CS Variables and Expressions

To introduce students to variables and expressions, I used a flipped lesson on using formulas to calculate area, and then a pairs programming activity on divisibility.

Relevant CSTA and CCSS standards. I decided to have the kids work with the area of an ellipse because they enjoyed that connection with the area of a circle – it’s a challenging formula to write in a program, as well.

CSTA:L2:CPP:5 Implement problem solutions using a programming language, including: looping behavior, conditional statements, logic, expressions, variables, and functions.

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Apply properties of operations as strategies to multiply and divide rational numbers.

To give the students vocabulary and build knowledge of syntax, I made a little video lesson for them to create shapes and calculate their area. This is their first introduction to assignment statements.


STARTER PROGRAM: Variables and Expressions

One solution to drawing and calculating the area of an ellipse.

One solution to drawing and calculating the area of an ellipse.

Their individual assignment was to finish the program, drawing an ellipse and calculating its area using a formula they found in a search engine. Many students didn’t process that the height and the width of the ellipse weren’t the same as the two radii, so they calculated pi * height * width to calculate area.  I mentioned that I had remembered a circle had just about the same area as 3/4 of the area of the square enclosing it, so could it make sense that the ellipse had a greater area than a rectangle with the same width and height? The students partnered up to troubleshoot and write the expression correctly – some form of ea = 3.14159 * eh / 2 * ew / 2;  We had a good discussion about whether or not parentheses were necessary in the formula.

Next, we did a quick whole-class lesson on floor division and modulo operators. Divisibility is a really important concept in mathematics and in computer science. In JavaScript, the two operations look like this.

a = floor (b / c);    // divides b / c.  truncates to a whole number with floor().

a = floor (6/3);    // a is assigned to 2

a = floor (10/3);   // a is assigned to 3

a = floor (104 / 10);  // a is assigned to 10

a = b % c; // divides b / c and assigns a to the remainder.

a = 6 % 3; // a is assigned to 0

a = 10 % 3; // a is assigned to 1

a = 104 % 10; // a is assigned to 4

The next activity was a pairs-programming activity. I asked the students to find a partner. One would type, the other would look over their shoulder, read the prompt, make suggestions, and help troubleshoot. I set a timer so the roles would switch after 10 minutes. Students have a hard time switching roles! The one using the keyboard gets very comfortable in that position and the one not typing often is self-conscious about it. It will take some coaching for the kids to get more comfortable with pairs programming, but it will be worth it.

I gave the students a scenario. Let’s say I walk into a bank with 2778 pennies. I want to come out with the smallest number of coins and bills possible, so what will the bank give me and how did you come up with it?

We had a whole-class discussion about using division and modulo to come up with a twenty, a five, two ones, three quarters, and three leftover pennies. The students then got a starter program and started pairs programming. The starter program was about a fictional money system and making change.


This was a really challenging task and it would need quite a few catch-and-release times. I should have used more! During the summary, two different approaches to solving the money problem came out.

Solution 1: Convert to the biggest currency unit first, then divide up the leftovers.  Some students related the problem to how we convert money. If I have 2778 pennies, I’ll look for how many hundreds, fifties, or twenties I can make first and work down. These kids had to calculate that there are 105 zinks in a zab and then work from there.

Solution 2: Convert to the second-smallest currency unit first, then make groups of the next-smallest, and so on. Each time the leftovers get assigned to the small currency units.

Great intro to variables and expressions – next we would tackle conditionals.


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About dupriestmath

I'm a former software engineer who has taught middle school math and computer science for the past 6 years. I believe every kid has the right to be a thinker. I started this blog to save resources for integrating programming in the Common Core math classroom. I also use it to save my lessons and reflections from teaching budding computer scientists! Coding has transformed how I teach and think. You'll love what it does for you. You should try it.

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