# How to draw the patterns without calculators - Association of

код для вставкиMT178-2 5/12/02 10:13 am Page 43 В© ATM 2009 вЂў No reproduction (including Internet) except for legitimate academic purposes вЂў copyright@atm.org.uk for permissions. How to draw the patterns without calculators Lucy Cartwright When drawing a pattern without calculators, firstly choose the word you wish to draw. For example: Lucy This word has four letters, then you add 1 to this total. So now effectively, you have 5 letters.) Lucy П© 1 П 5 Next, make 5 columns, and write out the alphabet underneath, like this: 1 2 3 4 5 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Now we can make some co-ordinates using the letters, numbers and the original word. Write the word in a vertical line and then go back to the beginning of the word and add the first letter again. In this case the extra letter is an L. Then, directly next to this column, begin another column starting this time with the second letter of the word, U for Lucy, and going down to U again. LU Now, using these letters, we can UC start making some co-ordinates CY to plot the graph. YL LU LU (2,1) (L in 2nd column, U in1st) UC (1,3) (U in 1st column, C in 3rd) CY (3,5) (C in 3rd column, Y in 5th) YL (5,2) (Y in 5th column, L in 2nd) LU (2,1) (Same as 1st set) We found out all the permutations of the letters of вЂ�wordвЂ™ you could have. We found there were 24 possible. All of these we tried on a graphical calculator to see what picture they would form when converted to a picture. We found out that there were 3 different pictures. However, a number of other pupils also investigated a word with four letters; but found more pictures. In groups we have been investigating how many possible permutations there are for each word, and then linking our findings to how many pictures there are for a word. We discovered that for a four letter For the next column of co-ordinates, you take the second numbers of the 1st set of co-ordinates. In this case the numbers copied will be 1,3,5,2,1. For the 2nd numbers of the 2nd column, do 5, the total of all the letters, take away the 1st numbers of the 1st column. Do the third column in a similar way. For the 2nd number of the 3rd column, do 5 minus the 1st numbers in the 2nd column. (2,1) (1,3) (3,4) (1,3) (3,4) (4,2) (3,5) (5,2) (2,0) (5,2) (2,0) (0,3) (2,1) (1,3) (3,4) The final column is the 1st, repeated: (2,1) (1,3) (3,4) (2,1) (1,3) (3,4) (4,2) (1,3) (3,5) (5,2) (2,0) (3,5) (5,2) (2,0) (0,3) (5,2) (2,1) (1,3) (3,4) (2,1) And these are the co-ordinates for the graph! We have found that plotting each of the columns in a different colour is quite effective. Also colouring the spaces between the lines looks good, especially if rotational symmetry is used. word with different letters in different columns, there are 24 permutations and 6 pictures. If, for example, the word вЂ�starвЂ™ was chosen, it could be written like this: STAR RTSA TRAS TARS TSAR RAST ARST SART ASTR RSTA ARTS STRA SRTA ATSR ATRS RTAS TSRA TRSA TASR SRAT RSAT ASRT RATS SATR MATHEMATICS TEACHING 178 / MARCH 2002 Academic copyright permission does NOT extend to publishing on Internet or similar system. Provide link ONLY 43 The attached document has been downloaded or otherwise acquired from the website of the Association of Teachers of Mathematics (ATM) at www.atm.org.uk Legitimate uses of this document include printing of one copy for personal use, reasonable duplication for academic and educational purposes. It may not be used for any other purpose in any way that may be deleterious to the work, aims, principles or ends of ATM. 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