Calculating/Measuring: Students have been using calculators for years, but there’s never been a single device as versatile as iPad—which means a wealth of new reckoning and measuring options for science and math lessons.
Not your old Texas Instruments
The iPad is a prodigious mimic, able to replicate an entire curiosity store’s worth of gadgets on a single device, but it comes into its own when it extends what was possible in those original machines. So when you search for “calculator” on the app store, you can expect to retrieve much more than the gadget you may have used at school…and with it, some exciting new teaching possibilities.
Calculation with working(!) and rewind(!!)
Traditional calculators are great for working out one-step problems, but can be unwieldy when multi-step calculations are involved, particularly if you need to track down errors. Students trying to work out what a 35% discount on twenty bananas that are $9.60 for a box of a dozen will need to keep notes as they go—especially if the same question also features similar calculations for apples, apricots and oranges. Even if the student is well across the concepts involved, all those numbers can tend to mingle and then escape, like kittens from the open door of a pet store.
iPad apps such as Soulver offer students a way to manage the chaos: it allows students to enter their problem as words on the left, and then see the corresponding calculations on the right, with each individual step of the process listed and retraceable. Similarly, Digits allows students to give labels to each calculation in a sequence, so that they remember exactly what each of those steps was for.
Either way, it means that when a student puts up their hand, you’ll not only be able to see all the steps in their solution, but can jump back to any one of those steps. Make a change to any line item, and that change then cascades through the rest of their calculation—it means you can correct what’s wrong without having to discard what’s right.
So much more than just numbers
Certainly, there are plenty of calculator apps that reproduce real world school calculator functions, working with arithmetic, factorials, exponentials, logs, fractions and the like. But calculator apps for the iPad can also draw graphs, solve algebra and calculus problems, work with vectors and matrices, perform currency and measurement conversions, and can convert natural language problems (“what is 50% of $230?”) into both formulas, and solutions.
One brilliant illustration of just where this sort of lateral thinking from developers can take students is an app called Algebra Touch (see the movie on the previous page)—the student is able to combine like terms, simplify fractions, regroup, factorize, all just by dragging terms around. But when it reaches the stage where 73y+134y-27y are all on the same side of the equation, the calculator will allow the student to tap to automatically complete the required addition and subtraction, because the arithmetic is not the point—a bit like tapping in a putt once you’ve done the hard work of a solid drive and a tight iron shot.
The result? For those lessons when the emphasis is on process rather than doing the final steps monkey-work of actually nutting out the answer, the right iPad calculator can ensure that students get through many more examples than they would have otherwise.
Another example of advanced calculation is the Wolfram Course Assistant series of apps, covering everything from calculus to chemistry to music theory—in each case, the student can input whatever the problem is, and the calculator will generate both an answer, and a step-by-step guide for how to get there.
For those of us who grew up knowing that calculators could add and multiply, this is a whole new world…whether you’re using tools like these or not though, be certain of this: your students will be using them. I mean that both as a call to opportunity, and a warning. The back of the textbook is not the only place that students can now look up worked answers to complex problems.
Fun, pizazzy options
It’s not just the functionality of calculators which has been transformed when you use iPad versions. A great deal of thought has also gone into the appearance of some of these apps, which means that the calculator your 4th graders are introduced to doesn’t have to look like it’s escaped from an accountant’s bottom drawer.
A developer called Goatella offers a range of weird and wacky calculators through the app store; if you’re running a unit on money, their Coin Calculator is a currency-themed calculator that lets you click on coins or notes to add them up, with support for US, Australian, UK, Canadian and Euro coins and notes. Alternatively, students could work with the SteamPunk Calculator, and actually see the cogs and wheels turn as the app crunches the student’s numbers.
Other developers have created calculators that mimic old-world classics (search for Vintage Calculator) or typewriters (Red Valentine), or just plain crazy (look for Stone Tablet Calculator at the app store to see perhaps what Fred Flintstone used to do his taxes on)
Useful? Probably not. Engaging? Absolutely. These are calculators students will want to use.
Calculators on demand
Even if iPad calculators were no more than duplicates of physical machines, they still offer one huge advantage over their 1980s counterparts: students don’t need to remember to bring them. Because students have their iPads with them at all times, calculators can be summoned at any time with a single tap.
And when they’re put away afterwards, they don’t take up a single square inch of space, or weigh even so much as a shadow—they just disappear safely back inside the Big Bag Of Holding that is the iPad, along with all the other lesson-transforming apps that you’ve packed it with.
Well, perhaps not everything, but there are plenty of science lessons that could make good use of the multi-function marvel that is Multi Measures. Load it up, and your iPad can measure decibels, the strength of magnetic fields (I’m not making this up. The app promises it can. Please don’t ask me to explain how it works though), distances, angles, time elapsed…it even includes a seismometer, metronome and spirit level. Not as accurate as specialized hardware, but certainly enough for a host of in-class experiments.
Another app called EasyMeasure will use the iPad’s built in camera to tell you how far away distant objects are—again, probably not something a surveyor will depend on when constructing a bridge, but a great tool for students trying to map their surrounds.
Similar to this—and not to be confused with the earlier described Multi Measures—is Multimeasure, which calculates the length of straight lines in photos you take. So, for example, you can take a snap of the classroom, and have it work out the width of your whiteboard, or the distance from the floor to the ceiling. (See also the chapter on planning)
Musicians aren’t left out either, with ClearTune’s feedback on instrument tuning being accurate to within 1/100th of a semitone. (Which is a good deal more accurate than instrumentalists are likely to be when playing)
…and convert anything
Whether it’s converting yards into kilometers, kilogram forces into Newtons, or BTUs into Electronvolts, Ultima Utility (for iPhone, but works fine on iPad) will instantly re-render your raw data into the units you need. It’s one of those apps that you won’t need at all for 99% of your teaching time…until, quite suddenly, you really need it…although…
…you could just ask Siri
If you’re using iPad 3 or later, many of your basic calculations can be performed simply by asking Siri your question. So when I asked “What is two-thirds of the square root of one hundred and forty-four?”—it came back with the correct answer faster than I could have loaded up a calculator and input the question. (see the screenshot on the next page)
A couple of caveats. First of all, it doesn’t cope so well yet with problem-based questions. So when I asked “If bananas are $10 for a dozen, how much would one banana cost?”, it offered to look that up for me on the web, at which point I was able to learn a great deal about pricing models for bananas in general, but no illumination for the bananas in question.
Secondly, as a voice-activated service, you do need to be alert to errors in transcription. I find Siri to be almost creepily accurate most of the time, but every so often, it mishears you, and you end up with a howler.
If you’re running iPad 1 or 2
Unfortunately there’s no Siri for these older iPads, but if you install Google Search, you end up with much of the same voice-activated calculation. Simply speak your question, and let Google figure it out for you.
We’ll look again at both Siri and Google Search in the chapter on Researching, but if a student needs a quick and straightforward calculation, there’s really no faster way than simply asking their iPad…
…something you’ll need to be aware of if the whole point of the task at hand is for them to practice whatever it was that Siri is now figuring out for them.
Timers and stopwatches
iPad’s inbuilt clock app also includes both a stopwatch and a countdown timer, which should cover most of the basic timing you need. A more feature-rich option is an app simply called Timer which will allow an otherwise standard countdown to be punctuated with whatever reminders and messages you need—”halfway there” “10 minutes to go everyone”—useful for time-limited in-class multistep projects.