Hayes AM105R Mastering the Standards Grade 5 MATHEMATICS By Jill Evely Osofsky
Mastering the Standards Mathematics Grade 5 By Jill Evely Osofsky 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 Number and Operations Benchmarks, Vocabulary, and Teaching Suggestions...1 Transparency Master...2 Mastery Check Test: Numbers and Operations... Place Value Concepts through Billions and Thousandths...4 Expressing Numbers in Exponential Form...5 Identifying Prime Numbers...6 Estimating and Rounding Numbers...7 Multiplying Larger Numbers...8 Dividing Larger Numbers...9 Adding and Subtracting Decimals...10 Multiplying Decimals...11 Dividing Decimals...12 Adding Fractions...1 Subtracting Fractions...14 Multiplying Fractions...15 Dividing Fractions... Understanding Percents...17 Identifying Fraction, Decimal, and Percent Equivalents...18 Comparing and Ordering Integers...19 Adding Integers...20 Subtracting Integers...21 Algebra Benchmarks, Vocabulary, and Teaching Suggestions...22 Transparency Master...2 Mastery Check Test: Algebra...24 Analyzing Patterns...25 Using Variables to Write Algebraic Expressions...26 Evaluating Expressions with One Variable...27 Identifying Multiplication Properties...28 Substituting Values for Two Variables...29 Graphing Equations...0 Geometry Benchmarks, Vocabulary, and Teaching Suggestions...1 Transparency Master...2 Mastery Check Test: Geometry... Identifying Lines and Using Symbols...4 Measuring and Classifying Angles... Identifying and Classifying Triangles...6 Identifying and Classifying Quadrilaterals...7 Identifying Congruent Figures and Transformations...8 Identifying Attributes of Geometric Solids...9 Identifying Parts of a Circle...40 Problem Solving with Geometry...41 Measurement Benchmarks, Vocabulary, and Teaching Suggestions...42 Transparency Master... Mastery Check Test: Measurement...44 Using Formulas for Perimeter and Area...45 Finding Area of Parallelograms and Triangles...46 Identifying Measures of a Circle...47 Finding the Volume of Solids...48 Finding the Surface Area of Solids...49 Changing Customary Units of Length...50 Changing Customary Units of Weight and Capacity...51 Changing Metric Measures...52 Data Analysis and Probability Benchmarks, Vocabulary, and Teaching Suggestions...5 Transparency Master...54 Mastery Check Test: Data Analysis and Probability...55 Identifying Points on a Coordinate Graph...56 Identifying the Mean, Mode, Median, and Range...57 Interpreting Data in a Line Graph...58 Interpreting Data in a Circle Graph...59 Choosing an Appropriate Graph...60 Finding Probability...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: MATHEMATICS 1
,082 Place Value Concepts through Billions and Thousandths 10, A place value chart shows the value of a digit in a number. 6 billion, 514 million, 291 thousand, 891 and 65 thousandths the value of the 5 in each number. 1. 5,672,16 2. 9,99.052. 742.015 4. Write 4,2,690,8 in expanded form on the line below. Write <, >, or =. 5. 25,494,487,152,494,42 6. 5.88 5.7 7. 777,000,185 777,128,000 8. 0.25 0.250 Order from least to greatest. 9. 9.6, 9.58, 9.95, 9.12 10. 55.2, 56.98, 56.89, 55.2 Write the number in each pair in which 6 has the greater value. 11. 4.65 or 6.45 12. 8.61 or 8. Write a number that meets the following rules. The number must be greater than 1 million. Use the same even number in both the thousands and the thousandths place. The number in both the hundreds and hundredths place must be the same odd number. The number in both the tens and tenths place the same prime number. Describe how you chose your number. 4
4,082 Expressing Numbers in Exponential Form 10 Repeated multiplication of the same number can be shown in exponential form. 10 10 is the base number is the exponent The exponent tells how many times the base is multiplied by itself. Exponential form 10 Expanded form 10 10 10 Standard form 1,000 Write each number using exponents. 1. 10 10 2. 10 10 10. 10 Write each number in exponential form. 4. 10,000 5. 100,000 6. 1,000,000 7. 100 8. 10,000,000 9. 1,000 Write each number in expanded form. 10. 102 11. 105 Write each number in standard form. 12. 102 1. 104 14. 106 A google is 10100. Suppose you had homework using google numbers. Which form of the number would you prefer to use to express the numbers: exponential form, expanded form, or standard form. Describe why. 5
,082 Identifying Prime Numbers 10, A prime number is a number that has exactly 2 factors 1 and itself. A factor tree can be used to find the prime factors of numbers. 0 2 15 2 5 2,, and 5 are the prime factors for 0 Complete each factor tree. 1. 10 2. 12. 0 2 List the prime factors for each number. If a number is prime, write prime. 4. 9 5. 8 6. 19 7. 24 8. 9. 20 10. 6 11. 2 12. 49 1. 14. 44 15. 7 A number is divisible by if the sum of the digits is divisible by. For example, 72 is divisible by because the sum of the digits is 9, and 9 is divisible by. two other divisibility rules you can use to help you find the prime factors of a number. 6