Numeration & Fractions

Transcription

1 Editor Mary S. Jones, M.A. Cover Artist Brenda DiAntonis Managing Editor Karen J. Goldfluss, M.S. Ed. Creative Director Karen J. Goldfluss, M.S. Ed. Numeration & Fractions Art Production Manager Kevin Barnes Art Coordinator Renée Christine Yates Imaging Denise Thomas James Edward Grace Nathan Rivera Includes objectives, practice pages, assessments, and extensions. Topics support national and state standards. Self-contained units are great for review of specific math skills! Publisher Mary D. Smith, M.S. Ed. Authors Gloria Harris, Angela Toohey, and Garda Turner (Revised and rewritten by Teacher Created Resources, Inc.) The classroom teacher may reproduce copies of materials in this book for classroom use only. Reproduction of any part for an entire school or school system is strictly prohibited. No part of this publication may be transmitted, stored, or recorded in any form without written permission from the publisher. Teacher Created Resources, Inc Industry Way Westminster, CA ISBN: Teacher Created Resources, Inc. Reprinted, 2010 Made in U.S.A.

2 Table of Contents Introduction Numbers to 999, Unit 1: Understanding Numbers to 999, Expanded Notation Place Value Rounding Order Powers of Ten Comparisons Assessment What Am I? Activity Unit 2: Working with Numbers to 999, Place Value Expanded Notation Ordering Numerals Rounding Mixed Examples Estimate and Exact Assessment Place Value and Estimation Unit 1: Place Value and Rounding Numbers and Words Decimals Place Value Rounding Whole Numbers Rounding Decimals Did You Know? Assessment Unit 2: Estimation Rounding Hundreds and Thousands.. 37 Estimation and Calculation Rounding Decimals Estimating Measures Estimating Money Estimating Large Numbers Assessment Number Systems Unit 1: Number Systems Roman Numerals More Roman Numerals Binary System Your Number System Codes Ancient Egyptian Assessment Common Fractions Unit 1: Understanding Common Fractions Using Common Fractions Common Fractions and Decimals Equivalent Fractions Comparing Fractions Fractions of a Group Assessment Fraction Festival Activity #8997 Targeting Math: Numeration and Fractions Teacher Created Resources, Inc.

3 Understanding Numbers to 999,999 Unit 1 Place value Rounding Ascending/descending Powers of 10 Comparisons Objectives read and represent large numbers expand large numbers to separate their component parts express large numbers using powers of ten state the place value of any digit in a number count on and back by 100, 1,000, 10,000, and 100,000 compare the relative size of numbers and use <, >, and = recognize patterns in numbers order numbers, ascending or descending round to determine whether a number is close to another number round to assist with estimation compute mentally and with a calculator, after simplifying large numbers show an interest in and an enjoyment of the pursuit of mathematical knowledge by researching facts Language expand, expression, digit, grid, rounded, means is roughly equal to, estimate population, series, ascending, descending Materials/Resources calculators Contents of Student Pages * Materials needed for each reproducible student page Page 8 Expanded Notation expressing large numbers using hundred thousands, ten thousands, thousands, hundreds, tens and ones; adding 100,000, 10,000, 1,000, etc. Page 9 Place Value identifying place value of given digits; writing numerals vertically using aligned placement Page 10 Rounding how to round and estimate; rounding off to any place; estimating using +,, and x * calculators Page 11 Order descending and ascending order Page 12 Powers of Ten using indices to express numerals in powers of ten Page 13 Comparisons smallest, largest, <, >, and ; identifying numbers in a range Page 14 Assessment Page 15 What am I? Activity using clues to find mystery numbers Remember q The use of atlases, almanacs, gazettes, and encyclopedia is very valuable in this work. q Contributions from current event news are also appropriate to help children see the everyday application of understanding large numbers. #8997 Targeting Math: Numeration and Fractions Teacher Created Resources, Inc.

