Featured Lessons
Grades K-5
My teaching license is in 7-12th grade mathematics. However, I have studied the development of mathematical skills from subitizing to subtraction, counting to calculus. I have also tutored elementary school students. Here are some of my favorite activities:
Rekenrek: helping children visualize 5s, 10s, and 20s is foundational to numerical fluency
Rolling Coins: a big pile of change is a fun, tactile task that practices counting, making groups, and organization. Learning the value of coins can be confusing, especially since the size of the coin doesn't always align with its relative value!
Baking: Measuring out ingredients is a great opportunity to help in the kitchen and get more comfortable with fractions.
There are so many great games that develop reasoning & strategy skills. Here are few that even young kids can play:
Dominoes & Triominos (be sure to buy a ceramic set with the spinner in the middle)
Connect 4
Mancala
Grades 6-8
Schools in the New York State Consortium have a Regents waiver. Rather than passing standardized tests as part of their high school graduation requirement, students complete Performance-Based Assessment Tasks (PBATs) and present them before a panel. The goal is for each student to demonstrate their highest level of independent mathematical reasoning by solving a non-routine problem. Included below are some of the collected problems and resources I use to help students achieve this lofty goal.
I am always on the lookout for low-floor, high-ceiling math problems. Over the years, I have curated this list of problems based on student feedback. Many of my favorites come from NRICH.
Problem-Solving Template (and graph paper version)
When I was head of the math department, we created this template based off of George Polya's problem-solving process. Students have space to work and reflect on their process as they go.
Students complete multiple practice PBATs throughout the year. I use these labels to give feedback by printing them out and selecting the appropriate boxes.
Rubrics: middle school & high school
Practice PBAT Problems
These problems have been perennial favorites. I've written up lesson plans so that you can share them with your students, too!
Grades 9-12
Unit Circle
As part of the 2014 Park City Math Institute, I had the opportunity to participate in Japanese lesson study on the development of the Unit Circle. Here is our Google Drive folder of resources and the final handouts.
Calculus
While teaching remotely last year, I joined a group of Math for America teachers to design Desmos activities that utilized the Computation Layer. It gave me an appreciation for both how amazing Desmos is and the insane amount of work it takes to develop a great lesson.
Graphs
Limits Definition: a visualization of delta-epsilon definition
Limit Definition of Derivatives: a tool to illustrate derivative approximations
Riemann Sums: a tool to illustrate rectangular & trapezoidal approximations
Fourier Series: demo of square waves and sawtooth waves
Slope Fields: a way to visualize differential equations
Gaussian Integers: visualization of multiples in Z[i]
Pendulum Wave: just for fun!
Activities
Graphical Analysis: students predict what a given graph will look like
Limits: students calculate limits algebraically and graphically
Derivatives Practice 1: students use the power, product, and chain rule to take derivatives
Derivatives Practice 2: bigger and better than the last
Post-Secondary
While attending Ohio State University, I participated in Reading Groups that learned about and presented a lecture on topics of personal interest. Below are three such lectures that I delivered.
