Math You ve Gotta Have This Book!

Transcription

1 If You re Trying to Get Better Grades & Higher Test Scores in Math You ve Gotta Have This Book! Grades 4-6 By Imogene Forte & Marjorie Frank Incentive Publications, Inc. Nashville, Tennessee

2 Illustrated by Kathleen Bullock Cover by Geoffrey Brittingham Edited by Patience Camplair ISBN Copyright 2005 by Incentive Publications, Inc., Nashville, TN. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photocopying, recording, or otherwise) without written permission from Incentive Publications, Inc., with the exception below. Pages labeled with the statement 2005 by Incentive Publications, Inc., Nashville, TN are intended for reproduction. Permission is hereby granted to the purchaser of one copy of IF YOU RE TRYING TO GET BETTER GRADES & HIGHER TEST SCORES IN MATH, YOU VE GOTTA HAVE THIS BOOK! GRADES 4 6 to reproduce these pages in sufficient quantities for meeting the purchaser s own classroom needs only PRINTED IN THE UNITED STATES OF AMERICA

3 GET READY... GET SET... GET SHARP 11 How to Use This Book 12 GET READY 13 Get Motivated 14 Get Organized 18 Get Your Space Organized 18 Get Your Stuff Organized 19 Get Your Time Organized 20 Get Your Assignments Organized 21 Get Yourself Organized 22 Get Healthy 23 Get a Grip (on Study Habits) 24 GET SET 27 Get Familiar with Math Tools 28 Know Your Numbers 28 Know Your Properties 30 Know Your Mathematical Symbols 32 Know Your Formulas 33 Know Your Measurement Units 34 Measurement Equivalents 37 Get Tuned-Up with Thinking Skills 38 Get Polished in Problem-Solving Skills 42 Get Serious About Study Skills 46 Better Listening 46 Careful Reading 47 How to Prepare for a Test 48 How to Take a Test 50

4 GET SHARP... on Number Concepts & Relationships 53 Numbers & Sets 54 The Roman Numeral System 56 The Decimal System 57 Counting Numbers 57 Whole Numbers 58 Even & Odd Numbers 58 Prime & Composite Numbers 59 Place Value for Whole Numbers 60 Reading & Writing Whole Numbers 62 Rounding Whole Numbers 64 Estimating 65 Factors 66 Multiples 67 Powers, Exponents, & Scientific Notation 68 Squares & Square Roots 69 Integers 70 Fractions 71 Decimals 72 Comparing & Ordering Numbers 73 Patterns 74 GET SHARP... on Operations with Whole Numbers 75 Addition 76 Subtraction 78 Multiplication 80 Multiplication with Renaming 81 Multiplication with Multiples of Ten 81 Multiplication by Larger Numbers 82 Division 83 Dividing a Number by Itself 84 Dividing a Number by One 84 Divisibility 84 Division with One-Digit Divisors 85 Division with Multiples of Ten 85 Division with Larger Divisors 86 Averages 87 Which Operation? 88 Some Interesting Number Tricks 90 Fast Facts 93 Addition & Subtraction Matrix 93 Multiplication & Division Matrix 94

5 GET SHARP... on Fractions & Decimals 95 Fractions 96 Proper and Improper Fractions 96 Reading and Writing Fractions 96 Fractions as Part of a Whole 97 Fractions as Part of a Set 97 Mixed Fractional Numbers 98 How to Change Mixed Numbers to Improper Fractions 98 How to Change Improper Fractions to Mixed Numbers 98 Equivalent Fractions 99 Fractions in Lowest Terms 100 How to Find the GCF of Two or More Numbers 100 How to Reduce a Fraction to Lowest Terms 100 Like and Unlike Fractions 101 How to Change Unlike Fractions into Like Fractions 101 Comparing & Ordering Fractions 102 Adding & Subtracting Fractions 103 How to Add & Subtract Like Fractions 103 How to Add & Subtract Unlike Fractions 103 How to Add & Subtract Mixed Numerals 103 Multiplying Fractions 104 How to Multiply Fractions 104 How to Multiply a Fraction by a Whole Number 104 How to Multiply Mixed Numbers 104 Dividing Fractions 105 How to Divide Fractions 105 How to Divide a Whole Number by a Fraction 105 How to Divide Mixed Numbers 105 Ratio 106 Terms of a Ratio 106 Reducing Ratios to Lowest Terms 107 Changing Fractions to Whole Number Ratios 107 Equivalent Ratios 107 Using Equivalent Ratios to Find Missing Numbers 107 Rates 108 Reducing Rates to Find Quantities 108 Using Equivalent Ratios to Find Other Rates 108 Proportions 109 Decimals 110 Terminating Decimals 110 Repeating Decimals 110

