By Michael Hartley
Here's a nice calculator game that will attract the word-lovers in your math class back to their arithmetic. You'll need a calculator. It should be a calculator with a so-called "7 segment" display - something like what is shown below :
The trick is, when this is turned upside down, the numbers look like certain letters (especially with a little imagination thrown in). So the number 17246 above becomes the letters ghZLI below.
On the calculator I use, the digit 0 becomes O, 1 becomes I, 2 becomes Z, 3 becomes E, 4 becomes h, 5 becomes S, 6 becomes g, 7 becomes L, 8 becomes B, and 9 becomes G. Of course, turning the calculator upside down also reverses the digits, so 1234 would be hEZI, not IZEh. With a little effort, one can easily find numbers that correspond to words. And then, to construct formulas that give those numbers.
For example, do you want your calculator to be more friendly? Try this calculation :
- enter 6.2
- multiply this by itself
- add 0.23
- divide by 50
- turn the calculator upside down, and you have a friendly greeting!
Or how about a nice breakfast? Try this :
- multiply 17 by 2
- multiply by 1000
- divide by 6
- throw away the part to the right of the decimal
- subtract 3
Mmm! Delicious! But be sure to throw the ( 68 x 68 - 7 ) x 5 x 5 x 5 + 220 in the trash!
Now some questions for animal lovers : Does the ( 19 + 19 - 1 ) x 19 + 2 x 3 x 5 have (47 x 47 + 10 x 10 ) x 5 x 5 - 3 x 3 or (47 x 10 + 47 x 10 + 47 x 10 + 47 x 10 - 1) x 3 ? or lay 7 x (800 + 9)? Is there one in your neighborhood 1 / 50 ? What about the 2 x 13 x 13 ? Or the 3 x 3 x 3 x 3 x 101 - 3000? The (50 x 50 x 3 + 1) x 6 - (50 x 50 x 4)? (Of course, the plural of (50 x 50 x 3 + 1) x 6 - (50 x 50 x 4) is (8 - 1) x 8 x ( 8 x ( 8 x (8 + 1 + 1) - 1 ) - 1 ), isn't it.)
If you'd like some help to create more such puzzles, I've provided a list of words, and the numbers that create them. Let your brain's verbal cogs spin and you'll be able to generate dozens of puzzles just like these ones.
Better still, why not photocopy the list for your class (I've created a pdf version that's only two pages), and get them to generate upside-down calculator word puzzles for each other? Complete with formulas, of course. As the kids experiment with their calculators, to come up with a formula for the words they've chosen, they'll find themselves happily absorbed with the math for long periods of time!
In the meantime, here's one last puzzle to decode : a whole sentence, one word per formula...
- "1 5x67 17x17+13 1+7x7+1 3x(2x2x2x2x2x2x2x2+1)", (3x4x7x13+3/10)x100/2 (4x6x4x6-7)x(5x5x5x5-8), "3/6 (3x17/2+1/5)x3 3/5 4.7x3/20"
Good news all the teachers out there - a Pennsylvania teacher named Betty Fry emailed me a worksheet she made up based on the tips above, and was kind enough to let me put it on this website.... so here it is,
- In PDF format (51kb), useful if you just want to print it exactly as-is,
- In OpenDocument Text format (11kb), useful if you use the Open Office office suite (it's free - very good for tight school budgets) and
- In Microsoft Word format (115kb), useful for those using Microsoft's famous software.
Another great idea for upside-down calculator words comes from Alice Oglesby. Alice is the daughter of retired math teacher Mac Oglesby, who has given me a lot of fantastic resources to share on this site. When Alice was 13, she made a Crossword Puzzle whose words are all upside-down calculator words, and whose clues are arithmetic problems. Why not get your kids to do the same? Feel free to send me your kids' work, I'd love to have a look!
Well, that's all for now! I really hope you and the kids you care for will enjoy this calculator word game!