I love teaching nth term! I am not going to lie it is one of my favourite favourite lessons.
I follow a great guy on TES called alutwyche https://www.tes.com/teaching-resources/shop/alutwyche (he is also on Twitter https://twitter.com/andylutwyche) from the very beginning of my teaching career his resources have saved me from dreary worksheets consistently. When you are teaching mixed ability groups his bank of lessons of grade A to G of the old GCSEs are a lifesaver. His explanation of the nth term was completely different to how I had been taught it how I've seen it before when I was training and how my department taught it when I qualified. I love seeing something taught in a different way.
I was taught, and I saw be taught and my colleagues were teaching, nth term as you work out the difference and then you write that in front of the n and then you work out what you would do to get to the 0th term, like this:
This guy introduced me to the times table method you may have seen it before but it blew my mind. You work out the difference then you write the times table of that number above the sequence then you calculate the difference and you end up with the nth term rule. Have a look at this example.
Learner's really respond to this because if they have been taught a way that hasn’t worked before for them, it's nice to give them something different. But like I always say if you have a way that works for you you use that way. I only offer alternatives when you don't have your own way of working things out consistently correctly.
Thinking about the working out the difference and what would the 0 term be I began to think about the steps that we were doing. We work out the difference you put that in front of the n and then you work out what the 0 term would be I wonder if there was a way we could make an acronym or a mnemonic for this and I thought Dino. A quick Google later and nth term with Dino is a thing and there are loads of resources out there! Phew I’m not going mad, others are thinking the same as me! So just like at famous Adams and famous Terry's appearing my lessons the amazing Rex the dinosaur from toy story also appears in my lessons. And it works like this
D is for difference
I in front of
N
and then the letter o is actually a number
0
This really helps learner's remember the steps they often know how to work out the difference and they know it goes in front of an it's just what are they adding or subtracting it's the final stages. With my famous Adams my famous Terry's my female mathematicians and now Rex the dinosaur from Toy Story on my walls hopefully now you can picture what my classroom looks like.
