Des-blog

At Desmos, we like to build things that get students talking, and sometimes even arguing (we’re looking squarely at you, Central Park!) There’s lots to talk about in this week’s Friday Fave, starting with the title.

Which do you prefer and why?

(a) Scatter Plot Capture

(b) Scatterplot Capture

© Scatter-Plot Capture

Having resolved (or not) the orthography issues, it’s on to capturing points! The beautiful thing about statistics is that right answers usually consist of ranges of numbers, and they are usually “better” or “worse” answers rather than “right” or “wrong”.

In order to capture a point, you’ll need to pay attention to the trend, and to the degree the points appear to adhere to this trend. A small interval that catches the point is a better answer, but that is not always the advisable thing to try.

So the best answer is one that is the smallest you can make it, while staying certain that you’ll capture the point. You’ll need balance the constraints, and you’ll have something to talk about while you do.

So pair students up, play Scatter Plot (Scatter-Plot (Scatterplot)) Capture!

And while you’re think about scatter plots, maybe give these a test drive too….

Alligator Investigation

Polygraph: Scatter Plots

Commuting Times

This week Desmos fellow Anna Scholl asked us where our inspiration comes from when building Desmos graphs and activities. The Desmos fellows shared their sources of inspiration as well as activities and graphs to help inspire others.

Like many others, Jenn Vadnais shared that “My inspiration often stems from need. Necessity is the mother of invention.”

While most of our group was inspired to create based on a need to help students learn, several of us were inspired by our own need to learn and grow, the need to figure out how things work, and interest in general. Several of the Desmos Fellows pointed to our Potluck activities as a source of inspiration as well as activities and graphs posted on Twitter and in our internal chat channel. Suzanne von Oy shared that she generally makes graphs just for fun, finding inspiration from websites, tweets, and even requests from coworkers and students such as the graph below.

Bob Lochel shares that “What inspires me most when creating activities is thinking deeply about the path a student will take during an activity - I want there to be a clear thread weaving through, but I don’t want students to encounter any brick walls.” Our group was similarly inspired by this need for connecting ideas and supporting students in their thinking. Read our list below of student needs that inspire our activity creation.

• The need to visualize. Patty Stephens built this graph to help her students visualize a 3-Act task called Frosted Cube Cake.
  

• The need to play and explore. Jade White finds that her students are more active in discussions with their partner when they are working through an activity. Including activity screens where students can explore a math concept can increase discussion and student questioning as well.
  
• The need to discuss and make sense of mathematics. Allison Krasnow has been choosing problems from her curriculum’s exit tickets and using those to build quick error analysis activities. After discussing both correct and incorrect ways of thinking, students are invited to improve their initial responses.
  

• The need to reflect. Paul Jorgens asked his students to spend time noticing how this set of class generated equations for the screen above were the same and different. “We wondered if they drew the same graph. Groups used their understanding of reciprocals, division and negative exponents in the process of arguing whether they were the same (or not).”

• The need for feedback. Nerissa Gerodias appreciates activities that help students see their misunderstanding immediately. She hopes that over time this feedback leads to both increased understanding as well as curiosity that will inspire students to explore on their own and see the beauty in mathematics.
  

What inspires you in your Desmos creations? Let us know on Twitter @desmos.

With Earth Day, the March for Science and the National Math Festival all descending on our nation’s capital this weekend, the Friday Fave turns its attention to analysis of the world we live in.

That means modeling. And one of the Fave’s Fave modeling lessons right now is Charge!

What is the relationship between time spent charging your phone and its percent charged? Can you use this relationship to predict how long it will take to fully charge your phone? Are piecewise-defined functions just a cute trick mathematicians play, or are they useful for describing actual phenomena?

These questions and more are in play in this week’s Friday Fave: Charge!

And while the Fave is in a modeling mood, here are three additional gems. Enjoy!

400-Meter Modeling

Card Sort: Modeling

Mocha Modeling