Module 3 Algebra 4 Homework Question

You are going to use an Excel spreadsheet to investigate one of your homework questions.

Open an new Excel Workbook.

The question asked you to investigate the mapping
Step 1
Copy all of the contents of this table (Ctrl c) and paste it (Ctrl v) into Excel.

n	10x + y	x	y	10y + x	10y + x - 1
0	27	=INT(B2/10)	=MOD(B2,10)	=D2*10+C2	=E2-1
1	=F2	=INT(B3/10)	=MOD(B3,10)	=D3*10+C3	=E3-1

What do the Formulae do?

You don't need to read this but you might find that this helps you understand what is going on.

INT(number)
rounds a number down to the nearest integer(whole number).
eg
INT(6.02)= 6
INT(4.75) = 4

MOD(number1, number2)
returns the remainder from number1 divided by number2.
eg
MOD(9,4) = 1
MOD(13,5) = 3

Step 2
Select the 2nd and 3rd rows of column A. If you grab the bottom right hand corner whilst holding down the left mouse button then you can fill down the A column as far as 100 simply by keeping the mouse button down as you drag. You don't need to go any further. Why?
Step 3
Now do the same with the third row of columns B,C,D,E & F.
Step 4
If all has gone well then the top of your spreadsheet should look like this. If you started with 27 in cell B2 then you should get the same numbers as me.
Step 5
Select columns A & B and draw an x-y scatter graph of them. Select the straight line with markers option. Your graph should look something like this one.

Step 6

Now answer these questions by experimenting with different starting numbers in cell B2.
Open a word document and write an illustrated answer.

Does the graph have any structure?

Does changing the start number make a difference?

How many patterns are there?

Is there a pattern to the graphs for different starting numbers?

Try alternate pairs of starting numbers like 63 and 36 or 28 and 82.
What happens?
What does the -1 mean?
Which number does it act like in this function?

What effect does the size and direction of the gap between x & y have?
Does 23 behave like 32?
Does 28 behave like 82?

Plot a graph of the x & y values in columns C & D.
Can you predict what it will look like?
Does 28 behave like 82?