I saw this activity on a twitter page https://twitter.com/letsplaymath and thought it has some interesting potential for high school math students. The activity published by Math Forum asks participants to create expressions for whole numbers 1-100 using only the digits 2, 0, 1, and 5, in any order*, with the operations +, -, x, ÷, ^ (raised to a power), sqrt (square root), ! (factorial), and !! (double factorial). Grouping symbols may also be used, and multi-digit numbers such as 20, 210, .02 may be used this year. *The order 2, 0, 1, 5 is preferred.
For Algebra 1, Geometry, and Algebra 2 – it would be a great review for basic operations practice. There are so many ways to extend this activity. On example could be that every odd number has to use a negative integer in the expresseion. For upper level math, it would be interesting to see what they could do with the additional operations that they have used – like the log of a number etc.
Think about the conversations this could start if students were encouraged to share their responses and then asked if could they come up with different way for the same value. Just the thought of this makes me smile.
Students could also be asked if they could come up with a strategy of attack when thinking of different number sets…like even numbers or multiples of 10 etc..
How about asking students before they start – to predict the numbers will be the hardest to find a combination that will work and then reflect afterwards if they were correct. Wow think of the thinking! (I am really smiling now with that “evil” smile a math teacher has when they are thinking about making student think 🙂 )
The original directions and worksheets can be found at the link http://mathforum.org/yeargameWorksheets/2015/2015.worksheet.html . Happy New Year!