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Year 6 algebra

Discussion in 'Mathematics' started by chele1987, Nov 5, 2015.

  1. chele1987

    chele1987 New commenter

    I teach top set year 6 maths and am wondering if I'm taking their learning on too far according to the new curriculum.

    Should we be teaching nth term?

    I'm not sure how far we are meant to be going with the teaching of algebra as the guidance in the curriculum isn't overly clear.

    Thanks
     
  2. star9

    star9 New commenter

    I think they need nth term. It willdepend how you approach it, but when I teach it to Year 6 they do enjoy it.
     
    colinbillett likes this.
  3. spartacus123

    spartacus123 Occasional commenter

    I can think of more important things year 6 need to learn. Nth term isn't even on the Foundation stage GCSE.

    I suspect there are many year 6 teachers who can't explain how Nth term works.
     
  4. Vince_Ulam

    Vince_Ulam Star commenter

    Best not. The Primary National Curriculum takes you as far as term-to-term rules. Position-to-term is KS3. If you find yourself with spare time then resist at all costs the temptation to venture into the KS3 curriculum and instead consolidate like crazy their existing knowledge, especially times tables. It does not matter how you get the tables into them as long as they are there with immediate recall. You would not believe the amount of teaching time and student potential that can be lost in Year7 because of this basic gap which can undo all of the other maths work Primary teachers have attempted.

    It needs to be remembered that top set Year 6 isn't necessarily going to remain top set for Years 7, 8, 9, 10 & 11 where maths success is less about speed at picking up novel topics but more about being able to slog, apply & develop efficiently what has been learnt, hopefully, in Primary. Your students will need to hit the ground running so provide them with the best shoes now and all the exercise they can get.

    If you must provide some occasional rich material then give them some simple problems which will develop their ability to solve via inspection and connect with reasoned arguments different areas of mathematics they should already know.
     
  5. Owen134866

    Owen134866 New commenter

    As a secondary teacher, I would prefer kids to come from Primary with better number skills, they don't need to do the nth term/algebra as we will cover it ourselves anyway. You could use activities from the nRich website, they are accessible at multiple levels (so all students can get involved) and can definitely extend the more able students. Some of these might be good?

    http://nrich.maths.org/9293
    http://nrich.maths.org/9294
     
  6. colinbillett

    colinbillett Occasional commenter

    My reading of Year 6 and the programme of study is that they do need it, and should be learning to generalise, even at this stage. Actually, I'd have thought it the best way to approach algebra and abstract thinking. One used to see a lot of 'fruit salad' algebra, with apples and bananas expressed in ways such as 2a + 3b, but happily such things seem to be of the past. But for many learners, algebra is taught, and learnt, as some sort of 'guess the missing number' game, in which they are presented with a mess of numbers and letters and expected to find an 'answer'. I find myself so often doing remedial work, taking algebra back to using symbols to represent mathematical relationships. This week I have been using matches to create patterns, or at least the learner did, and from the number pattern going on to a generalisation for the 'nth' term, but I try to make the symbol or letter more relevant than 'n'.
    So I disagree with the secondary teachers who say 'leave algebra to us', and say do what it says on the programme of study.

    Algebra

    Statutory requirements

    Pupils should be taught to:

    · use simple formulae

    · generate and describe linear number sequences

    · express missing number problems algebraically

    · find pairs of numbers that satisfy an equation with two unknowns

    · enumerate possibilities of combinations of two variables.


    Notes and guidance (non-statutory)

    Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:

    missing numbers, lengths, coordinates and angles

    formulae in mathematics and science

    equivalent expressions (for example, a + b = b + a)

    generalisations of number patterns

    number puzzles (for example, what two numbers can add up to).
     
  7. colinbillett

    colinbillett Occasional commenter

    I'm not sure which GCSE you are looking at, but I think the government has insisted on identical content. The Edexcel one says, to quote:

    Sequences

    What students need to learn:

    A23

    generate terms of a sequence from either a term-to-term or a position-to-term rule

    A24

    recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r n where n is an integer, and r is a rational number >0)

    A25

    deduce expressions to calculate the nth term of linear sequences
     
    DeborahCarol likes this.
  8. spartacus123

    spartacus123 Occasional commenter

    Algebra is great for generalising - expressing problems in terms of unknowns.

