Back"Choose a number from 1 to 4."
"3"
"All write 3 in your jotter"
On the board write: 3
"Now describe what you've written."
"One 3"
On the board write 13 underneath the 3.
"In your jotter all write 13 underneath the 3. Now describe what you've just written."
"One 1 and one 3"
On the board write 1113 underneath the 13.
"Write 1113 and describe it to me."
"three 1's and one 3"
"So what do you write underneath it?"
"3113"
"That's right. Describe it and write the next number. What have you written?"
"2123"
"Excellent. What's next?"
"221113 or is it 112213"
"Remember SMART numbers? Let's agree to keep the order: 1's then 2's then 3's. Sowhat is it?"
"112213"
"And next?"
"312213"
"Is this going to go on for ever? Keep going with your list. What happens eventually?"
Give the class time to develop this new technique. Group work is better so that they can check each other's answers as they go. Continue to allow them to construct the list and continue to get them to predict what will happen. Here is the list:
"What has happened?"
Allow the class to discover the implications of this repeated number. It's a SMART SENSIBLE number. In fact....
"Hey. That's the number you gave us in the first place!!"
"Well now you know my secret. That's how I discovered it in the first place. Wait a minute, maybe you could discover a different SMART SENSIBLE number using a different starting number. Try it now. Who is going to be first to discover a new one?"
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