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Manipulatives That Teach Direct Variation

Direct variation is one of the most important foundational concepts in the study of algebra. The idea is this: as one quantity goes up or down, another one does too -- and at the same rate. If you make $10 per hour, and you work three hours, you should earn $30. Each hour you work will increase your pay at the same rate. There are manipulatives you can use to demonstrate this concept.
  1. Tetris

    • Students playing the video game Tetris can learn the concept of direct variation in an entertaining way. For each level, the pieces descend at a set rate; as a result, every X seconds, a piece must be dealt with. As difficulty increases, so do the number of pieces per minute. Have students partner up and have one student play the game in your school's computer lab while the other tracks pieces per minute. Allow students to switch duties.

    The Gas Tank

    • Ask students to accompany their parents to the gas station the next time they have to fill up the car. Have the students stop the pump and write down the price total after every gallon. The price will increase at a direct variation with the number of gallons purchased.

    Line Mural

    • On one wall of your class, mark off a line segment that goes up from left to right, from near the floor all up within 3 or 4 feet of the ceiling. Mark the endpoints and two or three points along the segment. Have students measure the horizontal distance between points, going straight across from the bottom point, and then stop at each horizontal distance and measure the vertical distance. Dividing vertical distance by horizontal distance, from the original point, should result in the same ratio (this is the slope of the line) for each point. This indicates direct variation of vertical and horizontal distance.

    The Silent Game

    • Start with a cup full of pennies and tell your class that as long as everyone is getting answers correct on an oral assignment, you will give each of them a penny with every correct answer -- but subtract a penny from students who miss questions. This will give them a competitive view of direct variation -- and keep them focused on your review.

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