Exploring Algebra & Geometry Curriculum Outline


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1 Exploring Algebra & Geometry Curriculum Outline Department: Mathematics Date : November 2004 Course: Exploring Algebra & Geometry Rev Date: 2002, September 1999, June 1999, Sept l989, Aug 1993 Level: 9 Full Year This course description incorporates the New Jersey Core Curriculum Content Standards for Mathematics  Standards and Strands 2003 appropriate for grade 12: 4.1, 4.2, 4.3, 4.5 I COURSE DESCRIPTION This course introduces the subject of algebra, dealing with specific algebra topics in some depth, so that students are prepared to continue their learning with confidence in their preparation following this introduction. The focus will be on giving students a thorough understanding of the algebraic structure of the real number system. It applies these basic properties to the study of equations, graphing, and polynomials. A focus will be on giving students a thorough understanding of specific geometric topics at their level of ability so as to prepare them for a full course in Geometry. The focus will be on understanding, exploring real world applications and discovering concepts through handson lessons, computer labs, and activity based lessons. II COURSE OBJECTIVE The objective of the course is to give students a thorough understanding of some of the basic concepts in algebra and geometry, through handson activities, and relationship with the real world, so as to prepare them with confidence to undertake further studies in algebra and geometry. III MAJOR CONCEPTS AND TOPICS A. Rules of Algebra (5 days) 1. Order of Operations 2. Order sets of integers 3. Operations with integers 4. Distributive property to real numbers 5. Properties of real numbers B. Linear Equations (15 days) 1. Evaluate algebraic expressions 2. Translate written algebraic expressions into algebraic symbols 3. Combining similar terms C. Solving Linear Equations (20 days) 1. Solving equations using on transformation 2. Solving equations using two or more transformations 3. Solving equations with variables on both sides This document is for use by current faculty and current students of Paramus School District, Paramus, New Jersey. No part of this document may be used or reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic. mechanical, photocopying, recording, scanning, or otherwise, without the prior written permission of the Board of Education, Paramus School District, 145 Spring Valley Road Paramus, New Jersey, Exploring Algebra & Geometry February 2004 Page 1 of 4
2 Exploring Algebra & Geometry February 2004 Page 2 of 4
3 D. Graphing (20 days) 1. Graphing linear equations in one variable 2. Graphing linear equations in two variables 3. The slope of a line 4. Methods of graphing a linear equation on a coordinate plane Exploring Algebra & Geometry February 2004 Page 3 of 4
4 E. Polynomials (20 days) 1. Adding polynomials 2. Subtracting polynomials 3. Laws of exponents 4. Multiplying polynomials F. Radicals (20 days) 1. Square Roots 2. Geometry application ( Pythagorean Theorem ) G. Elements of Geometry (15 days) 1. Point, line and plane 2. Segments, rays, angles 3. Measure of segments and angles 4. Classification of angles, types of angles H. Introduction to some elementary geometric properties and their use (20 days) 1. Addition, subtraction of segments and angles 2. Perpendicularity constructions and elementary properties 3. Parallel lines constructions and elementary properties 4. Construction of angles, line segments, parallel lines, angle bisector, 5. Perpendicular lines, line bisectors 6. Obtaining information from geometric diagrams 7. Theorems which have particular relevance to the topics being taught I. Triangles (25 days) 1. Isosceles and equilateral triangles 2. Simple Pythagorean Theorem 3. Congruence of triangles, with emphasis on constructional methods 4. SAS, SSS, ASA 5. Construction of median, altitude and perpendicular bisector of a triangle J. Properties of Simple Geometric Figures (20 days) 1. Perimeter and areas of triangles, rectangles, and circles 2. (Optional) Volume and surface area of some geometric figures 3. parallelepiped, pyramids, cylinder, sphere, cone. IV STUDENT SKILL OBJECTIVES A B Rules of Algebra 1 Thoroughly review the order of operations with real numbers 2 Review the representation, order and use of numbers in a variety of equivalent forms: integers, decimals, percents, fractions 3 simplify algebraic expressions involving integers by performing the following operations: addition, subtraction, multiplication and division 4 develop and apply the Distributive Property to real numbers Linear Equations 1 evaluate expressions and replace for variables 2 identify in a monomial expressions the coefficient, the base and the exponent 3 identify similar terms and combine these terms using addition and subtraction Exploring Algebra & Geometry February 2004 Page 4 of 4
