Number Grids Investigation
Introduction
In the following piece of coursework, I intend to investigate taking a
square of numbers from a 10 x 10 grid, multiplying the opposite
corners and then finding the difference between the two products.
I was first asked to take a 2 x 2 square from a 10 x 10 grid, multiply
the opposite corners and then find the difference. This is the result
I received;
2x2 squares
15
16
25
26
Square 1
15 x 26 = 390
16 x 25 = 400
Difference = 400 – 390 = 10
Here I found that the difference was 10, to find out if the difference
was the same for every 2 x 2 square, I decided to test another 3
squares, and here are the results I received;
Square 2
18
19
28
29
18 x 29 = 522
19 x 28 = 532
Difference = 532 – 522 = 10
Square 3
32
33
42
43
32 x 43 = 1376
33 x 42 = 1386
Difference = 1386 – 1376 = 10
35
36
45
46
Square 4
35 x 46 = 1610
36 x 45 = 1620
Difference = 1620 – 1610 = 10
After calculating the differences between the products of four 2 x 2
square grids, I can conclude that the difference is always 10, and I
predict that the difference will always remain 10 for 2 x 2 square
grids. I then decided to look at a 3 x 3 square on a 10 x 10 grid, to
see if the difference would be 10, or anything different, and here is
the result;
32
33
34
42
43
44
52
53
54
6x6x6 cube and see if I can find a pattern. When I have found a
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They will use estimation, the base ten blocks, and area model, and they will record their answers on the scratch paper. Then, students will write a real-world story about a decimal multiplication problem that they have created with the base ten blocks. The story should contain each of the different numbers that are involved with the rectangular construction.
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Schattschneider, Doris. “The Fascination of Tiling.” The Visual Mind: Art and Mathematics. Ed. Michele Emmer. Cambridge: MIT Press. 157-164.
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
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The ratio for length to width of rectangles is 1.61803398874989484820. The numeric value is called “phi”.
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