When I began my teaching career in 1973, my primary subject was middle school mathematics. Specifically, I taught the ever-feared Pre-Algebra.
As I came to know my students, I slowly realized that, at ages 12 to 14, we humans are an extremely variable lot, so to speak. Some of us can discern a linear relationship. Many of us, alas, don’t have a clue!
In order to help our students dig deep into math principles, a colleague and I developed a series of hands-on activities we called “math labs.”
The idea was to involve our students in multi-sensory, 3-D activities. Topics covered were: probability in gambling (dice and playing cards); drawing 2- and 3-D geometric patterns with compass and straightedge; and figuring out the next best move in a particular chess situation.
It worked. Kids were motivated by the challenges to learn, and we had conversations linking the math labs to the content standards. This student engagement then carried over into the traditional computation-based homework and classwork.
Fast forward to 1998, when I became the “computer teacher” in a local middle school. By then, my school had networked computers. Every student had an account with email, access to the internet and Microsoft Office applications and a network drive in which to store files.
My students also had access to the MS Excel spreadsheet. I wondered, could we use this digital tool as another math lab? We created a game for the spreadsheet called, “The Combining Practice Puzzles.” The idea was to use a spreadsheet’s ability to calculate the value of any equation to help solve parts of the puzzle.
For example, one puzzle requires a student to combine the numbers 1, 2 and 3 using math operations to equal the numbers zero to 10? The student must use all three numbers, but only once for each number.
So, how do we make zero with the numbers 1, 2, and 3? Answer: enter the equation “= 3-2-1” into the appropriate cell in the spreadsheet, press the Enter key, and there it is, zero!
OK, how to make 1? Enter the equation, “=(3-2)*1” and press the Enter key. Note that multiplication is denoted with the “*” character rather than the “x”. Note also that we are using parenthesis to tell Excel, “do the subtraction first.” A good application of the order of operations rules.
Can you use division (/) to come up with an equation that equals 1? Yes, try entering “= 3/(2+1)”. It works! Again, students must remember that the parenthesis mean, “do this part first.” So, the equation is essentially, “=3/3”.
“Wait,” you say, “but how do you combine 1, 2, and 3 to make 10? Can’t be done with add, subtract, multiply and divide.”
Well, that is true, but we have other operators available to us in a spreadsheet. We can use the “^” operator to raise numbers to a power. It works like this, “=3^2+1.” This equation means, “multiply 3 by itself, then add 1”. Again, students must understand that “3^2” means “3*3”, not “3*2”.
Entering equations correctly into a spreadsheet helps students grasp the fundamental concepts of pre-algebra. It is a simple form of programming. The equation contains information that the spreadsheet understands. Students are thus learning that they can “design” equations, and technology, to do work for them.
In this environment, the mathematics has a concrete purpose: Use equations to make the spreadsheet do what you want it to and solve the puzzle.
This example of putting a spreadsheet in the hands of adolescent math students is fun, with multiple learning points. Try it. If you need help, I can send a copy of the Combining Practice Puzzles to you. Just email me a message and let me know if you want it in MS Excel format or in Google Sheets format.
But, please, don’t ask me to give you any more answers. That’s no fun! (But I will give hints.)
Tom Fanning is the technology teacher at Pelham Elementary School and co-director for technology for the Western Massachusetts Writing Project. He can be reached at richtfanning@gmail.com.