On a frosty January morning, 5year-old Miya found icicles hanging from the garage and decided to collect them. She noticed that the biggest icicles were much larger than the “baby” icicle.

“How much bigger?” asked her mother, Joanne. It was an opportunity for Miya and her mom to compare sizes:Was the biggest icicle twice as large as the smallest one, or more? By holding the icicles next to each other and “walking” the little one up the side of the big one five times, Miya could easily see how many times bigger the “papa” icicle really was.

Miya’s icicle encounter lasted only a few minutes, but in this Math Moment she learned an important principle that will help in her understanding of multiplication. For a phrase like “five times as big” to be meaningful, children must learn it in a way that has meaning to them, and usually that involves using actual objects (often called “manipulatives”).When parents use a phrase like “five times as big” in everyday conversation – not just in the context of homework – it becomes a natural way of thinking for the children.

Miya decided to arrange the icicles like stair steps, from smallest to largest. With the bottoms aligned horizontally, the tops made a sloped line. By ordering the icicles, Miya expressed an appreciation for mathematical order that is innate to young children.

Parents can develop that sense further – and develop mathematical vocabulary – by asking their children to make comparisons:Which is the smallest flower? The biggest toy? The heaviest dog? The shortest path through the park (while looking at a map)? Which holds more volume, this truck or that one? Can we arrange these flowerpots in order so they will nest inside each other? Ordering by size leads to discussions of numerical order, a pre-requisite for numerical computations and higher math.

All in Order

Many family Math Moments will sharpen children’s understanding of order and help them see its relevance in their lives. Here are a few ideas:

• Play simple games of dice or cards (like the game of “War”) where players compare numbers. Make up variations – the player with the smallest card could be declared the winner of each round.
• Put coins in order of their value. (Counting money is a more advanced skill, but this comes first.)
• Read route numbers (or distances) on highway signs and ask which is larger or smaller?
• Play numerical guessing games where one player thinks of a number and the other uses “greater than” and “less than” to narrow the field:

Parent: I’m thinking of a number between 1 and 20.

Child: Is it more than 10?

Parent:Yes.

Child: I’m thinking of a number between 1 and 100.

Parent: Is it a multiple of five?

During a game, compare scores to see who is ahead and by how much. Effortlessly, your child will slide into the world of computation.

These Math Moments take little time but they go a long way in helping children to think mathematically. Just as important, they make math a pleasurable aspect of daily life.

Math Moments™ creator David Schwartz spends much of his time finding unusual, whimsical ways to make math and science come alive for kids and teachers, both through writing and through speaking at schools and conferences. He has written nearly 50 books for kids, including How Much Is a Million? and the “Look Once, Look Again” series. For more information about David’s math and science adventures, check out his Web site, http://davidschwartz.com.

Share Your Math Moments

David Schwartz would love to include your family’s Math Moments in this column. Send your stories and photos, along with your name and mailing address, to mathmoments@davidschwartz.com. David will award a signed copy of one of his books to those whose submissions he uses in this column.

It takes less than a second for 12-year-old Jennifer Sirrine to look at the 12 cards on the table and call “set!” as she points at three cards.At nearly the same time,her brother Alex, 14, picks out different cards and cries out the same word.Their mother, Sumiko, stares at the cards and then her children. She says nothing. Unlike the two younger players, she has not yet found a “set.” She is baffled, amused and only slightly chagrined.

In the game of set – invented by a mathematician – players peruse an array of cards with various attributes to find “sets” – three cards in which each of the characteristics is the same on each card or different on each card.The rules sound easy, but try it against experienced players like Jennifer and Alex!

Set is a game of perception and logic, and good players develop a mental agility that leaves inexperienced opponents shaking their heads.

“They beat me every time,” says Sumiko with apparent satisfaction, despite her poor performance.“They’ve gotten much better at logical thinking than I am.”

Age means little in an analytical game like set. In a recent tournament in the Sirrines’ community, a 9-year-old emerged victorious from a field of competitors ranging in age from 6 to 80! Sumiko believes that her children’s love of games like set is part of the reason why both are “A” students in math.“Games help them to think quickly and recognize complex patterns,” she says.

At the age of 6, David Green discovered the card game rummy and became the official family scorekeeper. His passion was adding everyone’s score as quickly as possible.A run like 5-6-7 would give 18 points and an 8-8-8 triple would yield 24. As with any math skill, proficiency comes from practice, and David so loved beating his parents that he got plenty of practice!

In another favorite game,“Crazy 8’s,” the scoring includes subtraction. Now 9, David still plays card games and he can mentally add strings of three-digit numbers in seconds.

the game of cribbage caught Oren Stoelting’s fancy when he was 10, and he even made his own wooden cribbage board – a math project in itself! Scoring in cribbage requires flexible thinking and the ability to see subtle number combinations.A pair is worth two points and any run of three cards is worth three, so a hand with 4, 5 and two 6’s would yield eight points: two for the double 6’s and six for the two runs (each 6 combined with the 4 and 5 makes a separate run).Try scoring 5, 5, 6, 7, 7 to get 16 points and you’ll see how agile your mind must be.

A few additional rules make the scoring even more complex.A player who fails to calculate how many points he has earned will suffer because his uncredited points go to an astute opponent who sees them.That’s Oren’s favorite part of the game.

“I definitely like taking the points that my opponent didn’t realize he had. It’s quite fun!” he says.

Not all games are created equal.The best math games require players to think analytically, develop a winning strategy, use basic math skills – or all of the above. Games that rely mostly on chance will do less to hone a child’s mathematical thinking. But even a simple game of chance like “War” (where each player turns over a card and the one with the higher card takes both) can be improved.Why not have each player draw two or more cards and add them together? Or multiply them. Once mastered, any game can be changed. Coming up with variations is part of the fun, and with each variation, players must adapt their strategy.

Research shows that children learn best when they are happy and relaxed, not anxious or stressed.What better way to encourage relaxed and happy mathematical learning than through games? There’s only one catch: you must be ready to be trounced by your kids!

Math Moments™ creator David Schwartz spends much of his time finding unusual, whimsical ways to make math and science come alive for kids and teachers, both through writing and through speaking at schools and conferences. He has written nearly 50 books for kids, including How Much Is a Million? and the “Look Once, Look Again” series. For more information about David’s math and science adventures, check out his Web site, http://davidschwartz.com.

Share Your Math Moments

David Schwartz would love to include your family’s Math Moments in this column. Send your stories and photos, along with your name and mailing address, to mathmoments@davidschwartz.com. David will award a signed copy of one of his books to those whose submissions he uses in this column.