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Activity examples
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Mathematical challenges for able pupils in key stages 1 and 2
Palindromic numbers (Year 4)
Meanings
Look up the meaning of 'palindrome' in a dictionary.
Words can be palindromic, for example 'madam'.
Dates can be palindromic too, for example 17.8.71.
Can you think of some more examples?
Palindromic numbers
8, 33, 161, 222 and 2998992 are examples of palindromic numbers.
- How many palindromic numbers are there between:
| 0 and 100? |
100 and 200? |
200 and 300? |
300 and 400? |
| 0 and 1000? |
1000 and 1100? |
1100 and 1200? |
1300 and 1400? |
- Can you work out how many palindromic numbers there are between 0 and 2000?
What about between 0 and 10 000?
Backwards and forwards
| Start with a two-digit number, for example: |
32 |
| Reverse it and add the result to the original number: |
32 + 23 = 55 |
| The result is palindromic after one reversal. |
55
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| Now try it with another
two-digit number, such as:
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57
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| Reverse it and add
the result to the original number:
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57 + 75 = 132
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| Reverse and add again:
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132 + 231 = 363
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| This time the result
is palindromic after two reversals.
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363
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- Can you find two-digit
numbers that are palindromic after one reversal?
After two reversals? After three reversals? After more than three reversals?
The numbers 89 and 98 take 24 reversals!
- Investigate the same
process with three-digit numbers.
Continue the pattern
Continue each of these
patterns.
In each case, describe what you notice.
- 1 x 9 + 2 =
12 x 9 + 3 =
123 x 9 + 4 =
and so on.
- 11 x 11 =
111 x 111 =
1111 x 1111 =
and so on.
- 11 x 11 =
11 x 11 x 11 =
11 x 11 x 11 x 11 =
and so on.
Questions with palindromic
answers
Try to make up some questions
with palindromic answers.
You might need to work out what the answers should be first!
Hints and solutions (for teachers)
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| One-digit palindromes:
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1, 2, 3,...,9 are palindromic, so
there are 9 palindromic one-digit numbers. (But some people might want to
include 0 as well!)
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| Two-digit palindromes:
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11, 22 and so on are
palindromic, so there are 9 numbers.
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| Three-digit palindromes:
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1 ‡ 1 where
‡ stands for the digits 0 to 9
2 ‡ 2
and so on.
There are 90 three-digit
palindromes.
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| Four-digit palindromes:
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between 1000 and 1100
there is only 1001,
between 1100 and 1200 there is only 1111,
and so on.
Between 1000 and
2000 there are 10 palindromic numbers.
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Here are some other calculations
that have palindromic answers:
| 22 x 11
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33 x 11
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44 x 11
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407 x 3
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1408 x 3
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143 x 7
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Alternative multiplication (Year 6)
Look at these methods for
long multiplication.
Can you work out what is happening? Why do they work?
Try them for yourself using
other numbers.
Which method do you like
best?
Multiplication method
1
| 27 x 43
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1 x
43 =
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43
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43
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| 2 x
43 =
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86
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86
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| 4 x
43 =
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172
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| 8 x
43 =
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344
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344
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| 16 x
43 =
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688
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688
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| So 27
x 43
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=
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1161
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| 14 x 78
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1 x
78 =
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78
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2 x
78 =
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156
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156
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4 x
78 =
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312
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312
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8 x
78 =
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624
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624
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| So 14
x 78
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=
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1092
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Multiplication method
2
| 27 x 43
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27 x
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43
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43
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13 x
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86
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86
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6 x
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172
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3 x
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344
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344
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1 x
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688
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688
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| So 27
x 43
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=
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1161
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| 38 x 47
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38 x
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47
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19 x
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94
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94
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9 x
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188
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188
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4 x
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376
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2 x
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752
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1 x
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1504
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1504
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| So 38
x 47
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=
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1786
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