Hi Craig & teachers

I have to admit having a LOVE / HATE relationship with the 1997 problem. I

t's the problem I love to hate, OR

It's the problem I hate to love.

But now that you've started it I can't resist.

Yes, we did have a lengthy discussion (well in to April) on this problem and it's variations.

The conclusion: (yes there was one) Use the problem with what ever variations fit your students' level of mathematical sophistication to introduce/teach/review:

  1. number sense
  2. order of operations
  3. grouping symbols
  4. problem solving
  5. decimal division ( 9 Ö .9 = 10)
  6. repeating bar (as in .9 with a bar = 1)
  7. square root
  8. factorial
  9. ceiling function
  10. floor function
  11. double factorial (6!! = 6 x 4 x 2 = 48)
  12. trig functions
  13. what ever else you can think of, the sky is the limit.

But above all else HAVE FUN, when the kids stop thinking it is fun, STOP

Now here are MY bench marks, feel free to use them or make up your own.

Grades K-3: Be happy if they kids can find representations for at least 10 of the numbers 1 through 25. Be enthused with anything more. Accept 1 + 9 - 9 + 7 = 8 or even 1 + 7 = 8 (They don't REALLY have to use ALL 4 digits, but no others) Make BIG CARDS with 1, 9, 9, 7 and + and - then move them around and see what happens.

Grades 4-6 Attempt all 100 counting numbers. Be overjoyed once students have completed 50 or more. Insist that they use all 4 digits, but order and structure are not important. They might say 9 x 7 = 63 + 9 = 54 - 1 = 53 (at the next level we will insist that they say 9 x 7 + 9 - 1 = 53) Introduce square root and factorial when your students are ready. Floor function and Ceiling function can be fun but are strictly optional and at your discretion.

Grades 7-9 The goal is all 100 counting numbers. Be happy at 75 and elated when you hit 90. Insist that the students use all 4 digits. At this level structure is important. They should be aware of the rules for order of operations so 1 + 9 x 9 - 7 = 75 while (1 + 9) x 9 - 7 = 83 Make your own rule as far as order of the digits, this depends somewhat on when integers are introduced. 9 + 9 + 7 - 1 = 24 or -1 + 9 + 9 + 7 = 24

Grades 10-12 This level makes me laugh (sorry but I've been there and never want to go back). Some 10th grade classes might need to follow the 7-9 (or dare I say 4-6) grade bench marks while others can set their own rules. A trig class might just want to make all numbers using only trig functions. Or a calc or Alg II class exploring logs might make that the center focus. But a really tough problem accessable to most is to use only +, -, x, ÷, sq rt, !, grouping symbols with the numbers in the order 1, 9, 9, 7 to create the first 100 counting numbers.

There are only 3 things that I have trouble accepting and although I refuse to criticize others who use them in their classroom you won't see them in my room:

  1. Use of double digit numbers such as 97 - 19 = 78
  2. Squaring numbers 1 + 9^2 - 9 + 7 = 80 (calculators do have an x^2 key, but it can't be written with out the 2)
  3. Use of the integer function Int(9 ÷ 7) + 9 + 1 = 11

I think it is fun to hear how far other classes (other grades) have progressed so keep writing.

Judy

http://dimacs.rutgers.edu:80/~judyann/