Discover Patterns in Pascal's Triangle

Discover Patterns in Mathematical Models Bundle

A whole-group mathematical exploration of seven different mathematical models. This bundle of resources creates space for a learning community founded on discourse, theorization, generalization, and justification. Learners are encouraged to bring ideas forward within the conversation and prove or disprove each other’s theories about the patterns they discover within this model. These activities are used best to push learners toward deep, critical thought about a mathematical scenario. ## WHAT’S INCLUDED This resource contains: –> 7 mathematical scenarios –> Detailed instructions on how to lead students into deep, critical thought about mathematics –> 7 possible student discoveries for each model with explanations and lines of questioning –> Plenty of possibility for extension, deeper discussion, or lesson ideas ## STORY A lot of my work this school year has led me to really pushing learners outside the usual confines of the worksheet-based industrial model of education. More than ever, I am learning how to really push my learners to see beyond the obvious – making observations, developing generalizations and justifying their theories. Learning inside my classroom has moved from something I assign to learners to something that my learners explore and discover for themselves. These pattern exploration activities are examples of things I used this year to drive that deep thought. ## IMPLEMENTATION This resource is primarily for the teacher’s eyes only. It gives clear instructions for how to set up a conversation about the mathematics in play in each of the seven models. While seven expected discoveries are shown for each, it is certainly not an exhaustive list and it is not meant to be shared directly with learners. As the resource explains, the entire purpose is to have learners make the mathematical discoveries themselves. ## POSSIBLE EXTENSIONS Possible extensions are included in the file! There is always more research or exploration that can be done when we are drawing conclusions about sequences and patterns. ## MATERIALS/PREREQUISITES Besides this resource, you may require: –> Time and practice to condition your learners to know what a productive mathematical discussion looks like and sounds like –> Computer and Internet access