Secret Codes

7624 /www/nrich/html/content/id/7624/ 1 0000-00-00T00:00:00 <mdoxml version="1.0"><br></br> In these messages letters have been turned into numbers in this way.<br></br> <br></br> <mdo:image width="541" height="288" alt="Numbers for letters" src="NoAlph1.png"></mdo:image><br></br> <br></br> So A is $1$, and also $27$, B is $2$ and $28$, and so on.<br></br> [There are $26$ letters in the alphabet so you just start again if you get a number higher than $26$.]<br></br> <br></br> Can you change these numbers back into letters?<br></br> <br></br> $10.1. 3. 11. - 1.14.4. - 10.9.12.12. - 6.5.12.12. - 4.15.23.14. - 20.8.5. - 8.9.12.12.$<br></br> <br></br> In the next bit of code we have added $3$ to each letter-number and changed them back into letters.<br></br> Remember that when it comes to more than $26$ you need to take the $26$ from the number. So A is $27$ as well as $1$.<br></br> <br></br> Can you sort it out?<br></br> <br></br> SDW - D - FDNH, - SDW - D - FDNH, - EDNHU'V - YDQ.<br></br> <br></br> In the next bit of code we have added $3$ again.<br></br> You ought to be better at it now!<br></br> <br></br> VLQJ - D - VRQJ - RI - EODFN - ELRGV - LQ D - SLH<br></br> <br></br> In the next piece of code we have taken $2$ off the letter number.<br></br> Remember, B is $28$ as well as $2$, so if in this code it has Z, it stands for B.<br></br> <br></br> Can you sort this one out?<br></br> <br></br> JGRRJC - ZMW - ZUSC - AMKC - ZJMU - SNRFC - QAFMMJ!<br></br> <br></br> Can you make up your own piece of code like this?<br></br> You can take off two or add three to the letter-numbers or make up your own way of doing it BUT you must tell us what you have done to the letter-numbers, or we will never be able to read it!<br></br> <br></br> If you found this easy you might like to try a harder version.<br></br> <br></br> First you turn the letters into numbers as before. Then you add the special coding word (also in number form) then turn the whole thing back into letters. These are put into blocks of five letters, [not the word length]. Let's see how this works.<br></br> <br></br> I'll use the Code word NRICH In numbers 14. 18. 9. 3. 8<br></br> I'll put the word "Maths" into the code. In numbers it is 13. 1. 20. 8. 19<br></br> <br></br> So I add each letter and get 27.19. 29. 11. 27.<br></br> In letters this is ASCKA<br></br> <br></br> In the message below code word NRICH is used again. So I will turn my sentence into numbers, and add the code word, and turn it back into letters in blocks of five.<br></br> What does it say?<br></br> HSUOW - OCBJZ - COOUW - ADRWB - ZWJFW - FFB.<br></br> <br></br> Now for the really difficult bit!<br></br> This time there is a different coding word.<br></br> All I will tell you that it is from this list:<br></br> LEMON, CHAIR, EIGHT, HORSE, CAMEL, TIGER, TULIP<br></br> <br></br> Can you uncode this message? It's hard!<br></br> OJGYX - HCVWP - VJAFZ - HTGXT - RVYIS - HUGMQ - HBEQK - ZPERE<br></br> <br></br> Now can you make up your own piece of code like this?<br></br> You can add your own words BUT you must tell us what you have done to the letter-numbers, or we will never be able to read it!<br></br> That is the point of a Secret Code! It is what makes it secret! <br></br></mdoxml> <mdoxml version="1.0"><br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <a href="http://nrich.maths.org/7624&part=">This problem</a> practises working systematically on addition and subtraction. The activity requires some lateral thinking.<br></br> <h3>Possible approach</h3> <div>You could start by showing the group how the letters are turned into numbers and that A is both $1$ and $27$. <a href="/content/id/7624/LetterNos.pdf">This sheet</a> might be useful.</div> <div> </div> <div>The first piece of code, given in numbers, could be done as a whole group. Next it would be a good idea to change some letters into numbers. The children could, for example, change their own names. These could then be put into code by adding 3 to each letter number and changing back into letters.</div> <div>Take, for example, "William".</div> <div>WILLIAM in numbers is - $23. 9. 12. 12. 9. 1. 13.$</div> <div>Adding $3$ to each letter - $26. 12. 15. 15. 12. 4. 17.$</div> <div>Turned back into letters - Z L O O L D Q</div> <div> </div> <div>Perhaps they could work out each others' names and then change them back into the correct letters.</div> <div> </div> <div>After this the group could work in pairs on the problem as given. Then at the end of the lesson could get together again to show what they have done.</div> <br></br> <h3>Key questions</h3> <div>What letter does $32$ [for example] stand for?</div> <div>What letter does your name start with? What is the number for it?</div> <div>What are you going to add/subtract ?</div> <div>How do you think you can turn that back so you can read it?</div> <div>How do you reverse adding $3$/subtracting $2$?</div> <br></br> <h3>Possible extension</h3> The last part of the problem is reallly an extension. When this has been done learners could make up their own pieces of code.<br></br> <h3>Possible support</h3> Some children who have problems with reading or slight dyslexia may find this work extremely difficult. You could suggest just turning letters into numbers and back again as in the very first part of the problem or doing a quite different piece of work.<br></br> <br></br></mdoxml> 2 4 1 0 0 0 0 Secret Codes