1. sequences This is a discussion activity to develop students’ awareness of how a simple linear sequence grows. Students discuss in pairs or small groups and then feed back to the class. Mini whiteboards may help students record their thoughts. The questions on the presentation are prompts and are by no means definitive – students could draw the 4 th and 5 th patterns on whiteboards or develop further sequences which fit with this family, or sequences which don’t. This is just an introduction to justifying why the rule for a linear sequence looks the way it does but, at no point in the presentation, is any mention made of n or nth term. The idea of generalisation should arise through the students’ group discussion and they can, if appropriate, be guided to working with symbolic algebra. Otherwise, I think they’re doing the same mathematics if they can write a rule in words, they’re just presenting it slightly less efficiently.

2. 1st2nd3rd 1st2nd3rd Describe the 15 th and the 100 th pattern

3. ? ? How do you know how the 15 th pattern and the 100 th pattern look? How do you know how many holes there are in the 15 th and 100 th pattern? How could you explain how many holes there’ll be in any pattern in the sequence?

4. 1st2nd3rd 1st2nd3rd How do you know how the 15 th pattern and the 100 th pattern look? How do you know how many holes there are in the 15 th and 100 th pattern? How could you explain how many holes there’ll be in any pattern in the sequence? Describe the 15 th and the 100 th pattern

5. What do these three sequences have in common? What are the differences between the sequences? Describe how each of these sequences grows Describe how you’d find how many holes there are in any pattern in each sequence 1st2nd3rd