Blogs @Jonah's Math Corner

Patterns of Faces and “Touch Magic” (Faces are smileys and crying faces)


Let’s investigate the following questions:

  • (1) How many happy faces are in each row?
  • (2) What do you find by comparing Row two to Row one? What do you find by comparing row two to row three? (What’s same? What’s different?)
  • (3) Find the patterns in each row, and then for that row, continue to draw the next two faces.

Now is another challenge:

We describe a rule of changes called “touch magic”. Putting your fingers on one of the faces, then this face, and its immediate neighbor(s), will ALL change to the respective opposite (e.g. smileys will become crying, and crying faces will become smileys). If you touch in the middle, three faces will change (itself, its left and right neighbors). But if you touch on a side, such as the leftmost, then there are only two faces changing.

Let us look at row one (please ignore the other two rows for the time being).

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