Equality

If students have had any experience doing calculations, they will have some conception of that the symbol = signifies. My experience reveals that middle-grade students will give a wrong answer to the following over half of the time.

Fill in the blank to make the number sentence (substitute the word "equation" for students in middle school) true:

8 + 4 = ___ + 5

However, it is important to collect answers individually, and open up a discussion before stating out of hand that the view students have developed is just "wrong." These students have what appears to them to be a completely valid reason for thinking that 12 should go in the blank, or possibly 17. It is best to have other students explain that 7 should go into the blank, so that the two sides are "the same." If any students speak Spanish, it is more than worthwhile to go into the dual uses of the word "igual" in Spanish (same, equal), and the connections among English, Spanish, and Latin.

Have students make up their own fill-in-the-blank sentences. Show a few that illustrate how this concept can make tricky questions into easier ones (99 + 7 = __ + 6 or 9 x 8 = 80 - __). This can be great topic of investigation.