root Radicand Perfect square Irrational number Real numbers









April 24, 2012

MARKING PERIOD: 2

Unit: Chapter 3 – Solving Linear Equations


Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

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.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Keystone Connections: A1.1.2.1 Write, solve, and/or graph linear equations using various methods.

PA State Standards

Student Objectives:

Solving equations in one variable

Solving proportion and percent problems

Rewriting equations in two or more variables






Solve One‐Step Equations

Solve Two‐Step Equations

Solve Multi‐Step Equations

Solve Equations with Variables on Both Sides


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Write Ratios and Proportions

Solve Proportions Using Cross Products

Solve Percent Problems

Rewrite Equations and Formulas ASSIGNMENTS





Chapter Tests

Terminology Inverse operations, equivalent equations, identity, ratio, proportion, cross product, scale drawing, scale model, scale, literal equation









April 24, 2012

MARKING PERIOD: 3 Unit: Chapter 4 – Graphing Linear Equations and Functions


Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.


Keystone Connections: A1.2.1.1 Analyze and/or use patterns or relations. A1.2.1.2 Interpret and/or use linear functions and their equations, graphs, or tables. A1.2.2.1 Describe, compute, and/or use the rate of change (slope) of a line.

PA State Standards 2.8.A1.D. Demonstrate an understanding and apply properties of functions (domain, range) and characteristics of linear functions. 2.11.A1.B. Describe rates of change as modeled by linear equations.

Student Objectives:

Graphing linear equations and functions using a variety of methods

Recognizing how linear equations and functions affect their graphs

Using graphs of linear equations and functions to solve real world problems





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Plot Points in a Coordinate Plane

Graph Linear Equations

Graph Using Intercepts

Find Slope and Rate of Change

Graph Using Slope‐Intercept Form

Model Direct Variations

Graph Linear Functions ASSIGNMENTS





Chapter Tests

Terminology Quadrant solution of an equation in two variables graph of an equation in two variables linear equation standard form of a linear equation linear function x-intercept y-intercept slope rate of change slope-intercept form parallel direct variation constant of variation function notation family of functions parent linear function


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April 24, 2012

MARKING PERIOD: 3/4 Unit: Chapter 5 – Writing Linear Equations



Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Keystone Connections: A1.2.2.2 Analyze and/or interpret data on a scatter plot.

PA State Standards 2.6.A1.C. Select or calculate the appropriate measure of central tendency, calculate and apply the interquartile range for one-variable data, and construct a line of best fit and calculate its equation for two-variable data. 2.6.A1.E. Make predictions based on lines of best fit or draw conclusions on the value of a variable in a population based on the results of a sample. 2.8.A1.B. Evaluate and simplify not understood algebraic expressions, for example: sums of polynomials, products/quotients of exponential terms and product of a binomial times a trinomial; and solve and graph linear equations and inequalities. 2.8.A1.E. Use combinations of symbols and numbers to create expressions, equations, and inequalities in two or more variables, systems of equations, and inequalities, and functional relationships that model problem situations. 2.8.A1.F. Interpret the results of solving equations, inequalities, systems of equations, and systems of inequalities in the context of the situation that motivated the model. 2.9.A1.A. Use algebraic techniques to determine if two lines are parallel and / or perpendicular.

Student Objectives:


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Writing linear equations in a variety of forms

Using linear models to solve problems

Modeling data with a line of fit






Write Linear Equations in Slope‐Intercept Form

Use Linear Equations in Slope‐Intercept Form

Write Linear Equations in Point‐Slope Form

Write Linear Equations in Standard Form

Write Equations of Parallel and Perpendicular Lines

Fit a Line to Data

Predict with Linear Models ASSIGNMENTS





Chapter Tests

Terminology

Point-slope form Converse Perpendicular scatter plot positive correlation negative correlation relatively no correlation line of fit best fitting line

linear regression interpolation extrapolation zero of a function


April 24, 2012









April 24, 2012

MARKING PERIOD: 4 Unit: Chapter 6 – Solving and Graphing Linear Inequalities


Graph the solutions to a linear inequality in two variables as a half-plane (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.

Keystone Connections: A1.1.3.1 Write, solve, and/or graph linear inequalities using various methods.

PA State Standards 2.8.A1.B. Evaluate and simplify not understood algebraic expressions, for example: sums of polynomials, products/quotients of exponential terms and product of a binomial times a trinomial; and solve and graph linear equations and inequalities. 2.8.A1.E. Use combinations of symbols and numbers to create expressions, equations, and inequalities in two or more variables, systems of equations, and inequalities, and functional relationships that model problem situations. 2.8.A1.F. Interpret the results of solving equations, inequalities, systems of equations, and systems of inequalities in the context of the situation that motivated the model.

Student Objectives:

Applying properties of inequalities

Using statements with and/or

Graphing inequalities






Solve Inequalities Using Addition and Subtraction

Solve Inequalities Using Multiplication and Division


April 24, 2012

Solve Multi‐Step Inequalities

Solve Compound Inequalities

Solve Absolute Value Equations

Solve Absolute Value Inequalities

Graph Linear Inequalities in Two Variables ASSIGNMENTS





Chapter Tests

Terminology Graph of an inequality equivalent inequality compound inequality absolute value equation absolute deviation linear inequality in two variables solution of an inequality in two variables graph of an inequality in two variables half-plane








radnor high school · 2012. 9. 3. · mcdougal littell algebra i power presentations dvd rom...

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