Grade AM108R 7 + Mastering the Standards ALGEBRA. By Murney R. Bell

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1 Hayes AM108R Mastering the Standards ALGEBRA By Murney R. Bell Grade 7 +

2 Mastering the Standards Algebra By Murney R. Bell Illustrated by Reneé Yates Copyright 2008, Hayes School Publishing Co., Inc., Printed in USA All rights reserved. The purchase of this book entitles the individual teacher to reproduce the activities in this book for use with children. No parts of these publications may be stored in a retrieval system or transmitted in any form by any means, electronic, mechanical, recorded, or otherwise, without prior written permission of Hayes School Publishing Co., Inc. TABLE OF CONTENTS Letter to Teachers and Parents...1 Number and Operations Teacher Overview...2 Practice Assessment... Using Variables...4 Exponents...5 Order of Operations...6 Real Numbers...7 Adding and Subtracting Integers...8 Multiplying and Dividing Integers...9 Scientific Notation...10 Distributive Property...11 Graphing Data on Coordinate Planes...12 Linear Relations and Functions Practice Assessment...1 Relations and Functions...14 Function Rules, Tables, and Graphs...15 Writing Function Rules... Solving One-step Equations...17 Solving Two-step Equations...18 Solving Multistep Equations...19 Solving Equations with Variables on Both Sides...20 Formulas...21 Absolute Values Inequalities...22 Graphing Inequalities...2 Solving Inequalities Using Addition and Subtraction...24 Solving Inequalities Using Multiplication and Division...25 Ratios and Proportions...26 Percent of Change...27 Slope-Intercept Form...28 Standard Form...29 Point-Slope Form...0 Mathematical Models Practice Assessment...1 Scatter Plots and Equations of Lines...2 Graphing Absolute Value Equations... Zero and Negative Exponents...4 Multiplication Property of Exponents...5 Power of Powers of Exponents...6 Division Property of Exponents...7 Arithmetic Sequences...8 Geometric Sequences...9 Exponential Functions...40 Symbol Manipulations Practice Assessment...41 Solving a System Using Substitution...42 Solving a System Using Elimination...4 Solving a System Using Matrices...44 Adding and Subtracting Polynomials...45 Multiplying and Factoring...46 Multiplying Binomials...47 Perfect Squares and Difference of Squares...48 Factoring Trinomials...49 Factoring Perfect Squares and Difference of Squares...50 Factoring by Chunking...51 Change Analysis Practice Assessment...52 Quadratic Graphs...5 Quadratic Functions...54 Square Roots...55 Solving Quadratic Equations by Factoring...56 Using Quadratic Formulas...57 Simplifying Radicals...58 Pythagorean Theorem...59 Distance and Midpoint Formulas...60 Test-Taking Strategies...61 INTRODUCTION This book contains standards-based problems similar to those students will find on mastery tests in mathematics. The problems are based on standards from the National Council of Teachers of Mathematics and state standards from across the nation. Practice pages include problems in Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. Each section features a test for assessment and essential mathematical vocabulary terms for success. Problem solving is embedded throughout. One word problem on each page requires a written response on a separate piece of paper. The activities may be used at any time of the year to assess understanding, for additional practice, or for test preparation. MASTERING THE STANDARDS: ALGEBRA 1

3 10, ,2 Using Variables A variable is a letter or symbol that stands for a number. This number may change or may be a single number. When one of more variables are placed together, like a b, this means a times b. A number with variables is referred to as a coefficient. You will find that variables will be used as a translation of sentences into algebraic expressions. The basic phrases are: + (addition) The sum of 7 and is 10. as in 7 + = 10 (subtraction) The difference of 7 and is 4. as in 7 = 4 or (multiplication) The product of 7 and is 21. as in 7 1 ) or / (division) The quotient of 12 and is 4. as in )12 or 12 = 4 4 The quotient of divided into 12 is 4. as in )12 12 The quotient of 12 divided by is 4. as in = 4 Example: Write an expression for the following: A. the sum of a number and 12 B. the product of 5 and a number x x Write the following expressions using n as the number. 1. a sum of a number and 5 4. seven less than a number 2. the difference between 15 and a number 5. the quotient of a number and 6 6. eight times a number. a number increased by 15 Example: Write equations and solve for the variable using n as the variable. A. Three more than a number is 10. B. The product of 7 and a number is 21. n + = 10 7 n 1 n + = 10 7 n n = 7 n = Write the following expressions using n as the number. 7. Four less than a number is Seven times a number is The sum of -8 and a number is The product of and a number less 4 is The quotient of 28 and a number is A quarter of a number plus is 10. Write an expression using pennies and dimes that shows 78 cents. 4

4 10, , Exponents When working with variables, you will find that you need to understand exponents. Exponents are mathematical expressions for any real number b and any positive integer n, where b is the base and n is the exponent. b n = b b b... b 4 = = 81. is used as a factor four times. A zero exponent: b 0 = 1, if b is any nonzero real number. 5 0 = 1 Negative exponent: b -n = 1 b n 5 - = 1 5 = Properties of Exponents Examples: Product Rule: b n b m = b n+m 2 4 = 6 Quotient Rule: b n b m = b (n m) or = 5 7 = 5 4 Power Rule: (ab) n = a n b n (x) 4 = 4 x 4 = 81x 4 Simplify the following expressions = = = 4. ( 2) ( 2) 2 = = 6. n 2 n 5 = 7. n -4 n 6 = 8. (x) 4 = Evaluate each expression when x = -2 and y = x 2 = 10. (xy) 2 = 11. x 4 x 2 = 12. y y 2 = 1. y x = 14. (x + y) = 15. (-5x) =. (-4y) x = A certain type of bacteria doubles in number every hour. At 8:00 a.m., there were 200 bacteria. How many bacteria will be present at noon? 5

5 10, ,2 Order of Operations In problems with more than one operation involved, you will need to determine which order of operations will be performed. The rule for order of operations has been established. Order of Operations 1. Perform operations inside parentheses or grouping symbols. 2. Simplify terms with exponents.. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right. Example: Simplify (9 + 7) (4 5 6) 2 (9 + 7) (4 5 6) Work inside the parentheses first. 2 (4 5 6) Multiply and divide within parentheses. (20 18) Complete subtraction within parentheses. 2 Divide and multiply, left to right. = 8 6 Subtract. Simplify each expression = / 2 7 = / = / = = (15 8) = = / 4 18 / 9 = 9. 4(4 + 5) + 7(7 5) = 10. ( + 5) (2 + 5) = = 12. ( (5 + 2)) = = 14. ( ) (1 + 1) 2 = 15. 2((9 5)) = = = = Write an expression and simplify: You have pennies, 4 nickels, and 6 dimes. How much money do you have? 6

CURRICULUM CATALOG. Algebra I (3130) VA

CURRICULUM CATALOG. Algebra I (3130) VA 2018-19 CURRICULUM CATALOG Table of Contents COURSE OVERVIEW... 1 UNIT 1: FOUNDATIONS OF ALGEBRA... 1 UNIT 2: LINEAR EQUATIONS... 2 UNIT 3: FUNCTIONS... 2 UNIT 4: INEQUALITIES AND LINEAR SYSTEMS... 2 UNIT