#codemaths: algebra functions and image URLs

I've added some function (for my own benefit really) that saves time in anticipating many scenarios in generating random questions--reduce() and coeff() functions using the #codemaths application.

When used, the reduce function can simplify fractions. For example, for random variables a and b, reduce(a,b) would simplify a=4 and b=1 to 4 and a=2 and b=4 to 1/2. It is still your job to make sure b is not zero with the constraints.

The coefficient function allows expressions to be simplified--most helpful for anticipating the best final answer. There are some specific options to differentiate how it is used.

If I have the expression ax+by=c using random values for a,b and c (again making sure 'a' and 'b' aren't zero in the constraints), if I use the coeff function I can programmatically simplify the scenario 1x+-4y=5 to x-4y=5. 

To code it you need to use "lead" for a coefficient like a that is the lead coefficient in the expression and "constant" if a term you want to simplify is just a constant term with no variable. 

In the example above you would code <coeff(a,"lead")>x<coeff(b)>y=<c>. In this case you don't need the "constant" or coeff fuction for c. The equation 1x+-1y=3 would simplify to x-y=3.

That could be used in this example however: ax+b=c: <coeff(a,"lead")>x<coeff(b,"constant")>=<c>. The equation 1x+-1=3 would simplify to x-1=3.

You can also now use a url of an image to be included in a question such as this one:

Here is an example of a question set using pythagorean triples and this diagram.

#codemaths explained: Made to test and share code easily with students

I've since added some functionality to the #codemaths platform that will allow for easier exploration for students and some quicker editing for me (video). As I move into working with tables and graphs on a more regular basis I wanted a way to be able to display either or both of them in a question without having to recode it each time. Through the use of checkboxes a graph and/or associated table can be displayed alongside a question. I also have it set to automatically provide a link to the code (if a student gets the question wrong) so students can look under the hood of each practice question that I make for them and learn from seeing examples of working 'code'. In this example you can see the use of creating an array and sorting it so that the listbox choices are randomized a bit so the correct answer is not always in the same place.
I've also tweaked the code export a bit to be more stable so it really is just a cut and paste for me to build a question set to be used in the practice part of our learning cycle. This has been a really fun project for me as it has developed. As always I'm trying to take out some of the technical stuff so that it is more accessible to other teachers wanting to dabble in it.
To build question sets using custom code, check out this post.

Applying student learning to writing code

Today in class I worked with a small group of kids on applying Google Apps Script concepts to some basic algebra that they have learned in the past. I have not done anything like this before with students so I am beginning to think through some of the pieces that they will need to know. I am getting their feet wet by using the same computer generated practice template that I've been using to provide practice for students in my algebra classes.
Please know that I am not completely going computer math here--this is just what is used for the practice and remediation cycle for my students. We are still having class discussions on parallel tasks, open ended questions, pulling out algebra tiles and self-assessing our own work and understanding.
Here is a link to a presentation outlining some of the components needed to begin working in it.