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Mathematics with the Graphic Calculator
A-1 The Calculator 10-key Pad
(1) Take one counter-clockwise lap around the calculator 10-key
pad, pressing the three keys and adding the values produced
along each side. Make a note of the result obtained.
(2) Next, take a clockwise lap and compare with results (1).
This simple exercised produces results that are quite interesting.
(1) 123 + 369 + 987 + 741 = 2220
(2) 147 + 789 + 963 + 321 = 2220
Amazingly, the same result is produced by both the clockwise and the counter-clockwise
laps. Most of today’s senior high school students have been playing around with calculators
since elementary school and so they should already be aware of this fact. However, even
when conducting this exercise in high school, you can see the excitement and wonder in the
eyes of the students.
Why it works: 123 + 369 + 987 + 741
= 100 (1+ 3 + 9 + 7) + 10 (2 + 6 + 8 + 4) + 1 (3 + 9 + 7 + 1)
= 100 (1+ 7 + 9 + 3) + 10 (4 + 8 + 6 + 2) + 1 (7 + 9 + 3 + 1)
= 147 + 789 + 963 + 321
This is the place value system of decimal notation.
A-2 Confirmation of the Expression
Is the following expression correct?
(x + 3)
2
= x
2
+ 9
What other explanation is available besides the algebraic method?
You can also use the area of a square like the one shown to the right.
Let’s try using the graphic calculator.
Graph the following expression:
y = (x + 3)
2
– (x
2
+ 9)
Viewing this graph, we can see that the following is never true:
y = 0
This tells us visually that y = 0 would be an incorrect solution of the above expression.
In the GRAPH Mode, input the following.
Y1= (X + 3)
2
– (X
2
+ 9)
789
456
123
The Calculator 10-key Pad
9
x
2
3
x
x
3
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