Last week, I bumped into Judith Seidel (@seidelj) at a lecture at the Museum of Mathematics. She suggested I explore a Cardioid Activity on Geometer’s Sketchpad — and just in time for Valentine’s Day too! A quick Google search yielded these resources which I forwarded to the Math Department:
1. A Geometer’s Sketchpad lesson plan:
2. A video tutorial with doable paper/pencil/ruler instructions:
3. More information about cardioids and the math behind them:
I’ve had a deep love and respect for Geometer’s Sketchpad since I was first introduced to it in 1994 as an undergraduate Math major (and aspiring math teacher) at Bryn Mawr College.
Later, I used Geometer’s Sketchpad during my student teaching stint at Strath Haven High School and again as a pre-Algebra/pre-Geometry teacher at The Dalton School.
Today in 6th grade Math at The School at Columbia University, Katie Klein (@KKleinNYC) and her associate teacher, Jazmin Sherwood, facilitated a great lesson on Fractals blending direct instruction, video, and self-paced sketching with and without technology.
1. Homework from the previous night was to watch the first 20 minutes of Fractals, Exploring the Hidden Dimension.
2. Here’s a link to beautiful photos of fractals found in nature: http://io9.com/incredible-photographs-of-fractals-found-in-the-natural-480626285
3. Here are instructions for drawing Sierpinski Triangles with paper and pencil:
4. Here are instructions for drawing Sierpinksi Triangles using Geometer’s Sketchpad on their laptops:
5. Here’s another resource for making other fractals with Geometer’s Sketchpad: http://www.gwinnett.k12.ga.us/PhoenixHS/math/GSP-website/17_Fractals(51-61).pdf
6. With additional time, students could explore fractals with Scratch or Snap (both are web-based block-based programming environments). Here are some links I gathered:
So, now I know that hexaflexagons are awesome! On Vi Hart’s YouTube channel she describes herself as a professional mathemusician at KhanAcademy. Here’s the description of her latest video:
This video is based on a true story. Arthur H. Stone really did invent the hexaflexagon after playing with the paper strips he’d cut off his too-wide British paper, and really did start a flexagon committee (which we’ll hear more about in the next video). The details and dialogue, however, are my own invention.
More info coming soon, along with patterns. But in the mean time you can find instructions and printable patterns on other parts of the internet.
Follow Vi Hart on Twitter at @vihartvihart.