MathMagic and Game shows

I have continued to think about Math homework and the impact that drill sheets can have on math confidence and interest in our students.  Are there alternatives to repetitive drill sheets or questions that could be stimulating for all levels?  Two different assignments that I used to do were Mathmagic and some questions that were done in the style of a game show from France (Les Chiffres et Les Lettres).  The students were still doing math questions, but there was a challenge and a purpose as well as taking it as far as they wanted.


MathMagic
Why Math loves Wayne Gretzky
I would ask the students to tell me which hockey player is loved by mathematicians?
The question goes like this:
1) Choose a 2 digit number, but it cannot be a number with the same two digits (eg 26)
2) Reverse that number (eg 62)
3) Subtract the smallest from the largest (eg 62-26= 36)
4) Add the reverse number of the answer (eg 36 + 63 + 99)
The answer is always 99
The reason that you cannot use a number that has the same two digits is because at step 3 you would get 0.

The 1089 game
Similar question to the Wayne Gretzky question except that it is a 3 digit number and the number cannot be a palindrome (eg 323, 575).  I would take the kids through the steps and then have them turn the work upside down to show me that they have the number and then I walk around the class and whisper the answer to them and walk around and do the same for a number of kids.  The look of surprise on their face when I tell them the answer is 1089 is priceless.  If they do not have 1089 then I tell them they need to double check their work.
1) choose a 3 digit number (eg 367)
2) reverse the digits (eg 763)
3) subtract small from big (eg 763-367= 396)
4) Reverse the answer and add them up (eg 396 + 693 = 1089)
The kids should always get 1089

I would then challenge the kids to try a  few at home to try and prove me wrong.  Extensions that are possible:
1) ask them why palindrome questions do not work
2) Does this work for 5 digit numbers, 6 digit numbers, what are the exceptions...

6174
This is a subtraction game
1) Have the students choose a 4 digit number (eg 4518)
2) Have them put the digits in decreasing order (8541)
3) subtract the reverse (8541-1458= 7083)
4) Repeat steps 2 and 3 with the answer (8730 - 0378 = 8352)
5) Keep going until you get the same answer 2x in a row
8532- 2358= 6174
7641-1467 - 6174
You should always end up with 6174 after a max of 6 operations
The challenge on this one is again to see of they can prove you wrong
The extensions would be 3 digit numbers, 5 digit numbers and if there are rules that need to be applied with respect to the type of numbers that can be chosen.

Les chiffres et les lettres
This is based off a game show from France (Wikipedia YouTube).  The object of the games is to take 6 random numbers and get a randomly chosen total.  You are only allowed to use each number 1 time, although you do not have to use all of the numbers.  You can use addition, subtraction, multiplication and division.  I have them start off in groups and share their joint solutions.  We would then take another random set and the kids would try them at home.  The object is to get as close to the number as possible, and the solution is not always possible.
What I like about this one is that to get the exact answer is great, but more importantly it looks at number fluency, multiple operations and all of the kids can do it.  We do it as a game show with prizes in the class and that makes the math fun.

The main point of this is that it does allow me to assess their math operation skills and allows the strugglers to do just a few and those that love math and excel at it have an extension.  The kids can test this on their parents or siblings and makes them excited about math.  It accomplishes the same objective of math worksheets but it makes it interesting, fun and easily assessable.  The conversations that arise from the sharing is rich and the problem solving solutions lead to amazing math dialogue and sharing of strategies.

Parents and kids would sit side by side and test this out.  The usual fights were not there because the students were motivated to do the work to prove that Mr. Collins was wrong and they had huge smiles on their faces if they were able to find exceptions to the rules.  A number of parents commented on the fact that they enjoyed watching their children enthused about math and how much they enjoyed talking math with their kids.

Math homework with a purpose, that allows for differentiated learning, multiple levels and enrichment and the kids enjoy doing it. Something to think about.