Patterns Unit (updated version of our previous Functions Unit)
We usually teach this unit early on in the school year. The visual pattern problems are great for building the collaborative culture in your classroom and for getting students comfortable presenting their ideas to their peers . These problems also have a “low floor and a high ceiling” and they show students that mathematics is a beautiful, creative, and open subject. Our mathematical goal in this unit is for students to visually make connections to two very important concepts: Initial value: & Constant rate of change. The patterns unit is the prequel unit to the Linear Unit below.
The goal of this unit is to have students experience a set of contextualized problems that represent linear situations and lead to a deep understanding of slope, y-intercepts, and linear equations.
Transformational Geometry Unit
Traditionally, transformational geometry has been taught in a procedural way in which the teacher explains how to perform a transformation and the student practices the transformation. The students have no opportunity to think critically and they don’t see the need for transformations or the element(s) of each transformation.
Conversely, in our unit, students will discover and see the need for the most important elements of translations, reflections, rotations and dilations through a series of open ended problems. Additionally, students will learn how to use geometric transformations as a tool to prove congruence or similarity.
Our Student's Experience with the Transformational Geometry Unit
“I enjoyed the time where we would have to figure out how a shape was transformed by asking as few questions as possible. It was a hard problem but it was fun, and we would go to a harder problem when we figured it out.”
“A memorable problem was during the transformation unit where we had to ask specific problems and it was hard to explain things like why you turned a shape or why you flipped it.”
“I liked when we had to find out how many questions it takes to make a certain transformation. This was memorable because as a group we really had to come together with our ideas since this was very challenging problem at the time.”