Hey there!

We have some exciting news! The CL team is taking a break for the summer and will be back in August for the new school year. We’re also changing the cadence of our newsletter. We’ll be sending you less of what you don’t need and more of what you do need, so starting this year, we’ll send out more comprehensive newsletters on a quarterly basis—August, October, January, and April (we’ll aim for the start of your school quarters). There will be a fifth bonus newsletter in June to kick off your summer!

In the meantime, here’s a collection of the tips and tricks that we shared during this year’s CL Day:

### Counting variables

Combining substituteLatexVariable with countNumberUsage lets us count how many times a variable appears in an expression. Here’s how it works:

- Count the number of 1s that appear in an expression.
- Use substituteLatexVariable to replace every x with a 1 in parentheses. E.g., (1)
- Count the number of 1s that appear in the new expression.
- Find the difference.

Take a look at a demo of it here. One place we may use it is to check if students have fully simplified an exponential expression. We’d love to know how you use this trick!

### Recursive functions

Here’s a neat trick that lets us use evaluationFrames to evaluate recursive functions entered by students! Within an evaluationFrame, we can define a function that returns an element from a list:

In the code above, value would be equal to 20, the second element of the list we defined in the evaluationFrame. That’s pretty cool on its own, but check out this example we shared on CLDay to see how we can extend this idea to evaluate a student input such as f(n-1)+f(n-2).

### Lines with conics and conics with lines!

Want to interpret a student’s linear equation without multiple conditions for vertical and horizontal lines?

Use the conic tool!

If you pass an equation through the conic tool and make sure that every coefficient of a non-linear term is 0, you are left with the general form of a linear equation! Check it out!

Too simple? Try the opposite! Use some pattern matching to parse a factored equation and then xyLine to extract the parts of each term. Once it goes through xyLine, the coefficient can be derived from the slope and the y-intercept from the constant.

Have a great rest of your summer and we’ll see you again in August!