Sharp EL-531RH, Teachers Manual

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29
Junior high school
Palindromes
• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •
This is an activity that can first be given to students to work on and the results later discussed as a
group. The object is to discover a pattern in the results—the pattern being that the answer will
always be a whole number.
• • • • • • • • • • • • • • • Points for students to discuss • • • • • • • • • • • • • •
The pattern may be too obvious for the students to mention, so it may be necessary to give them
the following hint:
Try writing the number in its long form; for example,
2332 = 2 x 1 000 + 3 x 1 00 + 3 x 1 0 + 2
Further Ideas
• Try to explain the problem using algebra. You could start off by giving the class just the first
line of the calculation below and let them work on the rest individually or in groups.
a b b a = a x
1
000 + b x
1
00 + b x
1
0 + a
= a x 1 000 + a + b x 1 00 + b x 1 0
= a ( 1 000 + 1 ) + b ( 1 00 + 1 0)
= a x
1
00
1
+ b x
11
0
= a 9
1
x
11
+ b x
1
0 x
11
= 11 (9 1 a + 1 0b)
• Try the activity using 6-digit palindromes.
Have the class prove that not all 5-digit palindromes are exactly divisible by
11
.