0 1620 3681937 1 wag MODULE GRAPE THREE MATHEMATICS: PATTE RN$ EVERYWHERE Home Instructor’s Guide: Days 10-18 and Assignment Booklet 3B Grade Three Mathematics Module 3: Patterns Everywhere Home Instructor’s Guide: Days 10-18 and Assignment Booklet 3B Learning Technologies Branch ISBN 0-7741-2308-7 This document is intended for You may find the following Internet sites useful: Students / • Alberta Learning, http://www.learning.gov.ab.ca Teachers y • Learning Technologies Branch, http://www.learning.gov.ab.ca/ltb • Learning Resources Centre, http://www.lrc.leaming.gov.ab.ca Administrators The use of the Internet is optional. Exploring the electronic information superhighway can be Home Instructors / educational and entertaining. However, be aware that these computer networks are not censored. General Public Students may unintentionally or purposely find articles on the Internet that may be offensive or inappropriate. As well, the sources of information are not always cited and the content may not be Other accurate. Therefore, students may wish to confirm facts with a s econd source. ALL RIGHTS RESERVED Copyright © 2 002, the Crown in Right of Alberta, as represented by the Minister of Learning, Alberta Learning, 10155 - 1 02 Street, Edmonton, Alberta T5J 4L5. All rights reserved. Additional copies may be obtained from the Learning Resources Centre. No part of this courseware may be reproduced in any form, including photocopying (unless otherwise indicated), without the written permission of Alberta Learning. Every effort has been made both to provide proper acknowledgement of the original source and to comply with copyright law. If cases are identified where this effort has been unsuccessful, please notify Alberta Learning so that appropriate corrective action can be taken. IT IS STRICTLY PROHIBITED TO COPY ANY PART OF THESE MATERIALS UNDER THE TERMS OF A LICENCE FROM A COLLECTIVE OR A LICENSING BODY. UNIVERSITY LIBRARY Module 3 MODULE 3: PATTERNS EVERYWHERE DAY lO: In today’s lesson, the student learns how to use the calculator to skip count by 2s, 5s, 10s, and 100s. If y ou do not have a T I-108 calculator, you may have to modify the instructions for some of the activities. DAY lO: LESSON 1 Answers 1. 5 2. 10 3. 35 4. 352 5. 357 362 367 372 6. a. 738 743 748 753 758 763 b. 951 956 961 966 971 976 c. 497 502 507 512 517 522 7. a. 578 588 598 608 618 628 b. 793 803 813 823 833 843 c. 489 499 509 519 529 539 8. a. 567 569 571 573 575 577 b. 902 904 906 908 910 912 c. 599 601 603 605 607 609 DAY lO: LESSON 2 Answers Estimates and times will vary. Guesses between 30 to 60 seconds are fairly accurate for counting by Is. Most students will take 30 to 45 seconds to count by Is to 100. The student should realize that it will take about half as much time to count by 2s as by Is. Most students will take 15 to 25 seconds to count by 2s. The student should realize that counting by 5s will be less than half the time it took to count by 2s. Times will vary, but it should take less than 15 seconds to count by 5s. The student should realize that counting by 10s will take about half as much time as counting by 5s. It should take less than 10 seconds to count by 10s. Counting by 10s is the quickest way to count. Grade Three Mathematics Home Instructor’s Guide Module 3 DAY 11: In this lesson, your student will use a calculator to skip count by numbers that may not have been practised in earlier grades. Counting by 3s, 4s, 8s, and 9s helps prepare your student for work with multiplication later this year. Assist the student with the timed exercise and filling in the Subtraction Facts Graph. DAY 11: LESSON 1 Answers 1 2 3 4 5 6 7 8 9 10 16 13 II 12 15 17 18 19 20 14 28 21 22 23 24 25 26 27 29 30 33 34 35 36 37 38 40 31 32 . 