## DESCRIPTIVE NUMBERS INVESTIGATION

### 1. Introductory Example

Write "21322314" on the board.

"Is there anything special about this number?"

"It's even"

"It's got symmetry, well, sort of, about the middle apart from the ends"

"They all add up to 18, that means 9 goes into it"

"The middle bits add up to 6: 1+3+2=2+3+1. So do the outside numbers: 2+4=6"

"There's an even number of odd 3's and 1's and an odd number of even 2's and 4's"

"2x1+3x2+2x3=14"

"It's only got 1's, 2's, 3's and 4's"

Pick up on this last statement.

"How many 1's? How many 2's? 3's? 4's?"

Write "Two 1's, three 2's, two 3's, one 4" on the board

"Do you notice anything?"

There should be some who realise that the number describes itself. Get __them__ to explain to those who do not understand. If not every student understands then keep getting explanations from those that do understand.

Ask the class to __write down__ an explanation of why the number is special.

"What shall we call a number like this?"

"Self-describing"

"Descriptive"

"Boring ... because they are talking about themselves"

"Smart"

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