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# The World Is Maths

### graphs

My second Desmos activity is designed to reinforce understanding of the features of displacement-time graphs.  Students are asked to describe parts of graphs, interpret the gradient of the line, and write a mathematical story based on reading a displacement-time graph.

As always, all feedback is welcome.

(Photo by Martijn Van Dalen)

I’m intrigued by the Desmos Activity Builder and where it might be useful for my students.  One of the first activities I’ve made is based on the idea of fitting graphs to photos of naturally-occurring or man-made parabolas, which I first encountered in Adrian Oldknow’s book Teaching Mathematics Using ICT back in 2004.

In my activity, students are asked to fit some parabolas to photos of bridges and fountains.  And a banana.  They are also asked to explain their thought processes before they attempt the graphical transformations. Continue reading “Picture Perfect Parabolas (Desmos Activity)”

EDITED:  Thanks to the wonderful folk at Desmos, who helped me solve my problem within minutes of tweeting it, I now have fully functional models.  The problem was making the black dotted distance lines only point to the relevant focus/directrix and not both.  Writing lines parametrically – that’s how to impose conditions on when they appear.

I’ve been trying to make some models to show the relationship between the curve, focus and directrix on conic sections, Continue reading “Conic Sections (Desmos)”

I dislike education acronyms, but I can make exceptions for mathematical ones.  One of my favourite topics in A-level Maths is full to bursting with them: DRVs, CRVs, PDF, CDF.  This is a visual representation of the CDF (cumulative distribution function) of a CRV (continuous random variable), which is the function for the area under the curve from x=-∞ to any other value, a, or more specifically, P(X<a).  Take note of the syntax for piecewise functions. Continue reading “Continuous Random Variables (Desmos)”

You can do a simple model of projectile motion in Desmos and create sliders to alter the angle and speed of projection in order to see how these affect the motion.  Make sure you have angles set to measure in degrees (settings, above zoom, right-hand side).

Graphical inequalities aren’t quite how you’d want them to be on Desmos, simply because it shades the side of the line that produces true statements rather than false.  Of course, in linear programming with multiple inequalities, you really want the true sides left blank for clarity.  So you have to cheat and reverse your inequality signs to get Desmos to shade the way you want it to, but it’s still a lovely visual.

I’ve made up an example, and shown how you can use a slider to get the objective line to move within the region.  Since you can click on points of intersection, it’s easy to consider all the vertices of the region as well.

Quite simply, demonstrate the value of e using the fact that

$\frac{d}{dx}[e^x]=e^x$

with the sliders on this model.

Back in 2010 I, and 12 million other people, became slightly addicted to a little game called Angry Birds.  I stopped playing after a couple of months, like I always do with these things, not sure what happened to it then, probably petered out like so many other overnight success stories.

The premise of the game was to get your little birds to destroy some nasty green piggies who were stealing your eggs by launching them from a slingshot at the pigs’ defences.  I can see why those birds were angry, I would be if I were repeatedly being launched, projectile-style, at towers of wood and ice and stone.  That’s gotta hurt.

The programmers use some fairly simple mathematics to get those birds to move in a realistic way.  You intuitively expect the birds to move through the air in the way they do because all objects move like that, unless some force causes them to change their path.  Picture it now – imagine throwing a tennis ball, what shape does the path of the ball take? What about a diver jumping off a diving board, or a bullet flying through the air, or water spouts from a fountain? Continue reading “Flight and Fight”

Last year I made a couple of models on Desmos to demonstrate aspects of the normal distribution to my statistics students.

1.  Standardising

In this first one, you can set a normal distribution with any mean and standard deviation and then show what happens when you subtract μ and divide by σ to standardise the distribution (to do this, simply move the sliders).  It’s great because students can now visualise the procedure they are carrying out. Continue reading “The Normal Distribution (Desmos)”