Analysis of 2019 KS2 Maths SATs Arithmetic paper (Part 1)

    Published: 08 October 2019

    It’s that time of year again where we pull together some of what we have learned from the KS2 SATs papers, ready to share messages with schools.  We hope that this will give them a better lens with which to look at their current cohorts and consider the high value areas to pursue, which might be most useful across the school.  We are all Year 6 teachers in effect.

    Inevitably, what follows will not be the whole story for the children in your school.   Here we look at the national question level analysis data over the past three years to see what it can tell use about, in this instance, the Arithmetic paper. 

    More of the same

    There are aspects of the arithmetic paper that have stayed remarkably similar since its first incarnation in 2016. What follows are some examples that easily spring to mind.

    There are always two formal written multiplication and division questions with the divisor in the division questions always being a prime number – indeed 43 has been used twice in 2018 and 2016.  We know that these will be where the 2 mark questions will be, they are after all computationally more difficult than other questions requiring greater processing. 

    Children are also tasked with addition and subtraction of numbers with a different amount of decimal places in every paper so far too. 

    Additive place value has been tested twice in each test since 2017 with questions such as;

     

    sats question
    2018 KS2 Arithmetic paper
    Sats question
    2017 KS2 Arithmetic paper

     

    There are too many other things that have stayed the same to mention.  In fact an experienced year six teacher could probably predict what 2020 will look like – as far as the arithmetic paper goes.

    But there have also been some slight shifts and changes since 2016 as well.

    Simple shifts

    These slight shifts are not necessarily going to set the world on fire but they do show how national data might alter the focus of question selection. 

    Dividing by one has appeared in the 2016-2018 papers so far but this year the children were multiplying by zero instead which didn’t throw too many children off course with 94.7% correct.  National data shows they had got the hang of dividing by one with 95.1% of children correctly answering in 2017 and 98.1% in 2018. Time for a change then.

    In terms of percentages, in 2016 and 2017 there was one example per paper where a multiplication symbol was used.

     

    sats question
    2017 KS2 Arithmetic paper

     

    Since then, there have only been examples using the word of instead, perhaps reflecting the challenge the percentage questions seem to be posing (read on for more information about this).  

     

    Sats question
    2019 KS2 Arithmetic paper

    There are more missing number questions this year than before.  The first four questions all have boxes to test children’s understanding of the equals sign and later their use of inverse operations.  Previously, this was left until later in the paper.  It concerned some that this would ‘put off’ the less fluent children, but the national data shows children are now coping with this admirably.  

    Are the papers graded so that simpler questions come towards the front of the paper?

    Yes, by and large this remains the case, however, in 2017 the first question where about a fifth of the children answered incorrectly or did not respond was around questions 15 and 16.  In 2018 this was question 18 and 19. And in 2019 this was question 12.  Less fluent children are likely to begin to struggle beyond these points.  Looking through papers from my schools, demonstrates that they ‘skip’ questions they consider too hard.

    Which questions do children typically struggle with?

    There are a few trends we can see here from papers 2017-19. 

    It will come as no surprise that towards the end of the paper the percentage of correct response diminishes.  From question 25 in all years, the percentage of pupils providing a correct response tends to fall to less than 80% for the remainder of the questions.  Stamina plays a large part but so too does the grading of the paper with greater load questions towards the back.

    The types of question that children struggle with nationally are (less than 70% as an average across 2017-19 papers answering correctly);

    1. Fractions multiplied by whole numbers with average 49.4% answering these correctly. Perhaps if they substituted the word of for the multiplication sign that might help them better understand the maths here. After all they’ve been finding ½ of a number since Y2.
      Sats question
      2019 KS2 Arithmetic paper

       

    2. Percentages of amounts (average 67% answering these questions correctly overall) but when the question isn’t to find percentage of a multiple of 100 then this drops to an average of 61%.  Indicators from other question types in the papers show that multiplying and dividing by powers of ten still cause overall difficulty for the less fluent children. This may be in play for these questions, although there do tend to be some pretty inefficient methods here too.

      Sats question
      KS2 Arithmetic paper

       

    3. Multiplication of decimals by whole numbers (that are not 10 or 100). Although there were no examples of this in this year’s paper, in 2017 and 18 the average percentage of correct responses was 64.6%.  Again this is likely to be due to weaknesses in place value i.e. that old chestnut of multiplying and dividing by powers of ten (strangely) as well as linkage to related facts. 
      9 x 2 = 18 
      0.9 is 10 times smaller than 9 and 200 is 100 times greater than 2.
      So 0.9 x 200 is ten times greater than 2 x 9.

      KS2 sats question
    4. Formal long division of a four digit number.  This one will come as absolutely no surprise, I’m sure.  Whilst children cope a little better with short division and long division of a three digit number, the four digit version is at the end of the paper means that there is an average of 54% of correct responses across the three years.

    5. Addition and subtraction of fractions including mixed numbers, whether the denominators are the same or not, also cause difficulty. An average of 63% of correct responses are provided for these questions.  There may feel like a lot to do past a certain point in the paper, but is conversion of everything in the question always necessary?  What’s to stop children taking the 4 sevenths from the 1 here and adding the result (3 sevenths) to the other 3 sevenths?

      KS2 Sats question

    Whilst we may feel our children are 'well-drilled' in procedures to gain great marks on the arithmetic paper, I think that the areas above demonstrate some cause for concern regarding the foundational concepts children are still struggling with.  Looking at the papers themselves is extremely revealing.  Lately, I have consistently found children not making the 100+ scaled score, were skipping the majority of fractions questions and anything with decimals in.  When using the formal methods for multiplication and division, it is place value that is the weakness, see here for more on that.   I also see a lot of 'rules' taught for operating with fractions - for example the keep, flip and multiply rule taught for division of fractions by an integer or when multiplying by tens in formal multiplication 'add a zero'.  

    Consider the examples below. Where's the multiplication children might use in each case?

    fractions questions

    Are these less confident children (and for confident we must read fluent), not procedurally fluent or not conceptually fluent, or both?  How many of the fractions examples above require some multiplication in the procedure to solve?  Do these procedures just feel too similar to distinguish between due to only surface level understanding? 

    Do we really need to use the procedure keep, flip and multiply when dividing fractions by an integer? How many children know the reason keep, flip and multiply works when dividing fractions?  Instead perhaps our primary aged children could be using playdough to discover that if I want to share a quarter of a cake between 2 friends I can cut the quarter in half to make two eighths so that each friend gets an eighth.  Making links to the division structures children are already familiar with and using simple equivalences.

    We recommend;

    • Look at your QLA data over more than one year and compare to national;
    • Look at the papers of selected children that reached 100+ and those that hit 98 or 99 - was it stamina, over use of procedures (inefficient and no regard for the numbers in the question), underlying weakness e.g. multiplying/dividing by powers of 10;
    • Take note of which questions were 'skipped' to discover any commonalities;
    • Consider how you will develop fluency in these areas and encourage children to take note of the numbers in the example before calculating;
    • Feedback findings and consider whether the curriculum is sufficiently focussed on high value learning that supports fluency

    In the part 2 blog I aim to expose the ideas that are heavily tested in the arithmetic paper but hidden in the question level coding. 

    I am hopeful that these blogs provides enough to get schools thinking about how they might interpret the findings of the Arithmetic SATs paper outcomes, and how their findings might be translated into a thoughtfully weighted curriculum offering.

    For more insights into achieving mathematical age-related expectations in Y6, please join us for our popular CPD offer:

    Achieving mathematical age-related expectations by the end of Year 6

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