4 Additional Activities q Collect and record population figures for cities in your state. Discuss relative sizes and growth over years. q Model large numbers with base ten blocks where a cube equals 100,000 not 1,000. q Research statistics for the size of the Earth and the Moon. Answers Page 8 Expanded Notation 1. a. 70, , b. 200, c. 500, , , d. 20, a. 10,000, 1,000, 10 b. 100,000, 10,000, 100, 10, 1 c. 100,000, 10,000, 1,000, 4 d. 1,000, 100, a. 3,456, 345, 34, 3 b. 25,645, 2,564, 256, 25, 2 c. 4,680, 468, 46, 4 4. a. 38,056 d. 886,903 g. 297,620 b. 255,980 e. 440,275 h. 902,146 c. 160,750 f. 759,655 i. 75, , , , a. 50,000, 101 b. 4 x 100, 4,700 c. 6,600, 6 Page 9 Place Value 1. a. circled: 6, underlined: 5 b. circled: 4, underlined: 2 c. circled: 5, underlined: 0 d. circled: 2, underlined: 6 e. circled: 1, underlined: 0 f. circled: 7, underlined: 9 g. circled: 4, underlined: 7 h. circled: 9, underlined: 6 2. a. 238,723 d. 4,002 g. 522,000 b. 415,258 e. 699,569 h. 40,865 c. 80,612 f. 370, a. Th c. O e. T b. TTh d. H f. HTh 4. a. 987,654 c. Check individual work. b. 456,789 d. Check individual work. 5. a. 33,890 e. 816,546 i. 721,500 b. 35,890 f. 818,546 j. 741,500 c. 51,660 g. 35,670 k. 266,840 d. 53,660 h. 55,670 l. 286,840 Page 10 Rounding 1. a. T b. T c. F d. T e. F 2. a. 3,000 b. 18,000 c. 624, a. 30,000 b. 210,000 c. 10, a. 500,000 b. 200,000 c. 700, a. 63,000 (63,571) b. 22,000 (22,326) 6. a. b and d 7. a. 250,000 c. 360,000 b. 490,000 d. 4,500, Phillip Page 11 Order 1. a. 3,794, 3,974, 4,397, 7,943, 9,374 b. 17,058, 17,580, 17,850, 18,057, 18,570 c. 13,660, 30,360, 33,630, 36,030, 36,036 d. 174,487, 179,174, 194,487, 197,487, 197, a. 8,480, 8,500, 8,520 b. 8,671, 8,471, 8,271 c. 16,500, 16,750, 17,000 d. 627,995, 628,010, 628, b, c, e 4. Population Order 1. Utah 2. Louisiana 3. Arizona 4. Washington Area Order 1. Louisiana 2. Washington 3. Utah 4. Arizona Page 12 Powers of Ten 1. a. 110 c. 3,000 b. 101,000 d. 700, a. (5 x 10 3 ) b. (7 x 10 4 ) + (1 x 10 3 ) c (4 x 10 3 ) + (7 x 10 2 ) + (8 x 10) d. (7 x 10 5 ) + (6 x 10 4 ) + (5 x 10 3 ) + (4 x 10 2 ) e. 1 x 10 6 f. (1 x 10 6 ) + (8 x 10 5 ) 3. a. (1 x 10 6 ) + (4 x 10 5 ) + (3 x 10 4 ) b. (4 x 10 6 ) + (2 x 10 5 ) c. (1 x 10 6 ) + (8 x 10 5 ) + (1 x 10 4 ) + (7 x 10 3 ) d. (6 x 10 5 ) + (3 x 10 4 ) + (6 x 10 3 ) e. (4 x 10 6 ) + (2 x 10 5 ) + (5 x 10 4 ) f. North Dakota g million h million i million j million k. South Carolina, Kentucky, West Virginia, Idaho, North Dakota 4. a. 778,900; 788,900; 798,900; 808,900 b. 1,653,230; 1,663,230; 1,673,230; 1,683,230 c. 6,382,000; 6,392,000; 6,402,000; 6,412,000 Page 13 Comparisons 1. a. 1,289,899 b. 4,307,100 c. 556, a. 5,995,306 b. 283,299 c. 1,260, a. < b. < c. < d. = e. > f. < 4. a. Chicago, Cairo, London b. Istanbul, Athens, Sydney, Rome, San Francisco-Oakland, Bangkok, Beijing Page 14 Assessment 1. a. Six hundred forty-two thousand, two hundred seventy-five b. 642,276 j. ten thousands c. 643,275 k. 64,227 d. 652,275 l. 642 e. 642,175 m. 642,000 f. 542,275 n. 1,000,000 g. 1,642,275 o. 640,000 h. hundred thousands p. 600, ,000 + i. tens 2, a. 2 x 1,000 c. 700 x 100 b. 50 x 10,000 d. 3, a. < b. > c. > d. < e. = 4. 6,547,740, 767,566, 657,750, 647, a. 399,056, 409,056, 419,056 b. 1,577,765, 1,587,765, 1,597,765 Page 15 What Am I? Activity 1. 13, , , ,805,077 Teacher Created Resources, Inc. #8997 Targeting Math: Numeration and Fractions

5 Understanding Numbers to 999,999 Expanded Notation Name Date 1. Expand these numbers. Example: 34,689 = 30, , a. 76,834 = b. 200,909 = c. 585,600 = d. 20,906 = 2. Complete the following expressions. a. 28,090 = 2 x + 8 x + 9 x b. 640,921 = 6 x + 4 x + 9 x + 2 x + c. 398,004 = 3 x + 9 x + 8 x + d. 5,750 = 5 x + 7 x + 5 x 3. Break down each of the following numbers by place value. Example: 2,543,800 = 25,438 hundreds, 2,543 thousands, 254 ten thousands, 25 hundred thousands a. 345,600 = hundreds, thousands, ten thousands, hundred thousands b. 2,564,500 = hundreds, thousands, ten thousands, hundred thousands, millions c. 4,680,000 = thousands, ten thousands, hundred thousands, millions 4. Add 10,000 to each number. a. 28,056 b. 245,980 c. 150,750 d. 876,903 e. 430,275 f. 749,655 g. 287,620 h. 892,146 i. 65, The numeral 365,298 fell apart. Find all of its parts, shade them, and put it back together. 185,000 36,000 5, , ,000 60,000 6, ,298 = Circle each expression that does not have the same value as the number given. a. 502,961 two thousands 50,000 6 x ,961 b. 47,802 4 x , ,000 7 x 10 x 10 x 10 c. 99,660 9 x 100 x 100 6, ,000 6 x #8997 Targeting Math: Numeration and Fractions Teacher Created Resources, Inc.

