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First, take the white pawn. The small plastic piece represents a value, a number of some kind. Walk forward with it five steps ? forward, not backward. Hence, white = +5.

Now, take the blue pawn. Same size and shape, just different in color. Hold it up and walk five paces backward, back to the starting point. Hence, blue = -5.

One more step: place the blue pawn on one side of a scale, the white pawn on the other. (+5) + (-5). (-5) + (+5). The answer either way? Zero.

Blue = -(white). White = -(blue). With a miniature chess set and a few other props, Victoria Elementary School teacher Stacy Klase demonstrated the concept of positive and negative numbers to her fourth-grade class.

Earlier this year, Klase, who is in her third year at Victoria Elementary, ordered props for her math lessons with funds from the California Retired Teachers Assn. She got a few pawns and number blocks ? then was able to stock the entire class when the Newport-Mesa Unified School District adopted the “Hands-On Equations” program for all its schools.

In Hands-On Equations, students literally put their hands on x, y, and other variables that make up algebra problems. On Thursday morning, Klase showed the class how to keep track of positives and negatives by demonstrating equations on a legal scale. Students copied the problems at their desks with pawns, block and scales drawn on laminated sheets of paper.

Pencils out, then: what’s 3x + y + x + 1, if x = 4 and y = -4?

Well, make the blue pawns ‘x’ and the white pawns ‘y’. Since the two cancel each other out, we can remove one white and one blue pawn from the scale and shorten the equation to 3x + 1.

And if x = 4, then 3(4) + 1 must equal 13.

The negative numbers unit was the ninth lesson in the Hands-On Equations program. Klase said solid materials have made math lessons go more smoothly than they did a year ago.

“They look forward to it,” she said. “If we ever have to change our schedule, they say, ‘We’re not doing algebra this week?’”

Students usually start with the pawns and later get accustomed to solving problems on the page. Few of them had studied algebra before this year, but they got the hang of it quickly ? at least the basics.

“Sometimes she gives it to us without the pawns, so we have to do it on the board,” said Anthony Yaghnam, 9. “We work our way up to paper.”