Exploring Patterns ... extending thinking
Patterns are EVERYWHERE! Some suggest that the study of mathematics is the study of patterns ... identifying them, categorizing them, generalizing them.
Five universal generalizations are true about patterns:
- patterns have segments that are repeated
- patterns allow for prediction
- patterns have an internal order
- patterns may have symmetry
- patterns are everywhere
Here are a few ideas for exploring patterns in math in introductory ways ...
1). Read children's books! I love to connect with students using a read aloud ... talking through a picture book before getting started with math. AND yes! It works well even in middle and high school!
Some of these are more sophisticated than others ... and the last one (bottom right corner) is a coloring book.
2) Explore polygonal or figurate numbers. I have a task I've used with students ... you may find it helpful. "Explore Numbers in Shapes."
3). Check out the activities, explorations in YouCubed ... there are more than a dozen pattern activities ready to implement in your classroom.
4). Visual Patterns is an excellent site ... set up to use regularly as a key activity in your math program.
5). Mathigon has a great series of lessons, interactive, free ... ready to use to enrich students' understanding of patterns.
6) NRich is another excellent source for problem solving, stretching students' thinking and exploring topics. They have numerous pattern activities at all levels ... perfect for differentiating!
I am sure there are other great resources! What sources to you recommend for exploring patterns with students?