Review, Practice, & Mastery of

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1 Review, Practice, & Mastery of Grade 3 Reviewers Katie Copeland Glen Allen Elementary School Glen Allen, VA Sarah Costley Harry E. James Elementary Hopewell, VA Vicki Hill Westover Hills Elementary Richmond, VA Amy Lamb Northumberland Middle School Heathsville, VA Robin Lillis St. Theresa School Ashburn, VA Susanne Moore Harry E. James Elementary School Hopewell, VA Zaida Ramos-Williams Westover Hills Elementary School Richmond, VA Sally Springer Shelburne Middle School Staunton, VA 2007 Perfection Learning Corporation All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the publisher. Printed in the United States of America PP For information, contact Perfection Learning Corporation 1000 North Second Avenue, P.O. Box 500 Logan, Iowa Phone: Fax: ISBN

2 To the Student This book will help you review, practice, and master the Virginia Mathematics Standards of Learning. Here are the steps to follow to use this book. 1. Take the Tryout Test and check your answers. Use the chart at the bottom of this page to find out your strengths and weaknesses in the areas covered. Don t be discouraged if you don t get all the answers right or if you don t understand some questions. Remember the questions that are hard for you to answer. They will be the types of questions you need to work on the most. 2. Work through the lessons that follow the Tryout Test. Each lesson reviews example items and provides a practice test based on the Standards of Learning. Fill in the Keeping Score chart on page 91 as you complete each practice test. 3. After completing all the lessons, take the Mastery Test. Your score on this test will show your understanding of the Standards of Learning. By following the steps outlined above, you will increase your mastery of the Virginia Mathematics Standards of Learning. Lesson Tryout Test Items Mastery Test Items 1 Number Sense 1, 3, 4, 6, 9, 10, 11, 13 1, 3, 4, 6, 9, 10, 11, 13 2 Fractions and Decimals 2, 5, 7, 8, 12 2, 5, 7, 8, 12 3 Computation and Estimation 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 4 Measurement 25, 26, 27, 28, 29, 30, 31 25, 26, 27, 28, 29, 30, 31 5 Geometry 32, 33, 34, 35, 36 32, 33, 34, 35, 36 6 Statistics and Probability 37, 38, 39, 40, 41, 42, 43 37, 38, 39, 40, 41, 42, 43 7 Patterns, Functions, and Algebra 44, 45, 46, 47, 48, 49, 50 44, 45, 46, 47, 48, 49, 50 To the Student Perfection Learning No reproduction permitted.

3 Table of Contents Tips for Taking Tests..... Inside Front Cover To the Student Tryout Test Number Sense [3.1 4] Reading and Writing Whole Numbers.. 16 Place Value Rounding Comparing Whole Numbers Relating Addition and Subtraction Relating Multiplication and Division Test Practice Fractions and Decimals [3.5 7] Parts of a Whole Parts of a Set Fractions on a Number Line Comparing Fractions Reading and Writing Decimals Test Practice Computation and Estimation [3.8 12] Adding Whole Numbers Subtracting Whole Numbers Estimating Sums and Differences Adding and Subtracting Mentally Multiplication Facts Division Facts Multiplying and Dividing Two-Digit Numbers Adding and Subtracting Fractions Adding and Subtracting Decimals Test Practice Telling Time Equivalent Periods of Time Temperature Test Practice Geometry [ ] Flat Shapes Solid Shapes Line Segments Angles Congruent Shapes Symmetry Test Practice Statistics and Probability [ ] Collecting and Organizing Data Line Plots Pictographs Bar Graphs Probability Test Practice Patterns, Functions, and Algebra [ ] Patterns Equality Addition and Multiplication Properties 76 Test Practice Mastery Test Keeping Score Finding Percent Rulers Inside Back Cover 4 Measurement [ ] Counting Money Comparing Money Amounts Making Change Estimating Height Measuring Length Capacity Weight Perfection Learning No reproduction permitted. Table of Contents

4 Number Sense Reading, Writing, and Comparing Whole Numbers Place Value Rounding Relating Addition, Subtraction, Multiplication, and Division Directions: Read each question and choose the best answer. Reading and Writing Whole Numbers 1 The population of a city is five hundred four thousand, one hundred sixty-two. Which answer shows this number in standard form? A 5,004,000,162 B 540,162 C 504,162 D 54,162 Ways to Express Numbers Word form: Seven hundred forty thousand, six hundred two Standard form: 740,602 Expanded form: 700, , Step-By-Step Example 1 gives the number in word form. A place-value chart can help you write the number in standard form. hundred thousands ten thousands 5 0 4, Thousands Period thousands hundreds tens Ones Period ones 1 Read the number up to the word thousand. five hundred four 2 Write the number 504 and a comma. 504, 3 Then read the rest of the number. one hundred sixty-two 4 Write 162 to the right of the comma. 16 Number Sense Perfection Learning No reproduction permitted.

