In language arts class it is not unusual to have students freewrite or journal periodically, sometimes even daily. The idea is to practice fluency in writing, generate ideas for stories, create characters or settings, and much more. The activity only takes a few minutes and usually gets students focused and ready for the main lesson of the class.
I propose a similar activity for math classes where students play around with numbers and patterns – something known under the general heading of “recreational mathematics.” The purposes would be similar to journaling, but of course, geared toward mathematics and numeracy: get students focused, generate ideas, make connections between numbers, create and/or extrapolate patterns, and much more.
What would this look like? Well, of course, it would depend on the lesson plans, specific goals, and time available, but this “thought experiment” time could be as short as a two minute doodle or as long as half a period of working with geoboards or other manipulatives.
Here are some ideas to get things started:
1. Turn a 6 upside-down and you get a 9. Turn an 8 sideways and you get the ∞ symbol. But what other patterns or ideas are there when you rotate or morph various digits and numbers? Have students doodle in a notebook to see what they can discover.
2. Square numbers actually form squares: 1, 4, 9, 16… Triangular numbers can form triangles: 1, 1+2, 1+2+3, 1+2+3+4 and so on. Have students draw different figurate numbers to visually see the patterns inherent in numbers. Many of them could probably create their own named patterns!
3. The number 13 is associated with bad luck. 666 is supposed to be “the number of the beast.” But what about other numbers? What are their associations and potential meanings? Have the entire class pick a number and compile as many examples of how that number shows up in history, nature, mythology, school, etc. See the Beyond Infinity Wiki for more: http://beyondinfinity.wikia.com/wiki/Beyond_Infinity_Wiki
4. Have the students play a game and analyze and extrapolate the various math concepts. I have seen plenty of teachers use decks of cards, backgammon, checkers and more. How about a game of Connect Four? Check out Numberphile’s video: http://youtu.be/yDWPi1pZ0Po
5. There are even and odd numbers, composite and prime numbers, happy and unhappy numbers. What are some of the other types of numbers and can your students create their own type? All they really need to do is find a unique pattern! Here are some other types to give you some ideas: Keith Numbers, Brown Numbers, and Perfect Numbers.