This session was a preview of a new (as yet unreleased) book by AIMS on solving equations. Four different discovery/investigation style projects were presented. Three of them are available in this pdf file.

The fourth lesson is not included in the above packet, and is a variation on the classic balancing scale.

The scale is made using:

Fold open the paperclips to make an s shape, hang them on each end of the yardstick, and hold them in place with small pieces of tape. Punch holes in a top corner of each zip lock bag, and hang on the paper clips. The binder clip is attached to the middle of the yardstick, and adjusted until the yardstick hangs level.

The weighed objects are made using:

If you have 20 lb paper, you will want to cut strips that are 4 3/4"x11". If you have 24 lb paper, your will want to make the strips 4"x11" (the heavier paper will allow you to make two strips per sheet). This will make your strip of paper equal to the weight of one penny.

Make the strips into footballs. Once they are made, you can unfold them, and add pennies on the inside. Put the same number of pennies inside each football of the same color. Use a small bit of tape to seal the footballs.

You probably want 4-8 footballs of each color, with 0 to 4 pennies inside. This will actually give you weights of 1-5 pennies, since the paper accounts for one penny's worth of weight.

You can then create equations by putting, say, 2 footballs and 3 pennies on one side, and 4 footballs on the other side. Have the students add pennies to the second side until the scale balances. They may then add or remove items from either or both bags, with the condition that you hold the scale steady while they do so, and that the scale must balance when they are done adding or removing.