5 Place Value 2 What digit is in the thousands place in 136,579? F 3 G 5 H 6 J 7 Rounding 3 Maxwell the moose weighs 883 pounds. Step-By-Step For example 2, you can use a placevalue chart to find the digit in the thousands place. 1 Write the number in a place-value chart. hundred thousands ten thousands thousands hundreds tens ones 1 3 6, Find the answer choice that matches the digit in the thousands place. How much does Maxwell weigh to the nearest ten pounds? A 800 lb B 880 lb C 890 lb D 900 lb Tip Circle the place you are rounding to. Then look at the place to the right. If the number to the right is... 5 or more, round up; 4 or less, round down. Step-By-Step You must round the number 883 to answer example 3. 1 To round to the nearest ten, circle the digit in the place you will round to Look at the digit to the right of that place. If the digit is 0, 1, 2, 3, or 4, round down. If the digit is 5, 6, 7, 8, or 9, round up. Should you round up or down? I should round. 3 The digit in the rounding place stays the same if you round down. It increases by one digit if you round up. Write zeros in the places after the rounding digit. To the nearest ten, 883 rounds to Perfection Learning No reproduction permitted. Number Sense 17

6 Comparing Whole Numbers 4 Ben has 4,199 stamps. Zoe has 4,287 stamps. Which number sentence correctly compares these numbers? F 4,199. 4,287 G 4,287, 4,199 H 4,199, 4,287 J 4, ,287 Remember... Use these symbols to compare numbers., means is less than 4, 5. means is greater than means is equal to Step-By-Step Follow these steps to answer example 4. 1 Start with the largest place and compare the digits. In this case, both numbers start with 4 in the thousands place, so move on to the hundreds place. 2 Compare the hundreds digits. 1 is less than 2, so you know the numbers are not equal. You also know that 4,199 is less than 4, Write, or. in the boxes below to make true statements. Find the answer choice that matches one of the true statements. 4,199 4,287 4,287 4,199 Relating Addition and Subtraction 5 Jennifer used the fact to solve a different problem. Which could be the problem she was solving? A B C D Remember... Fact families can help you use addition facts to solve subtraction problems Think It Through For example 5, look for a problem that uses the numbers 6, 7, and 13. Remember that is one of four addition and subtraction facts that uses these numbers. The other facts are: Which addition or subtraction problem matches one of these facts? 18 Number Sense Perfection Learning No reproduction permitted.

7 Relating Multiplication and Division 6 Which multiplication fact can help you solve this problem? F G H J Step-By-Step For example 6, remember that multiplication facts can help you solve division problems. 1 Think: What number times 6 is equal to 42? This fact will help you find the quotient for Tip Two factors and a product give you the four number sentences in a fact family Fact families can help you use multiplication facts to solve division problems. 7 Which number makes this open sentence true? A 5 B 32 C 48 D Step-By-Step The number sentence in example 7 has a missing factor. Use the related division fact to find the missing factor. 1 Write the problem and the related division fact Divide 40 by 8 to find the answer. Go for it! Perfection Learning No reproduction permitted. Number Sense 19

8 Test Practice 1 Test Practice 1: Number Sense Estimated time: 30 minutes Directions: Read each question and choose the best answer. 1 Which multiplication fact can help you solve this problem? A B C D Look at the number below. Which digit is in the ten-thousands place? F 0 G 3 H 5 J 7 305,712 3 The population of Grand Junction is 56,277. Which choice shows 56,277 in written form? A Fifty-six thousand, two hundred seven B Fifty-six thousand, two hundred seventy-seven C Five hundred sixty thousand, two hundred seventy-seven D Five hundred six thousand, two hundred seventy-seven 4 There were 2,463 tickets sold to a concert. What is 2,463 rounded to the nearest hundred? F 2,000 G 2,400 H 2,460 J 2,500 5 Which of these is true? A B C 612, 576 D Isadora used one of the number sentences below to solve this problem Which number sentence did she use? F G H J Which choice shows one hundred fiftytwo thousand, twenty-eight written in standard form? A 15,228 B 152,028 C 152,280 D 100,052,028 8 A total of 6,745 people attended a county fair. To the nearest thousand, how many people attended the fair? F 6,000 G 6,700 H 6,800 J 7, Perfection Learning No reproduction permitted.