    I hate the apples and bananas idea . 2a + 3b because a and b can be numbers. Not things.

    But - if there are x children in class 5 and they each paid £5 to Children in Need, how much money do we have?

    5x

    We raised £200. How do we work out the value of x?

    Extend it. x children in school A, y children in school B
    There are twice as many children in school A than there are in school B.

    In terms of x, how many children are in school B? (use real numbers to get them thinking)

    100 in A, 50 in B
    200 in A 100 in B

    Can they generalise to
    x in A
    x/2 in B

    This is useful (ish) algebra. Makes them think.

    Then tell them there are 250 pupils altogether in both schools. How many in each school?

    Using algebra to solve problems.
     
    colinbillett likes this.
  9. Vince_Ulam

    Vince_Ulam Star commenter

    The Primary National Curriculum is not for exegesis: It mentions term-to-term rules only. Position-to-term rules are not introduced until the Secondary National Curriculum.


    The statutory 'programme of study' i.e. the National Curriculum says leave position-to-term rules until Secondary and this is precisely what Primary teachers should do while getting on with the vital work of consolidation. This is how they best prepare their students.
     
  10. colinbillett

    colinbillett Occasional commenter

    It seems to me we are having a problem with communication. Foundation GCSE is clearly as I've quoted, or indeed copied and pasted. As for KS2, the current version is likewise clear - no mention of term-to-term in the current version, unless someone can find one later than 2015. But it does say '· generate and describe linear number sequences' and 'generalisations of number patterns'. However, the latest sample assessment for KS2 includes three papers - one on arithmetic and two on reasoning - and there aren't any examples of an algebraic approach to number patterns. Not sure I shall be around in a year or so when we have more examples of actual KS2 tests, or sample material, but until then I'll assume it may well come up, whether I think it useful or appropriate. Meanwhile, for those who want to, go back to drill, slog and tables, if you think that's what you ought to be doing.
     
  11. chele1987

    chele1987 New commenter

    Sorry! I didn't mean to cause a huge debate :oops: Thanks for all of your replies.

    I totally agree that it is important that we do consolidate learning before morning on. I totally understand how frustrating it if for you to receive children with poor times table recall- if frustrating with them coming into year 6! Children are now meant to know their times tables by the end of year 4 so it is more of a focus earlier and hopefully you'll see this coming through in a few years.

    However, I have a child in the group who is very bright and passed the 11+ with a very high score. Sometimes the natural progression for her within a lesson is to begin look at rules when explaining her reasoning.

    We were exploring the internal angles within polygons earlier in the week. She picked up the pattern quickly and the natural progression within that lesson was to consider the rules and think about why it happens.

    So what I am trying to say is there any harm in these situations touching on the nth term to extend her learning? The sorts of algebra described above we will teach later in the year as whole class lessons.

    I am hoping to contact the grammar school she is hoping to go to and see if we can arrange anything later in the year for her.

    Thanks.
     
  12. spartacus123

    spartacus123 Occasional commenter

    With that, I would see if she can generalise. If I had "n" sides, what would the angle be?

    Is that Nth term? Or algebra?

    Not sure of you should necessarily teach nth term as in

    4,7,10,13 3n+ 1

    But can they work out a pattern and why it's so. e.g you're starting with 1 side and add 3.

    Then add 3 more sides etc. Get them to think.
     
  13. Vince_Ulam

    Vince_Ulam Star commenter

    Yes, there is a problem: You have mistaken my references to term rules in the Primary National Curriculum for a global position on algebra. Of course algebra is to be introduced in Primary - I have not said otherwise.


    The Primary National Curriculum, updated 6th May 2015, makes no mention of position-to-term rules and mentions term-to-term rules in non-statutory notes & guidance only therefore there is no necessity, none, for Primary teachers to introduce their students to term rules. They may do so, but it would be folly to venture further when there is consolidation to be achieved.

