I would always start the beginning of each new school term by welcoming my students to their journey through one of the most beautiful of all subjects – mathematics! Of course, that got their attention, and they often wondered what in the world were they getting themselves into. And, as the term progressed they did come to realize that “Mrs. Jones, you are not like any other teacher I have ever had!” I would thank them for the compliment! One thing they knew for sure, I did find mathematics beautiful. They knew my mathematical hero was Galileo – and why!

*Mathematics is the alphabet by which God has written the universe.* – Galileo Galilei

Patterns are one of the beautiful aspects of mathematics. This week’s free activity offers my favorite one-pager that I gave to students at the beginning of each school term. It went into their Mathematician’s Notebook and on the first day – when we have all the “stuff” to do – students determined the next THREE patterns because if they just find the next pattern, they might have made a lucky guess. I would have linking cubes available if students wanted to use the manipulative to support their investigation. Throughout the term, we revisit this sheet as we encounter different function types and sequence types. Studying the multiple representations of the sequences – the table, the set of ordered pairs, investigating for a common difference, the abstraction of the symbolic function, the graph, pictorial vs. numeric….all of this helps support students’ developing functional fluency.

Of course, this is but a few of the many sequences and patterns that would be investigated throughout the semester or year. (Note – not sure where I first came upon this sheet – but got it years ago at a conference). The second sheet, Number Patterns, is just a different perspective on operating with numbers. (again, an idea received at a conference somewhere, sometime) These are also great activities for middle school and upper intermediate students. The four basic operations can be extended to include raising to a power, taking a root, etc.

Enjoy these with your students, think about all the possibilities as you share the beauty that is mathematics. And of course – one of my favorite patterns & sequences – Pascal’s Triangle from which can be found, the Fibonacci Sequence, but that is for another day.