42 43 45 46 48 39 41 44 47 49 50 51 52 53 54 55 56 57 58 59 60 70 61 62 63 64 65 66 67 68 69 73 75 71 74 76 77 78 79 00o 85 81 82 83 86 88 90 84 87 93 95 96 98 89 100 91 92 94 97 99 2. In the columns with even numbers, alternating numbers are coloured. The student may say, “Every other number is coloured going up and down the even numbers.” 3. After 20, the last digit starts repeating. Grade Three Mathematics 2 Home Instructor’s Guide Module 3 1 2 3 4 5 6 7 8 9 10 16 1 1 12 13 14 15 18 19 20 17 21 22 23 24 25 26 27 28 29 30 40 31 32 33 34 35 36 37 38 39 46 41 42 43 44 45 47 48 49 50 51 52 53 54 55 56 57 58 60 59 61 62 63 64 65 66 67 68 69 70 78 71 72 73 74 75 76 77 79 80 90 81 82 83 84 85 86 87 88 89 91 92 93 94 95 96 97 98 99 100 5. Diagonal (or “slanted”) lines are formed on even numbers. 6. The last digit starts repeating after 40. 7. The numbers coloured in the 8s chart are also coloured in the 4s chart. Timed Exercise Answers: 12-5 = 7 16-7 = 9 17-8 = 9 10-7 = 3 13-4 =9 15-8 = 7 11-4 = 7 14-5 = 9 16-8 = 8 18-9 = 9 12-6 = 6 - 9 6 - 5 13-7 = 10 -1 18 13 12 - 6 4 3 8 3- 3 - 6 14 -1 59 10 11 - 7 7 6 4 8 Grade Three Mathematics 3 Home Instructor’s Guide Module 3 PAY 12: The student will learn to count by 25s. This is difficult for some students. Spend extra time skip counting and writing the pattern if y our student has difficulty with this. Relate counting by 25s to counting by quarters. Ask the student to count quarters for extra practice. PAY 12: LESSON 1 Answers and the 70s row and that the 50 and 100 squares would be coloured in, too. Some students may draw a d iagram like the one below. I 2 3 4 5 6 7 8 9 10 16 1 1 12 13 14 15 17 18 19 20 22 23 24 25 26 27 28 29 30 21 31 32 33 34 35 36 38 40 43 45 46 37 48 39 41 42 44 47 49 50 .1 The student should realize that one square would be coloured in the centre of the 20s row 51 52 53 54 55 56 57 58 59 60 62 63 65 66 67 68 69 70 61 64 78 71 72 73 74 75 76 77 79 80 83 85 86 87 88 90 81 82 84 98 92 94 89 91 93 95 96 97 99 100 2. The hundreds digit would change, but the pattern of 25, 50, and 75 would continue. 3. 25 4. and Q ( Tj O Grade Three Mathematics 4 Home Instructor’s Guide Module 3 6. 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 7. The hundreds digit increases by one each time. 8. a. 350 375 400 425 450 475 b. 275 300 325 350 375 400 c. 725 750 775 800 825 850 d. 875 900 925 950 975 1000 DAY 12: LESSON 2 Answers 1. Most students will show how they counted by 25s. 25, 50, 75, 100, 125, 150 Your student may also add. 25 + 2 5 + 2 5 + 2 5 + 2 5 + 2 5 = 1 50 Sarah and her dad made 150 cookies. 2. Most students will count by 5s to find the answer. 5, 10, 15, 20, 25, 30, 35, 40 Your student may also add. 5+5+5+5+5+5+5+5=40 Fiona made 40 pastries. 