Another+Conjecture...

(To identify and explain patterns and sequences)
 * To make and test Mathematical statements

NB- Y8 Spec day, PLUS some students from Team E on Athletics rotation.**

S/C- Why do you think you should be able to do in order to meet the learning intention?

WEDS 21/10/09


 * Starter**; Play online [|COUNTDOWN]- AIM; Solve the puzzle using only the 6 numbers ONCE each, and any combination of the 4 operations in LESS THAN 30 seconds. TIE BREAKER- in the event of a tie for time, the person who has used the least amount of operations will be the winner.

New conjecture; Investigate this conjecture- HINT; there are exceptions. Record your thinking THEN... http://etherpad.com/ ** *&%#!!? ** BUT the *&%#!!? represents the solution itself! Whoever finds the number to replace the *&%#!!? in the etherpad address can leave their name behind, save the revision and bask in the glory!!! (TIP; *&%#!!? does not necessarily represent a 7 digit number!)
 * Main**; Reflect on the conjecture we investigated on Mon/Tues. Try to summarise the type of numbers which require most steps to reduce to 1.
 * TREASURE HUNT!** You will find the solution to the LOWEST possible exception to this conjecture at;

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers? Take, for example, four consecutive negative numbers, say  ** − 7− 6− 5− 4 **Now place  ** + and/or −    signs between them. e.g . <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px; font-weight: normal; line-height: normal; white-space: nowrap;">−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 7+−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 6+−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 5+−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 4 //or// −<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 7−−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 6+−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 5−−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 4 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 99%; font-weight: normal;">There are other possibilities. Try to list all of them. Now work out the solutions to the various calculations. e.g. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 16px; font-weight: normal; line-height: normal; white-space: nowrap;">−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 7+−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 6+−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 5+−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 4=−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 22 //or// −<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 7−−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 6+−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 5−−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 4=−<span class="spacer" style="border-width: 0px; display: inline-block; margin: 0px 0px 0px 0.05em; padding: 0px; text-align: left;"> 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 99%; font-weight: normal;">Choose a different set of four consecutive negative numbers and repeat the process. Take a look at both sets of solutions. Notice anything? Can you explain any similarities? Can you predict some of the solutions you will get when you start with a different set of four consecutive negative numbers? Try to explain and justify your findings.**
 * EXTENSION; Design your own conjecture
 * Test out any conjectures you may have.