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MATH MATH WORLD

THE BEST OF

1992 - 1996

WITH ANSWERS

OVER 50 REPRODUCIBLE ACTIVITIESo f Wes te rn Austra l ia

Inc.

MA WAThe

Mathematical Association

1. Magic Squares 32. Making Magic Squares 43. Reflecting Magic Squares 54. Magic Square Investigation 55. Even-order Magic Squares 66. Magic from the Calendar 77. Magic Formula 78. The Game of 15 89. In the Long Run 810. Do or Die 811. Baffling Birthdays 912. Fair Go 913. Dice Cricket 914. Perplexing Polyhedra - The Tetrahedron 1015. Frenzied Folding - The Tetrahedron 1116. Perplexing Polyhedra - The Hexahedron 1117. Codes and Ciphers 1218. Polybius Code 1219. Codes and Ciphers II 1220. Codes and Ciphers - ISBN 1321. Codes and Ciphers - The Binary System 1422. Codes and Ciphers - Bar Codes 1423. Patterns in the Hundred Square 1524. Multiple Patterns in the Hundred Square 1525. Patterns in the Hundred Square II 1626. Patterns in Pascal’s Triangle 1627. Pascals Triangle and Probability 1728. Patterns in Pascal’s Triangle II 1829. Pascal’s Stocking Pattern 1830. Figurate Numbers 1931. Fibonacci Numbers 1932. Golden Rectangles 2033. Golden Fibonacci 2034. Calendar Capers 2135. Calendar Corners 2236. Calendar Perimeter 2237. Calendar Count 2238. Calendar Cross 2239. Missing Area 2340. Prime Time 2441. Multiple Madness 2442. Multiple Madness II 2443. Number Novelties 2444. 9 Guzinta 2545. 99 Guzinta 2546. Multiplication Shortcuts 2547. Multiplication Shortcuts II 2548. Mind Reader 2649. Magic Numbers 2650. Card Shark 2651. Hearing Things 26 Solutions 27

ContentsAcknowledgementsMath Math World is produced by the Mathematical Association of Western Australia and the Australian Association of Mathematics Teachers for the enjoyment of upper primary and lower secondary students across Australia.

Numerous requests have been received for back issues of math Math World and answers to the various activities. The Best of Math Math World 1992 - 1996 is an attempt to put together the most popular activities for the five year period from 1992 - 1996.

The support of MAWA and AAMT is gratefully acknowledged along with the work of previous editors of It’s a Math Math World which was the West Australian forerunner to the National Math Math World.

Editor: Paul SwanTypesetting: J. Swan, L. Swan and D. Swan© Copyright Paul Swan

Copyright notice: Copies may only be made for non-commercial classroom use.

P. Swan2Best of Math Math World 1992-1996

44. 9 GuzintaA little algebra helps to explain this. If a and b represent the digits we get 10a + b - (a + b) = 9a.

Therefore the result is always divisible by 9.

45. 99 GuzintaIf a, b and c represent the three digits we get:

(100a - 10b + c) - (100c + 10b + a) = 99 a - 99b = 99(a - c)

Therefore the result is alwayus divisible by ninety-nine.

46. Multiplication Shortcuts (a + b)2 = a2 + 2ab + b2

eg 452 = (40 + 5)2 = 2025

47. Multiplication Shortcuts II (a + b)2 = a2 + 2ab + b2

562 = (50 + 6)2 = 3136

48. Mind ReaderLet ‘n’ denote the chosen digit. The steps produce (10n + n) x 9 x 11 = 1089n. This number is always divisible by nine and eleven. This means that the sum of the digits that make up the number will equal nine or a multiple of nine. 89 x n always produces a number where the tens digit is one less than the units digit eg 4 x 89 = 356. The units digit and the hundreds digit will always add to nine. The zero in 1089 ensures that no digits are carried over into the thousands place. The thousands digit will be the same as the single digit multiplier (n), because 1 x n = n. The thousands digit and the tens digit add to make nine.

49. Hearing ThingsA person is often tricked into writing down the wrong number because he/she focusses on the place value signals.

50. Card SharkDrawing a table which locates the required card in the 16th position on the first sorting will help to show that successive sortings based on removing the left hand column of cards eventually leaves only one card remaining in the right hand column. The first deal produces 13 cards in each row. The left row is discarded. The second deal produces 7 cards in the left row and 6 in the right. The third deal produces three cards in each row and so on until a single card is left.

More Dr Paul Swan titles may be found at drpaulswan.com.au

More MAWA resources and student activities may be found at mawainc.org.au including:

P. Swan 31 Best of Math Math World 1992-1996

Maths @ Home

Number Chains

Mathematics Education Starter Kit

Tangram Adventure Puzzle Book

Activity Guide

Calendar Capers

Mathematics Tic-Tac-Toe

Countdown Wiz

Hexagone

Take Sum Risks

ISBN 0 646 30961 7