6 Mixed Decimal Numbers 110 Place Value in Decimals 111 Reading & Writing Decimals 111 Rounding Decimals 111 Operations with Decimals 112 Adding & Subtracting Decimals 112 Multiplying Decimals 112 Dividing Decimals 113 Money 114 Operations with Money 115 Fractions & Decimals 116 How to Write a Fraction as a Decimal 116 How to Write a Decimal as a Fraction 116 Percent 117 How to Write a Decimal as a Percent 117 How to Write a Percent as a Decimal 117 How to Write a Fraction as a Percent 117 How to Find a Percentage of a Number 118 How to Tell What Percent One Number is of Another 118 How to Find the Base When You Know the Percent 118 Taxes, Tips, & Discounts 119 Simple Interest 120 GET SHARP... on Geometry & Measurement 121 Plane Geometry 122 Points, Lines, & Planes 122 Angles 124 Angle Relationships 125 Parallel Lines & Angles 126 Bisecting Line Segments & Angles 127 Plane Figures 128 Polygons 128 Triangles 129 Quadrilaterals 130 Circles 131 Congruent & Similar Figures 132 Tessellations, Transformations, & Symmetry 133 Space Geometry 134 Space Figures 134 Measurement 136 Measuring Weight 136

7 Measuring Length 137 Measuring Perimeter & Circumference 138 Measuring Area of Polygons 140 Measuring Surface Area of Space Figures 142 Measuring Volume of Space Figures 144 Measuring Capacity 146 Measuring the Earth 147 Measuring Time 148 Measuring Rate 149 Measuring Temperature 150 More Measures 151 GET SHARP... on Statistics, Graphing & Probability 153 Statistics 154 What is Statistics? 154 Range, Mean, Median, & Mode 155 Frequency 156 Graphing & Statistics 157 Bar Graphs 157 Histograms 158 Circle Graphs 159 Pictographs 160 Line Graphs 161 Scattergrams 162 Probability 163 What is Probability? 163 Outcomes & Events 164 Outcomes of Two Actions 165 Probability of Independent Events 166 Probability of Dependent Events 167 Tree Diagrams 168 The Counting Principle 169 Permutations & Combinations 170 Odds 171 Sampling 172 GET SHARP... on Pre-Algebra 173 Integers 174 Operations with Integers 176 Expressions & Equations 178 Mathematical Expressions 178

8 Equations 180 Inverse Operations 181 Solving Equations 182 Solving Multi-Step Equations 184 Problem Solving with Equations 186 Graphing on a Coordinate Plane 188 GET SHARP... on Problem Solving 191 Approaching Problems 192 The Problem-Solving Process 194 Problem-Solving Strategies 196 Guess & Check 196 Trial & Error 196 Simplify 197 Find a Common Element 197 Make a Model 198 Draw a Diagram or Picture 199 Make a Table or Graph 200 Estimate 201 Extend a Pattern 201 Work Backwards 202 Use a Formula 202 Use Mental Math 203 Write an Equation 204 Write a Proportion 204 Use Logic 205 Solving Open-Ended Problems 206 Reviewing Your Answers 207 Problem-Solving Process Scoring Guide 208 GET SHARP... on Math Terms 209 Good Words to Know for Number Concepts & Relationships 210 Good Words to Know for Operations & Computations 214 Good Words to Know for Fractions & Decimals 217 Good Words to Know for Geometry & Measurement 219 Good Words to Know for Statistics, Graphing, & Probability 229 Good Words to Know for Pre-Algebra 231 Good Words to Know for Problem Solving 233 INDEX 235

