*By Michael Hartley*

Love them or hate them, calculators are here to stay. One of the ugliest things I saw as a math educator happened in my first year of full-time teaching. I was watching my students as they did a test. This group of students were doing university level math as part of their economics degree.

I wandered over to see how one of my best students was performing. This student, I was confident, would do well in the test, and indeed get an A for the subject. I was right. But what I saw as I looked over her shoulder will stick in my mind until the end of my career.

The student had almost completed a difficult problem. All that remained to get the right answer was to multiply one and a half by two. A piece of cake, for that student's ability and academic level. Then, to my horror, the student reached for the calculator, and punched in the keys :

**1 . 5 x 2 =**

I could hardly believe it. How could this student be doing so well in math, even up to university level, and still need a calculator for a result like that? Amazing!

Calculators : A Blessing Or A Curse?

There's no question that calculators are a useful tool. Kids should be familiar with them before leaving school, if they are to function effectively in modern society. A calculator makes arithmetic faster and more accurate, by transferring part of the brainwork to electronic circuitry. What is the effect of all this on a student learning math?

In one way, a calculator is like a crutch. A student struggling with arithmetic might use a calculator to confirm the results of their own efforts. In this way, the student will gain confidence, until they no longer need the calculator for that level of problem. On the other hand, a student might become dependent on the crutch, unwilling to try to walk without it, and eventually losing the ability to walk correctly as his or her mental math muscles atrophy.

Calculator games!

Below I give a couple of games involving the use of a calculator. The goal with these games is to put kids in a situation where using the calculator helps them with their math, in a fun and interesting way. They use calculators in these games to explore numbers, and so gain some kind of intuition for the relationships between them as they manipulate them to achieve the goal set for them.

**Alice Oglesby's Cross-Number Puzzle**is actually a crossword puzzle - but the clues are all arithmetic sums. How is that possible? Once you've worked out each sum on a calculator, you turn your calculator upside down, and each number becomes a letter. You can download and print Alice's puzzle, solve it, and then make your own upside-down calculator cross-number puzzle with the help of the long lists of calculator words linked from

**the puzzle page**.

**Printable Space Birthday Worksheets**lets you calculate how many years old you'd be if you were born on Mercury, Venus, Mars, Jupiter, Saturn or Uranus. This site also has an

**Online Space Birthday Calculator**, but the printable worksheets may be more useful in a classroom context.

**Grid Of Sums**is a puzzle game by the French newspaper "Le Monde." (They called it

*La Grille De Sommes*.) You start with an empty grid, then you fill the cells one by one. Each cell gets filled with the sum of its neighbors. On my

**Le Monde 'Grid Of Sums' puzzle page**you can read the rules in more detail, find a link to Le Monde's original video, download printable puzzle grids of many different shapes and sizes, and get ideas for variations on the original puzzle - including how to make it a two-player game!

**Modern Rice-And-Chessboard Story**and see for themselves how rich the reward was.

**Magical Calculator Birthday Trick**and the

**"Threes" Math Trick**, one child gives a sequence of arithmetic instructions to another, then performs a few simple mental steps on the result. Almost like magic, the other's birthday (or another secret number) appears as the result of the sum! Good for fourth grade kids and up.

**Magical Calculator Birthday Trick**and the

**"Threes" Math Trick**, one child gives a sequence of arithmetic instructions to another, then performs a few simple mental steps on the result. Almost like magic, the other's birthday (or another secret number) appears as the result of the sum! Good for fourth grade kids and up.

**free "fours" contest**closed on the 20th of October, 2009. The idea was to make as many numbers as possible using the digit '4' (as many times as you like) and the operations plus, minus, divide and times. Soon I'll upload the contest results, and ideas for how you can run a contest like this one in your own classroom.

**Math Architect Online Game**the goal is to design an apartment with the given area. The catch? Each room is a square, and you must have as few rooms as possible! This makes the game challenging enough to keep kids occupied, and deep enough to keep them learning as they play. There is also a high scores table showing the best players each month, year and for all time, and some ideas for

**playing math architect as a paper and pencil game**.

**This is one of two**math tricks on this site that let you guess someone's birthday after a sequence of mathematical operations.

**The Upside-Down Calculator Word Game**is recommended for kids in fifth grade and fourth grade, and maybe also third grade. Younger children may find it too challenging - although my son's grade one teacher recently gave an exercise like this one to her class! The aim is to find numbers that make words when keyed into an upside-down calculator. See the game's page for more details.

**Easter Date Worksheets**allow a child to compute the date of Easter Sunday in any year at all, with no math more complex than long division. Alternatively, try younger kids on the simpler versions of the worksheets - fewer calculations, smaller numbers, but they only work in certain centuries.

**MathGolf**is a simple game to play, and a very hard game to master. The high scores for each month are recorded on the website. The

**tips for parents and teachers**explains how to help your kids get the most out of the game.

**make as many numbers as you can**using only the given four digits and the basic arithmetic operations. I've worked out which sets of four digits make this puzzle the most interesting, and provided worksheets on this page. Good for grades four and up.

**Number Mazes**you need to find a path across a grid of numbers, stepping only vertically or horizontally each step. The tricky part is that you have to make sure the total of the numbers you pass is correct! You can download a set of easy 3x3 mazes, or harder 4x3 mazes, or really tough 5x3 or 4x4 mazes. Each time you visit the page you'll get new sets of mazes, uniquely generated for you. You might find a calculator handy to check the totals as you try and try and try again!

**April Fool's Date Calculator**worksheet lets kids calculate the date of April Fools Day for any year. It works like the

**Easter Date Worksheet**- write the year in a box in the worksheet, copy numbers along arrows, and the date of April Fools appears at the end! Ok, in all seriousness - the real educational value in this worksheet - besides arithmetic practice - is to make kids wonder how on earth the worksheet manages to get the

**right date for April Fool's Day**every time.

**Angle Geometry Quiz**tests your knowledge of a few facts relating to angles. Race against the clock as you prove your skills! Topics covered include the interior angles of triangles and quadrilaterals, angles near parallel lines, lines meeting at a point and others.

**Power Puzzle**is an exercise to get kids exploring numbers with their calculator, and observe patterns in the numbers they explore.

Well, that's all for now, but stay tuned! I'm continually adding new games to this site. Even now, ideas for more calculator games are percolating in my mind....

Yours, Dr Mike.

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