Des-blog

The Friday Fave has been playing with the Desmos geometry tool this week. Tessellations, kaleidoscopes, and many other varieties of fun are to be had over there. Our new transformation tools make such constructions straightforward—you can translate, rotate, dilate, and reflect.

The rotation tool requires a center and a degree measure. The dilation tool needs a center and a scale factor. In both cases, it’s really handy to be able to specify the relevant number directly in the tool.

But what if you want to have the rotation be driven by an angle that arises in your construction? Or have the scale factor be the ratio of two lengths in your sketch? Well, that’s when the rotation/dilation tool comes to the rescue.

A rotation/dilation is defined by three points:

1. A center
2. A preimage point
3. An image point
   

Make those three points collinear, and you’ve got a straight-up dilation.

Put the last two points on the circle centered at the first point, and you’ve got a rotation.

Do anything else, and you’ll end up with something that dilates according to the ratio of the two distances from the center, and also rotated according to the difference between the two points’ directions from the center.

This construction by Sean Sweeney—which is this week’s Friday Fave—is a great way to explore how the dilate/rotate tool works. Go play with it yourself, and be sure to share your creations with us!

While you’re thinking about rotation, here are some great activities for helping your students explore the mathematics of rotations.

Transformation Golf: Rigid Motion

Des-Patterns

Laser Challenge

Polygraph: Transformations

Two years ago the Desmos Fellowship was born. The idea behind the Desmos Fellowship was simple: Bring together a group of talented, reflective, and diverse educators, and support and learn from them however we could. We flew the Desmos Fellows out for an all-expenses paid trip to our headquarters in San Francisco, where we spent the weekend learning, activity building, collaborating, community building and setting up relationships that would carry us through the year and beyond. After that weekend we continued to support the Desmos Fellows by offering weekly prompts to help them reflect and learn from each other, and we continue to build community through both virtual and face to face events.

What we didn’t anticipate was that the fellowship would become an integral part of the work that we do in the math education world. We receive far more from the Desmos Fellows than we could ever give. We are so grateful for the opportunity to learn from and with this amazing group. In the past two years the Desmos Fellows have had the first look at all of our new features and activities, offering feedback to help us make them the best we possibly could. Desmos wouldn’t be the same without its Fellows.

We look forward to supporting and learning from them the following teachers, our third Desmos Fellowship cohort:

• Allyson Timko. Miamisburg High School. Dayton, OH
  
• Andy Schwen. Anoka Hennepin School District. Blaine, MN
  
• Angel Prado. Sweetwater Union High School District. San Diego, CA
  
• Annie Forest. Berwyn South District 100. Brookfield, IL
  
• Annie Perkins. Minneapolis Public Schools. Minneapolis, MN
• Audrey McLaren. Learn. Dorval, QC
  
• Bob Janes. Capitol Region Education Council. East Hartford, CT
  
• Christelle Rocha. Robert Louis Stevenson Middle School. Los Angeles, CA
  
• Cindy Whitehead. Arlington School District. Stanwood, WA
  
• Dave Cesa. Charlotte Latin School. Charlotte, NC
  
• David Fier. Williamsburg Charter High School. New York City, NY
  
• David Petro. Windsor Essex Catholic District School Board. Harrow, ON
  
• Geeta Makhija. Berkeley Unified School District. Oakland, CA
  
• Joanna Stevens. Lincoln County High School. Lancaster, KY
  
• Jodi Donald. Independence R 30 School District. Lee’s Summit, MO
  
• Joe Dziuba. New Brunswick Public Schools. New Brunswick, NJ
  
• Juan Gomez. Carmel Unified School District. Monterey CA
  
• Justin Brennan. Community Unit School District 303. Plainfield, IL
  
• Kathleen Carter. North Hunterdon High School. Easton, PA
  
• Lara Metcalf. Georgia State Schools. Atlanta, GA
  
• Lauren Baucom. University of North Carolina at Greensboro. Wingate, NC
  
• Larissa Peru. Sunnyside Unified School District. Tucson, AZ
  
• Lauren Johnson. Hacienda La Puente Unified School District. Fullerton, CA
  
• Liz Caffrey. Atrium School. Arlington, MA
  
• Lori Bodner. Brooklyn Technical High School. Brooklyn, NY
  
• Martha Mulligan. Chicago Public Schools. Chicago, IL
  
• Mary Watson. Cedar Falls Community Schools. Cedar Falls, IA
  
• Mary Williams. Midlothian High School. Powhatan, VA
  
• Michelle Griffin. Maine-Endwell Central School District. Endicott, NY
  
• Nico Rowinsky. Toronto District School Board. Toronto, ON
  
• Oscar Perales. Richardson Berkner High School. Dallas, TX
  
• Patrick Aquino. The Chapin School. New York, NY
  
• Paul Chun. Downey Unified School District. Downey, CA
  
• Richard Hung. Palo Alto Unified School District. Santa Clara, CA
  
• Stephanie McBride-Bergantine. Bozeman School District #7. Bozeman, MT
  
• Steve Phelps. Madeira High School. Cincinnati, OH
  
• Tim Hébert. Sacramento City Unified School District. Sacramento, CA
  
• Tim Marley. Troy High School. Royal Oak, MI
  
• Wendy Menard. New York City Department of Education. Brooklyn, NY
  
• Yannabah Weiss. Hawaii Dept of Education. Hilo, HI
  

Please join us in welcoming these amazing teachers to the Desmos Fellowship!

Desmos is in full effect at #NCTMAnnual and we’re announcing the release of three major new features.

Transformations in Geometry

We continue to upgrade our Geometry tool. First constructions. Now transformations. You’re going to love how easy it is to explore congruency or generate geometric art.

Computation Layer

For the last year, Desmos has been building activities using a scripting language called Computation Layer. Computation Layer allows us to ask students questions on one screen, then give interesting feedback on their answers on another. It allows us to ask students for a sketch here, then render the sketch as an animation over there.

We spent a large part of the last quarter getting the documentation of those features in great shape, creating a support community around the language, and making the building experience as smooth as we can. It’s now available to you.

Activate it in labs. Start playing with basic connections between components. Ask questions. Build something amazing.

Trivia

Last night, one hundred attendees showed up for the Best Dang Happy Hour & Trivia Contest anywhere at NCTM. For the first time, we ran the trivia contest through our Activity Builder which allowed us to ask more interesting questions in more interesting ways and to be able to hook you all up the trivia questions today.

Check ‘em out and many congrats to Leigh’s Lemmas for their triumphant finish.