    Primary teachers have an amazingly important job in setting mathematical foundations per the National Curriculum upon which Secondary teachers may build per the National Curriculum, so the next time a Primary teachers asks advice on the National Curriculum then be certain of the facts per the National Curriculum. Carrier-bag academies may not feel the need or wish, if able, to work to the National Curriculum because they don't have long-term responsibilities for the success of their students but Secondary teachers have to work within statute and a developmental framework and we'd rather not have to spend our time resetting a foundation after someone has been at it with a pneumatic drill.
     
  14. Vince_Ulam

    Vince_Ulam Star commenter


    You are welcome, thank you for asking your questions but there is no debate, just some misreading of the Primary National Curriculum.

    Term-to-term rules themselves are not mandatory in Primary so in going that far with your class you have already raised their attainment above expectations, assuming their competence. You've done well by them but there has to be a limit and consolidation must be achieved even if the doing of it is not exciting. There is a reason why your position is termed Primary - it's of the first importance and not everyone can do what you do, so Secondary is counting on you. All teachers like to see children grasping new techniques and mastering new ideas but, hypothetically, to risk the radical mastery & Secondary success of all children in a class for the sake of one girl's grammar school career would not be fair to the rest of the class and may not be considered good practice.

    These things said, you can take steps which will help this girl:

    1. If you have the time and consider the reward adequate then tutor her privately yourself or, if she has not one already, recommend a private tutor to her parents. If either of these then ensure your own understanding and that of the tutor, and that the way you or the tutor are teaching the topic, is how it is to be taught in Secondary. For this consonance a tutor recommendation from the grammar school may be sought.
    2. Recommend to the girl's parents that she studies the subject herself without the help of a tutor, it may not be beyond her. This is the preferred option, as finding a private tutor who both understands the material and can instruct a child in it is like can be like hunting for a unicorn given that most good Secondary teachers are far too busy to work as private tutors. I'll PM you some with suggested materials.

    Good luck.
     
  15. kimothy39

    kimothy39 New commenter

    Many Primary Maths terms do include teaching the nth term, and last week's SATS papers included at least one question based on a fairly simple version of the idea. I have taught it and it does challenge the more able.
     
  16. Vince_Ulam

    Vince_Ulam Star commenter

    Which supports a point I made above: If your attempt to teach the nth term is challenging the most able Year 6 students then it's leaving the rest behind. Consolidate the statutory requirements of the Primary National Curriculum and leave the Secondary material to the Secondary teachers so that we don't have to reteach to students Primary material that their Primary teachers haven't consolidated.
     
  17. caterpillartobutterfly

    caterpillartobutterfly Star commenter

    Collins BusyAnt maths scheme has the nth term as an extension in year 6.

    In our school about the top 50% regularly do the extension work, possibly lower in other schools. But still a fair number of pupils will be heading to it.
     
  18. Vince_Ulam

    Vince_Ulam Star commenter

    The Primary National Curriculum, updated 6th May 2015, makes no mention of position-to-term rules and mentions term-to-term rules in non-statutory notes & guidance only therefore there is no necessity, none, for Primary teachers to introduce their students to term rules. They may do so, but it would be folly when there is consolidation to be achieved.
     
  19. caterpillartobutterfly

    caterpillartobutterfly Star commenter

    For some children, extension beyond the KS2 curriculum is necessary.
    Not for all, nor indeed for most.
    However, for some children much of primary maths is so obvious to them, they need little teaching, let alone consolidation. These children should have the opportunity to study abstract maths.
     
  20. darhar

    darhar New commenter

    Edexcel spec for GCSE:
    A25 deduce expressions to calculate the nth term of linear sequences

    So, yes, nth term is on GCSE. Sometimes "planting" an idea to extend more able students is a good thing - they will learn it at KS3, and will need it for GCSE (extending to nth term of a quadratic sequence for Higher students)
     
    colinbillett likes this.

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