5 C D E F G H Solving Linear Equations 1 solve equations systematically using one of the following operations (addition, subtraction, division, multiplication) 2 apply two or more transformations to solve an equation, then check the solution (reinforcing evaluating an algebraic expression using order of operation.) 3 to collect variables on one side of an equation and solve systematically using previous methods 4 use algebraic models to answer reallife situations Introduction to Graphing 1 identify parts of a coordinate plane through plotting ordered pairs 2 graph horizontal and vertical lines to in the coordinate plane and read the point of intersection 3 graph linear equation from a table of values 4 interpret slope as a constant rate of change or an average rate of change and calculate the slope of a line given two points 5 define and find the x and y intercept of the graph of a linear equation and use the intercepts to sketch the graph of the line 6 to find the slope and yintercept of an equation and derive a method to construct the graph of the line 7 explore graphs and equations using the graphing calculator Introduction to Polynomials 1 identify the classifications of Polynomials as parts ( coefficient, degree, constant terms) 2 combine polynomials using addition and subtraction 3 using the multiplication properties of exponents to evaluate powers and simplify expressions 4 using algebra tiles the demonstrate multiplying two polynomials using the Distributive Property and the FOIL method Introduction to Radicals 1 identify perfect squares and irrational numbers 2 simplify radicals using calculator as well as finding the largest perfect square factor 3 explore the connection of algebra to geometry by making geometry applications Review of the Elements of Geometry 1 recognize points, lines, planes 2 recognize segments, rays, angles 3 using rulers and protractor to measure and construct segments and angles 4 classification of angles by measurement and identify types of angles Introduction to some elementary geometric properties and their use 1 calculate the measurements of segments and angles using addition and subtraction 2 understand the concepts of perpendicularity using patty paper activity 3 discover the concepts of construction and elementary properties of parallel lines and angles formed by parallel lines 4 use computer activities to construct angles, line segments, parallel lines, angle bisectors, perpendicular bisectors, line bisectors 5 a thorough study of the importance of a geometric diagram and properties that can be expressed on a geometric diagram. 6 use discovery and exploration to determine properties relating to major concepts and have students prepare and record general statements and theorems in a conditional format Exploring Algebra & Geometry February 2004 Page 5 of 4
6 I J Introduction to Triangles 1 discover and explore the properties of isosceles and equilateral triangles using the computer activities 2 study the concepts and properties of right triangles state and prove through examples of the Pythagorean Theorem 3 understand the concept of congruent figures and accurately identify the corresponding parts of figures 4 discuss and apply three ways to prove triangles congruent SAS, SSS, ASA using diagrams and writing paragraphs to support conclusions 5 construction of median, altitude and perpendicular bisectors of a triangle Properties of simple geometric figures 1 understand the concepts of area and perimeter for triangles, rectangles, circles 2 calculate the area of rectangles, triangles, and circles 3 find the surface area of prisms, pyramids and circular solids 4 use area of a prism or a cylinder s cross section to calculate the volume of parallelepiped, cylinder, sphere, and cones V EVALUATION PROCEDURES Evaluation of success will be based upon portfolios, tests, quizzes, class work, and examinations. VI SUGESTED MATERIALS Computer and calculator activities. Manipulative materials. Text: HRW ALGEBRA ONE INTERACTIONS COURSE 1 Kennedy et al 2001 * Exploring Algebra & Geometry February 2004 Page 6 of 4
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