Number Grid Investigation
My coursework task is to investigate why, in a number grid square of
1-100, when a section of two by two squares is extracted and the two
opposite squares are multiplied and then subtracted the result is
always 10.
I will also be testing and studying whether it is true for three by
three, four by four, five by five e.t.c number squares. I shall also
be studying what will happen if I change the size of the grid square
upon which I am extracting the numbers from.
E.g.
[IMAGE]
[IMAGE]
[IMAGE]
I shall also be using 4x4, 5x5 6x6 up to 10x10
[IMAGE]
[IMAGE] 2x2 square
[IMAGE]
[IMAGE]
[IMAGE]
3x3 square
2 by 2 Analyses
[IMAGE]
[IMAGE] (2x11) - (1x12) = 10
[IMAGE]
[IMAGE] (35x44) - (34x45) = 10
[IMAGE]
[IMAGE] (3x12) - (2x13) = 10
[IMAGE]
[IMAGE] (99x90) - (89x100) = 10
As we can see the results clearly show that no matter what selection
of 2x2 square we use the result will always be 10.
We can show how and why the result is always 10 by using Algebra,
(representing numbers by using letters).
[IMAGE][IMAGE]
=
This is how we can express numbers using letters. As with numbers we
can also put letters into a formula. This is how it would look:
(P+10)(P+1)- P (P+11) = 10
When we multiply out this formula it looks like this:
P²+11P+10 -P² - 11P = 10 As it shows the result is 10 once again
P²+11P+10 -P² - 11P = 10
Testing the Formula
Now we can put the formula to the test by using it with numbers:
(23x32)- (22x33) =10
[IMAGE][IMAGE]
=
As we can see the formula has proven to work well and the result is
once again 10 as the formula suggests.
Now that I have proven the formula with 2x2 squares extracted from a
The following assignment shows the progress I have made throughout unit EDC141: The Numerate Educator. Included are results from the first and second round of the Mathematics Competency Test (MCT). Examples from assessment two, which, involved me to complete sample questions from the year nine NAPLAN. I was also required to complete a variety of ‘thinking time problems’ (TTP’s) and ‘what I know about’ (WIKA’s). These activities allowed me to build on my knowledge and assisted me to develop my mathematical skills. The Australian Curriculum has six areas of mathematics, which I used in many different learning activities throughout this study period (Commonwealth of Australia, 2009). These six areas will be covered and include number, algebra,
19. Michael has c cds. He bought 22 more cds. Write the expression that shows how many cds Michael has now.
long been established” (p. 49). In the past few decades, research has been done to show that
- Compare how this is achieved in your prescribed text and ONE other related text of your own choosing.
So now that we have the desired answer and know what the formula is, we just need to know what it means and why it works. So
“Books and the movies are like apples and oranges. They both are fruit, but taste completely different.” -Stephen King. Stephen King was exactly right about that. The book called “Devil’s Arithmetic” has many differences compared to the movie. However, the theme in the movie and the book has been the same thing: ALWAYS remember. Furthermore, there are many other similarities that build up the theme of remembering. We must never forget what occurred during the Holocaust, because if people don’t pay attention to history, the event is doomed to happen again.
= 3 ´ E(C-H) + 1 ´ E(C-O) + 1 ´ E(O-H) + 1.5 ´ E(O=O)
The Devil’s Arithmetic is a book about a girl named Hannah Stern who finds herself thrown back to 1942, during the holocaust. She learns what it was like when her aunt and grandfather, as they too were in the camps. If you want to teach children about humanity’s single greatest atrocity, then The Devil’s Arithmetic is the best book for you to teach.
Ep C (P) + Ep F (P) = -2p +1(1-p) +1p-3(1-p) = -3p+1+4p -3 =p-2= -1.43
· When I have collected my results I will place them in a table like
Text Box: In the square grids I shall call the sides N. I have colour coded which numbers should be multiplied by which. To work out the answer the calculation is: (2 x 3) – (1 x 4) = Answer Then if I simplify this: 6 - 4 = 2 Therefore: Answer = 2
Step 1: EER = 354 – 207.3 + [1.45 X (9.361 X 59.02 + 726 X 1.651)].
an enzyme is used to speed up the process in the equation above. In my
This graph shows the result that I expect to get, I expect to see a
The reason as to why so many people are so fascinated by a Sudoku puzzle is that, even though the solving rules are simple, the reasoning behind the path to the correct solution can be very difficult, which is what will be explored in this paper.