Grade AM107R 7 + Mastering the Standards PRE-ALGEBRA. By Murney R. Bell

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1 Hayes AM107R Mastering the Standards Grade 7 + PRE-ALGEBRA By Murney R. Bell

2 Mastering the Standards Pre-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... Basic Operations...4 Exponents...5 Order of Operations...6 Prime Numbers...7 Fractions: Adding and Subtracting...8 Fractions: Multiplying and Dividing...9 Decimals...10 Scientific Notation...11 Integers Teacher Overview...12 Practice Assessment...1 Integers...14 Adding Integers...15 Subtracting Integers... Multiplying and Dividing Integers...17 Integers Practice...18 Basic Algebra Tools Teacher Overview...19 Practice Assessment...20 Variables...21 Properties of Arithmetic...22 Distributive Property...2 Solving One-step Equations...24 Solving Two-step Equations...25 Solving Equations Variable on Two Sides...26 Solving Equations with Parentheses...27 Solving Equations...28 Graphing...29 Linear Equations...0 Formulas...1 Square Roots...2 Pythagorean Theorem... Basic Geometry Ideas Teacher Overview...4 Practice Assessment... Metric Conversions...6 Properties of Lines...7 Triangles Classification...8 Quadrilaterals...9 Perimeter and Area Formulas...40 Sum of Angles of Figures...41 Transformations and Symmetry...42 Circle Properties... Geometric Solids...44 Surface Area of Solids...45 Volume of Solids...46 Figurative Numbers...47 Measurement Estimations and Conversions Teacher Overview Practice Assessment...49 Customary Measures...50 Metric Measures...51 Basic Statistics and Probability Tools Teacher Overview...52 Practice Assessment...5 Statistics Graphs...54 Finding Central Tendencies...55 Determining Quartiles...56 Creating Box Plots...57 Determining Linear Regression Lines...58 Interpolate and Extrapolate...59 Probability of Outcomes...60 Permutations and Combinations...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, a transparency master, 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: PRE-ALGEBRA 1

3 ,082 10, Basic Operations There are four basic operations in mathematics: + (addition) the sum of 8 and 2 is 10 as in = 10 (subtraction) the difference of 8 and 2 is 6 as in 8 2 = 6 (multiplication) the product of 8 and 2 is as in 8 2 = or ) (division) the quotient of 8 and 2 is 4 as in 2)8 or 8 2 = 4 the quotient of 2 divided into 8 is 4 as in 2)8 = 4 the quotient of 8 divided by 4 is 2 as in 8 4 = 2 There are several other words that are used: total (+), remainder ( ), times ( ), divide up ( ). In working these problems, read carefully and rewrite the problems so that you can do them correctly. Example: Find the sum of 15 and Do the indicated operation. Write the answer on the line. 1. Find the sum of 21 and. 2. Find the product of 5 and 12.. Find the difference of 2 and Find the sum of 567 and Find the quotient of 1,900 and Find the product of 1 and Find the difference of 21 and Find the quotient of 7,004 and Find the total of 57, 7, and What is 19 times 87? 11. What is the remainder of 694 minus 405? 12. What would you have if you divided up 256 into 8 equal shares? Describe how you would give change back to a customer that just purchased a sixtyfive cent bagel and paid you with a one dollar bill. 4

4 4, Exponents Recall that multiplication is repeated addition. So 6 times 2 means six 2 s added together or = 12. An exponent is making repeated multiplication happen, or three to the fourth power multiplied together would be = 81; thus, exponents makes a fifth operation. An exponent is a superscript number written to the upper right of a number. If 6 is the base and the 2 is the exponent, we say 6 to the second power, which is the area of a square with sides of 6 units. So some people will say, six squared. A problem would look like 6 2 or 6^2, which appears on computers and some calculators. The third power of a number such as four to the third power would look like this 4. So people will say 4 cubed, since the answer would be the area of a cube with sides of 4 units. Example: 8 2 = 8 8 = = = ^2 = = 100 Do the indicated operation. Write your answer on the line = = = 2. 2 = = =. 5 2 = 8. 6 = = = 9. 7 = = 5. = = = In a series of {2,, 4, 5,...} describe what you would have to add to find the next square number for the next four squares, starting with two squared. 5

5 ,082 10, Order of Operations The biggest rule in mathematics is the Order of Operations. Everyone must have the same rules so that the answers will match. Everyone uses these rules: businesses, engineers, and scientists. Computers and calculators use the rules as well. The rules are four steps: 1. Do the operations with parentheses first. 2. Do exponents.. Perform multiplication or division in order from left to right. 4. Finally, do addition and subtraction from left to right. Examples: (6 ) = =. 9 5 = = = = 15 Do the indicated operations. Write your answer on the line (4 + 7)= 9. (15 9) 92 = = 10. (7 21) (11 + 4) = = = 4. 5(7 )= = 5. 7 = = = (8 10) 15 = = 8. (87 6) = A mnemonic is a good method for remembering a series of things that need to occur in order. The order of operations has many mnemonics. Write your own mnemonic to remember the order of operations. 6

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic