Polygraph - Distance Time Graphs

Have you ever played the game "Guess Who?". In that game you have a grid of people to look at and you choose one. Your partner has the same grid and gets to ask you yes or no
questions. As they ask questions and get their answers they start to eliminate people until they have only one left. Well the crew at Desmos have created a gave called Polygraph that works the same way except for graphs (and other topics). So far they have created one for parabolas, lines, rational functions, quadrilaterals, advanced quadrilaterals and hexagons. The way it works is you start a new session and get the 4 character code. Your students then go to  student.desmos.com and enter that code. They will the get a brief (optional) training session on how to play the game and then the software will randomly select students to play against each other, taking turns as to who asks and answers the questions.

But that is not the best part. The best part is they have created the Polygraph editor so anyone can create their own Polygraph. So that is what we did. This one is about the characteristics of a Distance-Time graph (or more generally a piecewise linear graph). There are no scales on these graphs so students will have to use general terms but we still think they will be able to relate to these with appropriate questions.

• MFM1P, MPM1D - describe a situation that would explain the events illustrated by a given graph of a relationship between two variables 

• Each student needs their own device connected to the internet. A phone will work but the images will be small. You may want to group kids together if the number of devices is limited. 

1. Go to this link and click on Start a New Session. You will have to log in to start a session but you can do that with your Google account or create your own. This will keep track of how your students responded and you can look at this any time you wish. You will be give a 4 character code that your students type in at student.desmos.com.
2. Once students log in they will try a test round with faces (they can skip this once they know what to do) and then as students complete the test round they will be paired up automatically with other students who have finished the test round. 
3. Instruct students to ask questions as if they were distance-time graphs 
4. Circulate through your class if there are questions. 
5. Note that you will need an even number of players otherwise there will be always someone sitting out.

No downloads needed, just the link https://teacher.desmos.com/polygraph/custom/56251492a23c2d7208dfe072

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Combining Velocity Vectors

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).
In this activity, students will walk through a demonstration of how the combination of two linear motions can create a complex two dimensional motion (in this case circular motion). Some things that I think are important here are the fact that the two motions are completely independent of each other and the idea of how the look of a velocity vector changes as you speed up and slow down. The sketch is meant for students to walk through and answer questions as they go. You could also use it in the calculus part of the course to talk about velocity increasing/decreasing and what that looks like for motion.

• A1.1 - describe examples of real-world applications of rates of change, represented in a variety of ways (e.g., in words, numerically, graphically, algebraically)
• C1.2 - represent a vector in two-space geometrically as a directed line segment, with direction expressed in different ways (e.g., 320º; N 40º W), and algebraically (e.g., using Cartesian coordinates; using polar coordinates), and recognize vectors with the same magnitude and direction but different positions as equal vectors
• C2.1 - perform the operations of addition, subtraction, and scalar multiplication on vectors represented as directed line segments in two space, and on vectors represented in Cartesian form in two-space and three-space

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch

• CircleVector.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my full page

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Geometer's Sketchpad - Practice Line of Best Fit

When using the Geometer's Sketchpad it is often better to "start from sketch, not from scratch". That is, give students a premade sketch rather having them build something from nothing (as many textbooks would have you do).
In this activity, students practice placing the line of best fit on a linear set of data. It's not meant to be really difficult but just to reenforce the idea of what the line of best fit is. Students can check their answer and try as many as they like. Clicking the Medium or Hard buttons will spread the points out more randomly to make the line a bit harder to determine. This is not meant to be really hard but just a quick way to determine if students have the basic concept of what a line of best fit is

• MPM1D, MFM1P - construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources
• MAP4C - D1.4 - create a graphical summary of two-variable data using a scatter plot (e.g., by identifying and justifying the dependent and independent variables; by drawing the line of best fit, when appropriate), with and without technology
• MDM4U - D2.4 - generate, using technology, the relevant graphical summaries of two-variable data (e.g., scatter plots, side-by-side boxplots) based on the type of data provided (e.g., categorical, ordinal, quantitative)

• All that is needed is the electronic download (below)
• Note that this really works well on an iPad using the Sketchpad Explorer App (which is free)
• You can also use this on any web based computer (or Chromebook) with this Web sketch

Watch the video below to see how to use the sketch

• Line of Best Fit.gsp (iPad/V5)
• Web sketch here
• For more sketches like this go to my look at the dynamic web sketch tab above

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks