Every Day I’m Krall-in’ It


This is going to be less « explain » and more « try ».

Less « explain » because I wasn’t actually at Geoff Krall‘s NCTM presentation that he called Adaptation – I suggest taking a look to get a better sense and understanding for yourself.  However, from what I understand, the basic idea is adapting traditional textbook problems and transforming them to make them awesome (or at least better) by opening up their begining, their middle or their end– hence the illustration at the start of this post.  He proposes the « how » of each « opening up » of the problem in these ways:


Easy enough?  That’s what I’m trying to find out for myself.  So, here’s my first attempt at this.  Feedback is definately appreciated.  I also will post other trials to see where this goes- you know, the whole « The journey is the destination » thing.

Into the rabbit hole…

Starting problem:

Martin has 10 coins of 5 cents. Christine has 6 coins of 10 cents.

How much more money does Christine have than Martin?

15 minutes- Start with the answer (open up the begining)

The difference between the amount of money of Martin and Christine is 10 cents.  How much could Martin and Christine each have?  What coins could they have?

15 minutes- Would you Rather-ize It (open up the middle)

Would you rather 10 coins of 5 cents or 6 coins of 10 cents?

15 minutes- Choose your Own Problem (open up the end)

Write a word problem which contains at least the following words:

  • 5 cents
  • 10 cents
  • 10 coins
  • more than

1-2 hours- Blurrs and Beeps (open up the begining)


1-2 hours- Remove Steps (open up the middle)

Not sure here.  Is it possible with the original problem?

1-2 hours- Do the Dang Thing (open up the end)

Again, not sure how to do this with the original problem…

This is where being at the actual presentation might help because for the last adaptation aproaches – « Ask Why is this important », « Do the research » and « No really, do the dang thing » – I’m really not sure how to go about it…

Questions and comments I have…

  • Can all problems be transformed using all of the approaches?  (I feel like it may be a « no »…)
  • I feel like the « 1-2 hour » and the « 1 day » transformations would be better done with other teachers- I’m thinking something along the lines of « lesson study ».
  • What would be an approriate mix/balance of each of these types of problems to propose to a class?  Is there one?
  • I feel like I have others, but I can’t define them right now- i.e.- I reserve the right to have more at a later time!!

Question for you, the reader: Would a place to propose and try this approach out be useful?  If so, what format- website, Google Doc, Google Sheet, other?

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