9 Numbers & Sets A number is an idea! It is a mathematical idea about the amount contained in a set. A set is a collection of items called members or elements. This set has 6 members or elements. A numeral is a symbol that represents a number. A Venn diagram can be used to show the members of a set. (See diagram above.) Here is another way to show the members of a set: A finite set has a specific number of members. The set shown above is a finite set. An infinite set has an unlimited number of members. An empty set has no elements. It is also called a null set. The symbols { } and O represent an empty set. 54 Get Sharp: Numbers & Number Systems Better Grades & Higher Test Scores / MATH gr. 4 6 Copyright 2005 by Incentive Publications, Inc., Nashville, TN.

10 Subsets are sets made of any member of a set or any combination of members of a set. B is a subset of A. The symbol B A. means is a proper subset of. Equivalent sets are sets having the same number of members. C and D are equivalent sets. An intersection of sets is the set of members common to each of two or more sets. The symbol represents the intersection of sets. Q R. The intersection of sets Q and R is T, X, and P. A union of sets is a set containing the combined members of two or more sets. The symbol represents the union of sets. X Z. The union of sets X and Z is {8; 13; 20; 50; 77; 109; 444; 3,105; 100,000}. Better Grades & Higher Test Scores / MATH gr. 4 6 Copyright 2005 by Incentive Publications, Inc., Nashville, TN. Get Sharp: Numbers & Number Systems 55

11 The Roman Numeral System Number systems have been around for a very long time. Back in the days of the cave dwellers, people counted belongings and kept track of the calendar. One ancient system dates back over 2000 years, to the Roman Empire. The Roman Numeral system uses letters to represent numbers. In the Roman system, seven letters represent numbers. I = 1 V= 5 X = 10 L= 50 C = 100 D = 500 M = 1,000 Other numerals are made from combinations of the letters. 4 = 5 1 (one less than 5) or IV 9 = 10 1 IX 40 = XL 90 = XC 400 = CD 900 = 1, CM Can you read these numbers? XIX (19) MDCXCVII (1,697) XXXIV (34) MCMXCIX (1,999) CDLXXXIV (484) MMII (2,002) CMXLII (942) MMCMXC (2,990) 56 Get Sharp: Numbers & Number Systems Better Grades & Higher Test Scores / MATH gr. 4 6 Copyright 2005 by Incentive Publications, Inc., Nashville, TN.

12 The Decimal System The word decimal comes from a Latin root decem that means ten. A decimal system of numbers uses ten symbols. The decimal system we use today is the Arabic system. The ten symbols used are the Arabic numerals 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal system contains different sets of numbers (counting numbers, whole numbers, odd and even numbers, prime and composite numbers, integers, and rational numbers). Counting Numbers The set of counting numbers begins with 1 and continues into infinity. Sometimes these are called natural numbers. They are used for counting. You can count by ones: 1, 2, 3, 4... OR 237, 238, 239, Or you can skip count: (skipping over numbers in any regular interval you choose)... by fives... by tens 5, 10, 15, 20, 25, , 80, 90, 100, 110, by twenty-fives... fifties 225, 250, 275, , 950, 1,000, 1, by hundreds... by five hundreds 900, 1,000, 1, , 1,000, 1,500, 2, You can count backwards, too: 1,000, 999, 998, 997, 996, , 86, 84, 82, 80, 78, 76, , 495, 490, 485, 480, , 720, 710, 700, 690, 680, Better Grades & Higher Test Scores / MATH gr. 4 6 Copyright 2005 by Incentive Publications, Inc., Nashville, TN. Get Sharp: Numbers & Number Systems 57

13 Whole Numbers Whole numbers make up a set of numbers within the decimal system. The set of whole numbers includes 1 and all the numbers that follow it into infinity, PLUS the number zero (0) Even & Odd Numbers 58 Get Sharp: Numbers & Number Systems Better Grades & Higher Test Scores / MATH gr. 4 6 Copyright 2005 by Incentive Publications, Inc., Nashville, TN.