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Quadratic sequences lesson

Discussion in 'Mathematics' started by smiley_emma100, Jun 21, 2012.

  1. Hi!

    I have an observation on Tuesday with top set year 8's (level 7) on finding the nth term of a quadratic sequence. I have to admit that when I taught this last year I fell into the trap of teaching students the process rather than letting them discover the process and links themselves (and this wouldn't go down well with my observer). Has anyone got any ideas on how I could structure this lesson to encourage the students to start discovering this themselves? They are a bright class and good at team work (if lacking in confidence at times!).

    I was thinking of giving them some linear nth term to start (which they are all confident with) and throwing in a 'one that doesnt work' (quadratic)

    Thank you in advance!
  2. I was taught a very general method for finding quadratic functions. If students were asked to generate the sequences of n^2 and 2n^2 then n^2 + 1 before then going on to finding nth terms they might have greater chance of finding the nth term of a quadratic. How are they taught to find a nth term? Do they have a full understanding that a difference of two means they should consider the sequence 2n and adjust or a mechanistic understand that a difference of 2 means there is a 2 in front of the n?
  3. thank you! They have a good understanding that 2n means 2 times the position, although some of them use the put the 2 infront approach for speed
  4. adamcreen

    adamcreen Occasional commenter

    am I telling you something you already know when I say that nth term of quadratic sequences is not required at GCSE or A Level? It's great to guide them through the thinking and it's a nice method to learn, but of no use in exams. Doesn't mean we shouldn't teach it though!
  5. DM

    DM New commenter

    Surely that depends on whether you are preparing students for the Linked Pair or not?
  6. adamcreen

    adamcreen Occasional commenter

    Given this is for a top set Year 8 class, one would assume not. Anyway, yes you miight be preparing for any number of non-standard qualifications, but for a standard GCSE or A Level, not required.
  7. PaulDG

    PaulDG Occasional commenter

    As others have said, remember this is not in KS3, GCSE or even required in A level, so do make sure you flag this on your lesson plan as extension work!

    Anyway, I think the way I'd go about it would be to refresh finding the nth term of a linear sequence and get the kids to tell - or, if you're into group work, have them discover for themselves what happens when they try the same thing on a quadratic one.

    They'll normally notice the point that the sequence of differences is linear.. And with a few examples will be able to tell you the rule. If you're doing this as group work, one group will have to quickly present their findings to the rest of the group.

    If they're really sharp and quick, you could introduce calculus as a plenary.. Most top set year 8s quite like to hear they've just done something from A level.
  8. DM

    DM New commenter

    This simply isn't true.
    Level 7 Attainment Target 2007 National Curriculum for KS3
    "<font face="Univers-Light" size="1" color="#1b1c20">They find and describe in symbols the next term or </font><font face="Univers-LightOblique" size="1" color="#1b1c20">n</font><font face="Univers-Light" size="1" color="#1b1c20"><font face="Univers-Light" size="1" color="#1b1c20">th term of a sequence where the rule is quadratic."</font></font>
  9. You could get them to generate sequences from the nth terms, then see if they can spot the relationship between the second difference and the coefficient of x-squared. Then they should be able to see that a linear sequence is left when this term is subtracted from the sequence.
  10. bombaysapphire

    bombaysapphire Star commenter

    The triangle numbers form a quadratic sequence - plus you can come at them by thinking about the number of handshakes needed for n people.
    There are then two ways of explaining the resulting formula (1) from drawing the triangles and fitting two together to make a rectangle and (2) from thinking about the handshakes scenario.
  11. Handshakes is a lovely investigation for bright year 8's and all you really need to ask them is how many handshakes there would be if everyone in the school shook hands with everyone else. They can make some conjectures and then try to prove/disprove them. It usually gives rise to some interesting discussions! You can start to gather the numbers by getting them up to actually shake each others hands , get them to think about how they might record this and use diagrams to count without having to physically do it.
    Personally I like to do handshakes after quadratic sequences have been introduced however if they haven't really come across them before I think the Nrich tilted squares investigation is a great intro http://nrich.maths.org/2293 - its really worth watching the video clips to get a feel for the lesson (even if your students aren't all gifted mathematicians like the audience in the video)
  12. Thanks for the ideas everyone! I really like the handshakes idea and hopefully it will make the topic come to life a bit more for my year 8's! I'll let you know how it works!



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