Mr Brown says “Visual patterns are a great way to develop a range of problem solving skills at a range of levels. In this problem, students can be asked a variety of questions. A simple question is to ask how many circles in the next step or next three steps. Describing the pattern in words or with algebra takes it to the next level, especially if you ask for the nth term rule. Finally, how can you use the geometry of the pattern to give reasoning for your answer?”
Visual thinking can really be creative when considering this particular problem. Can you come up with the nth term rule for this pattern and then use it to find the number of circles required for the 43rd step?
Please email firstname.lastname@example.org">me with your answers.
Martin Brown, Head of Mathematics