247: Pan Balance Pandemonium

How many different ways can you balance a scale? Are all the ways different? What makes them different? What makes them the same?

Use this Java applet from the NCTM Illumination to help you think about balancing a scale: Pan Balance - Shapes

Play around with the applet. What do you notice?

Find one way to balance the scale (the more shapes you put on, the better). What can you take away and still balance the scale? What can you add and still balance the scale? Think of as many ways as you can.

Possible Questions:<

Question 1:

Kylie balanced a scale with 9 blue circles and 6 red squares on one side, and 6 yellow diamonds and 6 purple triangles on the other side. Will her scale balance with 3 blue circles and 2 red squares on one side, and 2 yellow diamonds and 2 purple triangles on the other?ps - I'm gonna replace/supplement this text with pictures when I figure out how

What would balance 6 blue circles and 4 red squares? How do you know?

What's a rule you could use to find another way to balance the scale using Kylie's pattern.

Question 2:

How many ways could you balance 3 blue circles and 2 blues squares using only diamonds and triangles?

Terry could only figure out one way to balance the scales, using two triangles. Could you tell him a rule for finding all the other ways?

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