Friday, October 31, 2008

Alternatives to stacking, II

I've received, both here and at kitchentablemath, a number of interesting non-stacking strategies for computing 825 - 267 that I had never thought of before. This made me wonder about just how far one can get without stacking. What happens when we add a few more digits?

For example, how about--using numbers randomly generated by my software program--885.66 minus 746.85?

My new question: Is there a way to subtract 746.85 from 885.66 that

1. Isn't massively facilitated by stacking one number on top of the other;
2. Only uses methods that grade school children can discover on their own;
and

3. Doesn't place excessive demands on short-term memory?
If so, please share it here!

2 comments:

Liz Ditz said...

Only uses methods that grade school children can discover on their own;

Hmmn. How many kids, without manipulatives, will "discover" regrouping on their own?

lgm said...

Sure, use mental math a la Singapore and break the problem up. My kid figured it out on his own as a 5 year old - he wanted to make change quickly while playing store plus solve Cluefinders on PC rapidly. I suspect not being able to write fluently promoted the facility, but the understanding of number bonds is essential. A child that has insufficient experience playing with quantities will have a hard time. A kid entering kindy that still doesn't have 1:1 correspondence will never get it in our system. An older elementary child that never has to check his subtraction by adding won't get it either.

My son would do your problem in parts for fun:

Decimal part first:

166-85 is 81 so there is the decimal He would subract tens then ones in either order (16-8, 6-5) since no regrouping is involved although count up to 100 (15+66) is almost as fast

884-746 is 184-46 regrouping is involved; count up gets you 54+84, that's 138

final answer 138.81


I remember in college one of my engineering profs would challenge us with back of the envelope calculations then tell us to assume no envelope available and do it mentally. No one in that class could beat him, but we were inspired to figure out how he did it and improve ourselves.