3. Most students will add the 6 q uarters to the 150 pennies by adding on six 25s. 175, 200, 225, 250, 275, 300 Your student may also add. 150 + 2 5 + 2 5 + 2 5 + 2 5 + 2 5 + 2 5 = 3 00 There were 300<t. Students may convert the answer to dollars and say there were $3.00. Grade Three Mathematics 5 Home Instructor’s Guide Module 3 DAY 13: Today, the student learns to count backward. Hundred charts and calculators are used to help the student understand the patterns. DAY 13: LESSON 1 Answers 1. a. 70 68 66 64 62 60 58 b. 54 52 50 48 46 44 42 c. 92 90 88 86 84 82 80 d. 38 36 34 32 30 28 26 2. a. 564 562 560 558 556 554 552 b. 206 204 202 200 198 196 194 c. 978 976 974 972 970 968 966 d. 720 718 716 714 712 710 708 3. a. 55 50 45 40 35 30 25 b. 90 85 80 75 70 65 60 c. 765 760 755 750 745 740 735 d. 570 565 560 555 550 545 540 4. 10 20 30 40 50 60 70 80 90 100 5. a. 100 90 80 70 60 40 b. 140 130 120 110 100 9500 80 c. 650 640 630 620 610 600 590 d. 510 500 490 480 470 460 450 6. 100 200 300 400 50C > 600 700 800 7. a. 800 700 600 500 400 300 200 b. 700 600 500 400 300 200 100 c. 1000 900 800 700 600 500 400 DAY 13: LESSON 2 Answers a. 615 610 605 600 595 590 585 b. 990 985 980 975 970 965 960 c. 430 425 420 415 410 405 400 a. 710 708 706 704 702 700 698 b. 532 530 528 526 524 522 520 c. 698 696 694 692 690 588 586 Grade Three Mathematics 6 Home Instructor’s Guide Module 3 DAY 14: The student is presented with a v ariety of different number patterns and must figure out the pattern “rule.” After assisting the student with today’s timed exercise, take the time to look at the graph and discuss the student’s progress. This would be a g ood time to encourage more practise using flash cards, some computer-generated exercises, or a website. The following websites may be helpful for extra practice: • http://www.aaamath.com • http://www.aplusmath.com DAY 14: LE$$ON 1 Answers numbers ended in Os. Rule: +2 b. Description: counting backward by 5s or decreasing by 5 Rule: -5 c. Description: counting by 25s or increasing by 25 Rule: +25 d. Description: counting backward by 10s or decreasing by 10 Rule: -10 e. Description: counting by 100s or increasing by 100 Rule: +100 Timed Exercise Answers: 12-7 = 5 16-9 = 7 17-9 = 8 0 1 CO ii .1 1T3h-e5 s t= u d8 e nt 1m5a-y6 m e= nt9i on 1t1h-at8 th= e 3 tens 1 d4i-gi7t i=n c7 r eased by 1 each time or that all the ~ 5 16-7 = 9 18-8 = 10 12-5 = 7 13-6 - =4 7 - 8 ~ 9 2The - 1 p50 5a .ttern decre-1a 41s7 e s by 10 ea1c3h time or sho128w- s2 counting backward by 10s. 3a. D.esc- 1 r64 i ption: cou n1t- 5 i8 n g forwar~d7 1 b-0y 9 2s or increa1s1i ng by 2 8 1 Grade Three Mathematics 7 Home Instructor’s Guide 4Answers . will vary. Make sur e the pattern shows a consistent repetition. Module 3 DAY 15: Extending number patterns is the focus of this lesson. The student discovers the number pattern and learns to then extend the pattern. Some problem-solving activities that require a p attern to be extended are also included. DAY 15: LESSON 1 Answers 1. The pattern shows counting by 5s backward or the pattern decreases by 5. 2. -5 3. 60 55 50 45 40 35 30 25 20 4. a. Rule: +10 150 160 170 180 190 200 210 220 b. Rule: +25 600 625 650 675 700 725 750 775 c. Rule: -2 876 874 872 870 868 866 864 862 d. Rule: -100 845 745 645 545 445 345 245 145 e. Rule: + 10 457 467 477 487 497 507 517 527 f. Rule: +5 208 213 218 223 228 233 238 243 DAY 15: LESSON 2 Answers 1 . a. The student has to find out the number on the next three licence plates. b. The student can solve the problem by continuing the pattern. c. The pattern rule is +10. The student may solve the problem by adding 10 to each number or by counting on by 10s. Grade Three Mathematics 8 Home Instructor’s Guide