Order of Operations
As we progressed through our unit on rational numbers, it became time to work with “Order of Operations”, always a tough concept for middle schoolers that takes a lot of practice.
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
I chose to add a “Wreck-it Ralph” programming activity, one of the first I created for this class. This was a troubleshooting activity in which I gave the students this premise: I made a program that showed how many students attended pep rallies over the last few weeks. I wanted to average the pep rally attendance and display the average. However, my bar graph doesn’t look right. Clearly, Wreck-it Ralph went into my program and broke it! The students’ challenge is to fix the errors.
I directed them to Khan Academy and the program that I had made.
I put them into groups and asked them to work together to troubleshoot the problem. They saw the first mistake pretty quickly: the bar for “d:119” couldn’t possibly be correct, because it was the same length as the bar for “c:312”. The error in the code is a pretty simple problem with a variable name in the wrong place, but it was powerful for students to see variables used in this way. For some, this made the “light bulb” go on that using a variable in a line of code actually substitutes the value of the variable.
The second problem, that of calculating the average incorrectly, was more difficult. When questioned, all of the students could tell that 703.75 was way too large for the average pep rally attendance, but they did not see quickly how to change it. Slowly, though, the solution spread throughout the room. Students needed parentheses in the averaging expression “a + b + c + d / 4”, otherwise only the last number was divided by 4. It was a classic “order of operations” mistake.
The activity only took half of a class period, but it marked a turning point in the class: a point after which most of the students understood the use of variables in math expressions. They loved that they got instant visual feedback on whether their answers were correct, and they found the activity engaging and interesting.
Neither the students nor the teacher needs to know how to code to make this troubleshooting activity work. It’s accessible for everyone!
What are some other good computer-based activities for order of operations? Knowing how to model a complex math formula with technology is a classic 21st century struggle. How would you approach it?