Mathematics is the science of patterns. Part of the math skill students need to learn in mathematics is to see regularities.  The usual way of introducing pattern searching activity is by showing a sequence of figure or numbers and then asking the students to find or draw the next one.   Here’s a more exciting way of presenting patterns. Bernard Murphy of MEI (Innovators of Mathematics Education) shared this with us. MEI is an independent charity committed to improving mathematics education and is also an independent UK curriculum development body.

The figure below is the third in a sequence of pattern.

How does the first, second, fourth, fifth figure look like?

Here are three of the patterns I produced and the questions you could asked the learners after they produced the sequence of patterns. Note that the task is open-ended. There are other patterns learners can make.

1. How many unit squares will there be in Figure 50?

2. How will you count the number of unit squares in Figure n in this pattern?

3. This is my favorite pattern. How many unit squares will there be in Figure n?

Note that in all the sequences, Figure 3 looks the same. Note also that for each of these sequences, you can have several expressions depending on how you will count the squares. Of course the different algebraic expressions for a particular sequence will simplify to the same expressions.

You can use this activity to teach sequences, linear function, and quadratic function. But this is not just what makes this activity a mathematical one. To be able to see regularity is already a mathematical skill and much more of course if they can generalize them as well in algebraic form.

I am so tempted to just give you the equations but that would mean depriving you of the fun. Anyway, here are two examples on how you can think about counting the squares in Figure n: Counting Hexagons and Counting Smileys. Have fun.

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