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= Team Project: Resource Based Learning =

Introduction
Our Team's Topic is: to complete the Valley Deep Mountain High Project in the right time frame, Our Team's primary resource is: Experimentation Our Team's secondary resource is: SONYA

__**//We found out that the rule that links F and V is the following V(superscript)n = 2(superscript)fn-1//**__ We created a triangle, which looks like the following

V --- F**
 * M

there is no link between m and f. a link can only be made by using v as a middle man.

= = = = =Patterns of Change = =Introductory Activity 1.06=

Valley Deep and Mountain High
 * 1. **[[image:file:C:%5CUsers%5CThom%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_image005.gif width="284" height="210" align="right"]] Take an A4 piece of paper (or an A3 if you have one).
 * 2. ** Mark one face with a cross to denote this to be the uppermost face.
 * 3. ** Lay it on the table (cross upwards) and fold it in half going from left to right. Be sure to crease the fold well.
 * 4. ** Open the paper so it is A4 sized again. It has only one crease line and that has formed a "valley". We will call this a valley crease.
 * 5. ** Returned the paper to the 'folded in half' position and fold it in half again.
 * 6. ** Open the paper so it is A-4 sized again. Notice this time that it has more valley creases but also some creases that form 'mountains' - we will call these mountain creases.
 * 7. ** Your job is to continue to fold in halves and keep track of the number of valley and mountain creases.
 * 8. ** Record your findings in the table below.
 * **Number of folds (f)** || **1** || **2** || **3** || **4** || **5** || **6** ||
 * Number of valley creases **(V)** || 1 || 2 || 4 || 8 || 16 || 32 ||
 * Number of mountain creases **(M)** || 0 || 1 || 3 || 7 || 15 || 31 ||
 * **Total** number of creases **(T)** || 1 || 3 || 7 || 15 || 31 || 63 ||

How many times can you physically fold a piece of paper? Why can’t you fold it more than this? If you were able to fold your A4 paper 20 times, could you stand on top of your folded package and still be below the ceiling? What would the dimensions be of this folded package? This activity was organised by, Eddie Fabijan and Vern Treilibs, ASMS, Jan 2003. It has been adapted from the LUMAT unit //Introduction to Algebra//, Harradine and Treilibs, Noel Baker Centre, 2002.
 * 9. ** Determine a rule that links V and f. : V(subscript)n = 2(subscript)fn-1
 * 10. ** Determine a rule that links M and f. : we have decided to find a link between m and v (take 1 etc.)
 * 11. ** Determine a rule that links T and f. : 2(subscript)n-1 plus 1
 * 12. ** Use your link rules to determine how many of each type of crease will be present if the paper is folded (a) 10 times (b) 20 times
 * 13. **** Challenge: **

//__Possibles that been tried so far__//
Tommy has found out that V1 add M1 equals M2 (this is still under collaboration though) Joe has realized that all the valleys are even, all the mountains are odd and the total number of creases are odd Sonja helped us with the following, that when you do something with powers something happens: THEN we realized each term in V is equal to 2 to the power of the term before it in F
 * V does not equal F x 3.2

RED THINKING-PAGE ISNT WORKIN!**


 * 1) Get an A4 or A3 piece of paper
 * 2) Now fold it a couple of times but put an x on one side so you know which way is up and then unfold it
 * 3) Count the mountains and valleys, to help their is a diagram explaining below that which is a diagram and that which is a mountain
 * 4) Now record the number of folds and the number of mountains and valleys you get from those folds in the table on the sheet but please do not use the diagram above as its just an example
 * 5) The user will notice a pattern in the table for example look at (f) 1 and 3, you should go through and under stand the pattern, this will help when it comes to explaining the rules and equations for v and f, m and f, i and f.


 * BLUE THINKING-PAGE ISNT WORKIN!**