9 Test Practice 1 9 In what place is the digit 6 in four thousand, two hundred sixty? A ones B tens C hundreds D thousands 10 Travis drove 1,255 miles in March and 1,279 miles in April. Which choice correctly compares the miles driven? F 1,255. 1,279 G 1,255, 1,279 H 1, ,255 J 1,279, 1, Which number makes this number sentence true? A 9 B 8 C 7 D Which statement correctly compares 5,055 and 5,255? F 5,055 is greater than 5,255. G 5,255 is equal to 5,055. H 5,055 is less than 5,255. J 5,255 is less than 5,055. Points Earned Total = 12 Perfection Learning No reproduction permitted. 21

10 Teacher Guide Grade 3

11 To the Teacher The Review, Practice, and Mastery program is a refresher course. It provides a self-directed approach to reviewing and practicing the Virginia Mathematics Standards of Learning. Use the following steps to incorporate Review, Practice, and Mastery into your classroom. 1. Have students take the Tryout Test and check their answers. Then have them use the reproducible Skills Chart on page 6 of this teacher guide to assess their strengths and weaknesses in the areas covered. You may wish to have students enter their answers in the Student Information and Answer Sheet on page 8 of this teacher guide. 2. Have students work through the lessons, paying close attention to the areas in which they need improvement. Each lesson is followed by a practice test that focuses on the skills covered in the lesson. Have students fill in the Keeping Score chart on page 91 of the student book after they complete each test. 3. After completing all the lessons, have students take the Mastery Test to check their progress. Then have them complete the Skills Chart on page 7 of this teacher guide. They can compare their totals with those from the Tryout Test. They can also enter their answers on the Student Information and Answer Sheet on page 9 of this teacher guide. The chart that begins on page 10 of this teacher guide correlates the lessons to the Virginia Mathematics Standards of Learning. Lesson Tryout Test Items Mastery Test Items 1 Number Sense 1, 3, 4, 6, 9, 10, 11, 13 1, 3, 4, 6, 9, 10, 11, 13 2 Fractions and Decimals 2, 5, 7, 8, 12 2, 5, 7, 8, 12 3 Computation and Estimation 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 4 Measurement 25, 26, 27, 28, 29, 30, 31 25, 26, 27, 28, 29, 30, 31 5 Geometry 32, 33, 34, 35, 36 32, 33, 34, 35, 36 6 Statistics and Probability 37, 38, 39, 40, 41, 42, 43 37, 38, 39, 40, 41, 42, 43 7 Patterns, Functions, and Algebra 44, 45, 46, 47, 48, 49, 50 44, 45, 46, 47, 48, 49, 50 2 Perfection Learning Review, Practice, and Mastery Virginia Mathematics Grade 3

12 Tryout Test Skills Chart Score your answers on the Tryout Test, then use this chart to find your strengths and weaknesses in the skills covered on the Mathematics part of the Virginia state test. 1. Place the number of points earned in each white box. For each incorrect answer, place a 0 in the white box. 2. Add each column and write the total points earned in the box at the bottom of the column. 3. For example, if you answer questions 1 and 3 correctly, you have 2 out of 8 points on the Number Sense (Lesson 1) part of the Math test. You may want to focus on these skills as you work through the lessons. Question Total /8 /5 /11 /7 /5 /7 /7 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 6 Perfection Learning Review, Practice, and Mastery Virginia Mathematics Grade 3

