We started off with determining the number of sticks used in a phase of a pattern. We began with a triangle pattern. The students quickly noticed that the number of sticks were increasing by 2, however this was not enough to create the 'rule'. After the students tested out their theories, I illustrated that the triangles could be split into groups of two, with one extra stick left over. Seeing the connection between the broken up sticks and the number of triangles helped them to notice the rule, n= (nx2) +1. After identifying the rule the learners were able to predict the number of sticks needed for the 8th, 27 and 38th pattern.
Following this, we moved on to a square pattern. I prompted the learners to think back to how we split up the triangles, and think about how they could split up the squares in a similar way. Some of the learners instantly 'saw' how they could split up the squares, whilst some tried other ways. This prompted discussions on why the learners chose to break the squares the way they did, and whether it would give us a rule for the number of sticks. This lead them to discover that the sticks should be split into groups of 3, with 1 left over; giving the rule n = (nx3) +1. Discussion was an important element of the lesson as it allowed learners to share their thoughts and justify their answers
I was surprised with how fast my learners were identifying the sequences and rules of the patterns, so I posed one more pattern to my learners. It was in the shape of a house, with 6 sticks. Most of the learners quickly figured out a rule to count the number of sticks in the sequence.
Following this my learners created a DLO that teaches someone else about calculating rules for triangle and square path patterns. It was the first time that they had created a DLO in maths, but they did very well. Here are two examples of the DLOs created after this lesson. You can visit their blog posts by clicking on the images
My learners grasped the concept of finding a rule really well. I am looking forward to challenging my learners with some more complex patterns and rules.Next I will move onto more complex patterns and get them to create their own patterns that follow an algebraic rule.