Creative thinking required

I think David mentioned the math game show "Countdown" in our course material. Here is an excerpt from one of the episodes:  

 

Link to the same video, in case the embedded video doesn't work:

https://www.youtube.com/watch?v=pfa3MHLLSWI 

This contestant's performance blew me away!

This reminds me of a problem that I got from Todd Romiens at the Faculty of Ed, University of Windsor, back in 2000, and I have used it ever since in my math class. It's perfect for grades 7 and 8, though for 7s I had to make sure they knew about order of operations, integers, square root, and exponents first.

Using the digits of the year 1999 in order, add operations and brackets if necessary to develop an expression equal to each of the natural numbers from 1 to 20. Consider: +, -, x, /, exponents, square root, integers, and order of operations.

The rules: For each expression, you must use all of the digits 1, 9, 9, and 9 in this order, with no added numbers.

I usually give a "freebie" for the value of 1 as an example, e.g.  1 x 1 x 9 / 9 = 1

Some of these will be very easy, and some values will be harder, but all are achievable by grade 7 and 8 students with an understanding of all the above operations. The task can be broken into two sections, 1 - 10, and 11 - 20.

Try it with your class!