13 Virginia Standards of Learning This chart correlates the Grade 3 Virginia Mathematics Standards of Learning to the lessons in Review, Practice, and Mastery. Lessons Lesson 1 Number Sense REPORTING CATEGORY: Number and Number Sense Grade Three SOL in This Reporting Category: 3.1 The student will read and write six-digit numerals and identify the place value for each digit. 3.2 The student will round a whole number, 9,999 or less, to the nearest ten, hundred, and thousand. 3.3 The student will compare two whole numbers between 0 and 9,999, using symbols (>, <, or =) and words (greater than, less than, or equal to). 3.4 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. Students will use these relationships to solve problems such as = 8 and 8 3 =. Lesson 2 Fractions and Decimals 3.5 The student will a) divide regions and sets to represent a fraction; and b) name and write the fractions represented by a given model (area/ region, length/measurement, and set). Fractions (including mixed numbers) will include halves, thirds, fourths, eighths, and tenths. 3.6 The student will compare the numerical value of two fractions having like and unlike denominators, using concrete or pictorial models involving areas/regions, lengths/measurements, and sets. 3.7 The student will read and write decimals expressed as tenths and hundredths, using concrete materials and models. REPORTING CATEGORY: Computation and Estimation Lesson 3 Computation and Estimation Grade Three SOL in This Reporting Category: 3.8 The student will solve problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping, using various computational methods, including calculators, paper and pencil, mental computation, and estimation. 3.9 The student will recall the multiplication and division facts through the nines table The student will represent multiplication and division, using area and set models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less The student will add and subtract with proper fractions having like denominators of 10 or less, using concrete materials and pictorial models representing areas/regions, lengths/measurements, and sets The student will add and subtract with decimals expressed as tenths, using concrete materials, pictorial representations, and paper and pencil. 10 Perfection Learning Review, Practice, and Mastery Virginia Mathematics Grade 3

14 Lessons Lesson 4 Measurement REPORTING CATEGORY: Measurement and Geometry Grade Three SOL in This Reporting Category: 3.13 The student will determine by counting the value of a collection of bills and coins whose total value is $5.00 or less, compare the value of the coins or bills, and make change The student will estimate and then use actual measuring devices with metric and U.S. Customary units to measure a) length inches, feet, yards, centimeters, and meters; b) liquid volume cups, pints, quarts, gallons, and liters; and c) weight/mass ounces, pounds, grams, and kilograms The student will tell time to the nearest five-minute interval and to the nearest minute, using analog and digital clocks The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used. Lesson 5 Geometry 3.18 The student will analyze two-dimensional (plane) and three-dimensional (solid) geometric figures (circle, square, rectangle, triangle, cube, rectangular solid [prism], square pyramid, sphere, cone, and cylinder) and identify relevant properties, including the number of corners, square corners, edges, and the number and shape of faces, using concrete models The student will identify and draw representations of line segments and angles, using a ruler or straightedge The student, given appropriate drawings or models, will identify and describe congruent and symmetrical two-dimensional (plane) figures, using tracing procedures. Perfection Learning Review, Practice, and Mastery Virginia Mathematics Grade 3 11

15 Lessons Lesson 6 Statistics and Probability REPORTING CATEGORY: Probability and Statistics Grade Three SOL in This Reporting Category: 3.21 The student, given grid paper, will a) collect and organize data on a given topic of his/her choice, using observations, measurements, surveys, or experiments; and b) construct a line plot, a picture graph, or a bar graph to represent the results. Each graph will include an appropriate title and key The student will read and interpret data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data The student will investigate and describe the concept of probability as chance and list possible results of a given situation. REPORTING CATEGORY: Patterns, Functions, and Algebra Lesson 7 Patterns, Functions, and Algebra Grade Three SOL in This Reporting Category: 3.24 The student will recognize and describe a variety of patterns formed using concrete objects, numbers, tables, and pictures, and extend the pattern, using the same or different forms (concrete objects, numbers, tables, and pictures) The student will a) investigate and create patterns involving numbers, operations (addition and multiplication), and relations that model the identity and commutative properties for addition and multiplication; and b) demonstrate an understanding of equality by recognizing that the equal sign (=) links equivalent quantities, such as 4 3 = Perfection Learning Corporation The purchase of this book entitles an individual teacher to reproduce certain pages for use in the classroom. This permitted use of copyrighted material does not extend beyond the building level. Reproduction, transmittal, or retrieval of this work is prohibited without written permission from the publisher. Printed in the United States of America PP Perfection Learning Corporation 1000 North Second Avenue, P.O. Box 500 Logan, Iowa Phone: Fax: perfectionlearning.com 72330