Number Grid For this task I will first be looking at a number grid from 1 to 100, like the one below : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 I will start my investigation by looking at 2 by 2 squares. I will draw a square around 4 numbers, find the product of the bottom left and top right numbers and the product of the top left and bottom right numbers, then calculate the difference between the 2 products. I will see if there are any patterns and if so I will try to work it out algebraically. I will then look at changing the size of the squares to see if there are any patterns. I will try looking at 3 by 3 squares, 4 by 4 squares and 5 by 5 squares; I will do the same with these squares as I have with the 2 by 2 squares, I will find the products of the top left and bottom right and the bottom left and top right numbers then calcula... ... middle of paper ... ... Product Difference Right Left Yellow Rectangle : 1 44 44 41 4 164 120 Green Rectangle : 16 59 944 56 19 1064 120 Purple Rectangle : 52 95 4940 92 55 5060 120 I have noticed that the difference of the products in each square is always one hundred twenty. I have worked out the formula for this pattern below: N N+3 N+40 N+43 N(N+43) - (N+3)(N+40) = D N2 + 43N - N2 - 40N - 3N - 120 = D -120 = D Difference = 120 This shows that the difference between the two products in each rectangle is always -120; I have shown the difference as 120 rather than -120 as I am only interested in the number and not the sign in front of it (+/-).
have no labels, 1 label, 2 labels and 3 labels. Once I have done this
The last activity that we did was taking ten Q tips and made three attached squares and her assignment was to make a 4th enclosed box without adding an additional items. Once I told her to start she immediately started moving the Q tips around trying to create another box. After trying for a few minutes she then say there is no way to add another box.
1) Sort the pictures into living and nonliving categories by using their definitions that they created.
0.96, 0.96, 0.97, 0.98, 1.01, 1.01, 1.02, 1.03, 1.03, 1.03, 1.03, 1.04, 1.04, 1.04, 1.04, 1.05, 1.05, 1.06, 1.07, 1.07, 1.08, 1.09, 1.09, 1.09, 1.09, 1.09, 1.09, 1.10, 1.10, 1.10, 1.10, 1.11, 1.11, 1.11, 1.11, 1.12, 1.16, 1.17, 1.17, 1.18, 1.18, 1.20, 1.21, 1.21, 1.21, 1.23, 1.26, 1.29, 1.31, 1.32, 1.66
sides on a cube and this gave rise to idea for a project. The final result
I can do this by setting up the diagram above. You need to get a
x 3, 4 x 4 x 4, 5 x 5 x 5, 6 x 6 x 6, 7 x 7 x 7, 8 x 8 x 8, 9 x 9 x 9)
60 1,45 0,56 0,90 0,84 1,00 0,05 0,59 0,77 0,40 80 1,45 0,62 2,00 0,65 0,65
on the entire left side of the triangle (column 3) to represent n things going into groups of 0. There is only one way to do this, so every cell with a blank box can be said to have one item in it. I am using a box because it does not have a specific “value” but it is more of a holding place for new elements. In cell (B, 4), I placed an “a” because this represe...
I am going to begin by investigating a square with a side length of 10
There are six diagonal lines. At one end there are circles on them giving the impression of three circular prongs. At the other end the same size lines have cross connecting lines consistent with two square prongs. These perceptions can violate our expectations for what is possible often to a delightful effect.
Noticing little problems like these could save you a lot of money and aggravation. They are simple problems and with a little knowledge they can be taken care of quickly and easily.
One only requires the use of simple mathematics i.e. simple addition and subtraction of single and double digit numbers ...
have noticed it before. That was all, now all I had to do was find the
The Golden Ratio is also known as the golden rectangle. The Golden Rectangle has the property that when a square is removed a smaller rectangle of the same shape remains, a smaller square can be removed and so on, resulting in a spiral pattern.