6 Understanding Numbers to 999,999 Place Value Name Date 1. For each of the following numbers, circle the digit in the ten thousands place and underline the digit in the thousands place. a. 165,890 b. 642,541 c. 50,700 d. 926,809 e. 110,005 f. 579,300 g. 47,845 h. 396, Write the following numbers in standard form using the place value grid. Example: seventeen thousand forty-seven a. two hundred thirty-eight thousand, seven hundred twenty-three b. four hundred fifteen thousand, two hundred fifty-eight c. eighty thousand, six hundred twelve d. four thousand two e. six hundred ninety-nine thousand, five hundred sixty-nine f. three hundred seventy thousand, three hundred seventy-eight g. five hundred twenty-two thousand h. forty thousand, eight hundred sixty-five 3. In each of the following numbers, identify the place value of the 3. a. 143,800 b. 738,120 c. 948,963 d. 590,368 e. 207,437 f. 380, Use the numerals 4, 5, 6, 7, 8, and 9 to: a. write the largest number possible. b. write the smallest number possible. c. write a five-digit number where the 8 has the smallest value. d. write a six-digit number where the 7 has the largest value. 5. Write numbers smaller and larger than those given. HTh TTh Th H T O ,000 smaller 1,000 larger a. 34,890 b. c. 52,660 d. e. 817,546 f. 10,000 smaller 10,000 larger g. 45,670 h. i. 731,500 j. k. 276,840 l. Teacher Created Resources, Inc. #8997 Targeting Math: Numeration and Fractions

7 Understanding Numbers to 999,999 Rounding Name Date 1. Circle true or false for the statements about this number: 487,264 a. Rounded to the nearest ten, this number is 487,260. true false b. Rounded to the nearest hundred, this number is 487,300. true false c. Rounded to the nearest thousand, this number is 488,000. true false d. Rounded to the nearest ten thousand, this number is 490,000. true false e. Rounded to the nearest hundred thousand, this number is 400,000. true false 2. Round the following to the nearest thousand. a. 2,564 b. 17,689 c. 623, Round the following to the nearest ten thousand. a. 34,678 b. 209,467 c. 12, Round the following to the nearest hundred thousand. a. 458,982 b. 231,097 c. 749, Round to the nearest thousand and estimate the answer. Check your estimate using a calculator. a. 37, ,081 = Est. Ans. b. 78,234 55,908 = Est. Ans. 6. Circle the correct statements. ( means is roughly equal to.) a. 9,580 10,000 b. 245, ,000 c. 760, ,000 d. 225, , Round to the nearest ten thousand and make an estimate of the product. Choose your answer from the following: 360,000; 4,500,000; 490,000; 250,000 a. 48,644 x 5 b. 65,187 x 7 c. 93,277 x 4 d. 500,378 x 9 = x 5 = x 7 = x 4 = x 9 = = = = 8. Damon said he thought the population of Australia was 18,400,000. Rani said it was more like 18,100,000, and Phillip said it was 18,350,000. The population of Australia is thought to be 18,261,469. Who was closest? 10 #8997 Targeting Math: Numeration and Fractions Teacher Created Resources, Inc.

8 Understanding Numbers to 999,999 Order Name Date 1. Write each set of numbers in order, from smallest to largest. a. 3,794 4,397 9,374 7,943 3,974 b. 17,850 17,580 18,570 18,057 17,058 c. 36,036 36,030 33,630 30,360 13,660 d. 197, , ,174, 174, , Write the next three numbers in each pattern. a. 8,420, 8,440, 8,460, b. 9,271, 9,071, 8,871, c. 15,750, 16,000, 16,250, d. 627,950, 627,965, 627,980, 3. Mark an X next to the sets of numbers that are in ascending order. a. 285,575, 285,755, 275,575, 255,275 b. 354,650, 356,650, 365,550, 365,650 c. 822,020, 822,040, 902,882, 982,020 d. 406,288, 406,822, 406,298, 406,889 e. 25,035, 25,053, 25,350, 25, Arrange the states according to area and population, smallest to largest. State Population Area (sq. mi.) Population Order Area Order Washington 6,287,759 71, Louisiana 4,523,628 51, Utah 2,469,585 84, Arizona 5,939, , Teacher Created Resources, Inc. #8997 Targeting Math: Numeration and Fractions 11