Using Restrictions in Innovative Ways

Let’s talk restrictions.  So helpful, so amazing.  I’ve seen people use restrictions in some very creative ways lately, so here’s the lowdown on cool ways to use restrictions.  Make sure to scroll to the end to see an Angry Birds activity that makes extensive use of restrictions.

First, the classic use: restricting x and/or y.

You can restrict just the x values, or you can restrict just the y-values, or you can stack restrictions.  Desmos even knows the difference between AND and OR:

Here, I’ve shown a graph with x > 0 OR y > 0
In Desmos, type the restrictions in the same bracket, separated by a comma: {x>0,y>0}

BTW, this is super helpful if you want to do something like this:

Restriction by List 2

Here, I’ve shown a graph with x > 0 AND y > 0
In Desmos, type the restrictions in separate brackets: {x>0} {y>0}

The team at Desmos has also made it possible to place restrictions on both x and y at the same time in an implicitly defined inequality.  Here is one example:

Link to Desmos: see how this is done!

Second: restricting parameters.  This allows certain aspects of the graph appear or disappear depending on a certain parameter.  It also can be used to make whole images appear or disappear.  Here are some of my favorite examples lately:

Here I built upon a graph that Desmos had featured, and set it up to turn on tangents by sliding a point on the graph.  This technique is awesome for building teacher activities where you want to make a graph into an interactive exhibit (i.e. students can’t access the expression list, just the  graph itself.)  Check out the graph here.

For another example, here is a tweet by Stefan Fritz showing a fantastic Angry Birds activity he created that gives students feedback as they work through the clever use of restrictions on parameters.  Here’s the link to the teacher activity for anyone who wants to use it!  Such a fun activity!


Ideas for Desmos PD Day

On Feb. 16, I will be running a PD session for my department on how to use Desmos effectively in the classroom.

I would say more than half the department is coming with little to no experience with, and limited experience with the calculator.  I am planning on assuming no prior knowledge.  We will have 3 hours together.  Everything is still a work in progress, but I’m hoping to get suggestions and feedback!

So far, here’s the plan: Continue reading

Rotating a Function

You can pretty easily use parametric equations to rotate a function through any angle of rotation.

  1.  Define a function, f(x)
  2. Either choose an angle measure, a, or leave a as a slider and type in this parametric equation: (t·cos f(t)·sin a, t·sin a+f(t)·cos a)
  3. You’ll need to specify the values of t.  I generally use -20 to 20, because that will cover what is visible in a normal zoom.  If you want to zoom out quite a bit, though, you may want larger values as your bounds on t.
  4. If you want to animate the rotation, specify the bounds on the slider a.

Check out this example!  Click on the Continue reading