Analysis of Calculation from the Y6 SATs, 2002 Paper A (no calculator) - DOC by alextt

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									     Analysis of questions involving calculation from the Y4 optional QCA test A




Ques    Framework objective                Objective   Calculations required   Possible strategies &
tion
        (Key Objectives in bold)           from Yr     A-abstract              knowledge/skills
                                           grp         C-contextual
        Understand the operation of
        multiplication and the
                                              2        A True or false?
                                                       8x2=8+8
                                                                               Understand multiplication as repeated
                                                                               addition
 2      associated vocabulary                          3 x 10 = 3 + 3 + 3
                                                       5x4=5+5+5+5
        Use known number facts and
        place value to add a pair of
                                              4        A Sequence (add 100)    Add 100 to any 3 digit number crossing
                                                                               100
 4
        numbers mentally                               946 + 100

        Develop pencil and paper
        methods for addition
                                              3        A                       Use a vertical (expanded vertically or
                                                                               horizontally) method for addition.
 6                                                     127 + 57                Or use empty number line, 127 + 50;
                                                                               177 + 7 (possibly + 3, + 4)

        Count on in tens and relate to
        addition
                                              3        A
                                                       Number line image for
                                                                               Use illustrated empty number line.

 8                                                     addition                43 + 30 = 73
                                                       43 + 30
        Use all four operations to solve
        word problems in ‘real life’,
                                              3        C word problem, money
                                                       Understand ‘how much
                                                                               Use complementary addition and empty
                                                                               number line.
 9
        using money or measures.                       more’                   £9.10 + 90p; £10.00 + £1.50 = £11.50
                                                       £11.50 - £9.10          Add hops.

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        Use all four operations to solve
        word problems in ‘real life’,
                                              2        C word problem          Know there are 12 months in a year.
                                                                               Double 12 (known fact)
        using money or measures.                       12 x 2
        Say or write a division
        statement corresponding to
                                              3        A
                                                       6 x 10 = 60
                                                                               Understand ‘number triples’ or ‘buy one
                                                                               get three free’.
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        a given multiplication                         Write corresponding     Use arrays as an image to develop this.
        statement                                      division calculation
        Find a difference by counting up
        from the smaller to the larger
                                              4        A                       Use compensation, subtract 90 and add 1.
                                                                               Use empty number line to illustrate
17
        number, partitioning & bridging                123 – 89                compensation. Or subtract 80, then 9 on
        through multiples of ten                                               empty number line.
        Develop pencil and paper
        methods for addition
                                              4        A
                                                       Choose two from these
                                                                               Use a vertical (expanded vertically or
                                                                               horizontally) method for addition.
19                                                     numbers to add
                                                       together:
                                                       246    367     458
        Use all four operations to solve
        word problems in ‘real life’,
                                              4        C word problem, money   Use grid multiplication.
                                                                                   x 30        5
22      using money or measures.                       35p x 7                     7 210 35
                                                       answer in £             or partition; 30 x 7 = 210, 5 x 7 = 35
        Solve mathematical problems.
        Derive pairs of numbers that
                                              4        A                       Reorder components of equation:
                                                                               100 + 60 + 7 + ? = 200
27
        total a multiple of 100                        1?7 + 6? = 200          use complement to 100

        Understand the idea of a
        remainder
                                              4        A                       Count up in 8s to 48 (use empty number
                                                                               line), count on to 53 for remainder
29
                                                       53 ÷ 8 (what is
                                                       remainder)
        Use halving and related facts.        4        A                       Use known fact 25 x 4 = 100 and adjust
                                                                               Or
31
                                                       ? x 4 = 96              Use inverse; 96 ÷ 4, halve and halve
                                                                               again
     Analysis of questions involving calculation from the Y4 optional QCA test B




Ques    Framework objective                 Objective   Calculations required        Possible strategies &
tion
        (Key Objectives in bold)            from Yr     A-abstract                   knowledge/skills
                                            grp         C-contextual
        Develop pencil and paper
        methods for addition
                                               4        A
                                                        Choose two from these
                                                                                     Use a vertical (expanded vertically or
                                                                                     horizontally) method for addition.
 1                                                      numbers to add together:
                                                        246    367    458
        Use all four operations to solve
        word problems in ‘real life’,
                                               4        C word problem, money        Use grid multiplication.
                                                                                         x 30        5
 5      using money or measures.                        35p x 7                          7 210 35
                                                        answer in £                  or partition; 30 x 7 = 210, 5 x 7 = 35
        Solve problems. Derive pairs of
        numbers that total a multiple of
                                               4        A                            Reorder components of equation:
                                                                                     100 + 60 + 7 + ? = 200
10
        100                                             1?7 + 6? = 200               use complement to 100

        Understand the idea of a
        remainder
                                               4        A                            Count up in 8s to 48 (use empty number
                                                                                     line), count on to 53 for remainder
12
                                                        53 ÷ 8 (what is
                                                        remainder)
        Use known number facts and
        place value to multiply or divide
                                               5        A                            Understand place value, understand
                                                                                     multiplication is the inverse of division.
15
        mentally                                        3400 ÷ ? = 100
                                                                                     ? x 100 = 3400
        Develop pencil and paper
        methods for addition
                                               4        A                            Use a vertical (expanded vertically or
                                                                                     horizontally) method for addition.
17
                                                        846 + 478

        Develop and refine written
        methods for multiplication
                                               5        A                            Use grid multiplication.
                                                                                          x 400 50 3
20                                                      453 x 8                           8 3200 400 24
                                                                                     or partition; 400 x 8, 50 x 8, 3 x 8.
                                                                                     Or double, double, double again.
        Use all four operations to solve
        word problems in ‘real life’,
                                               5        C word problem, length       Recognise relationship with 25 and 75.
                                                                                     Partition 75 into 25 & 50, subtract 25cm
21      using money or measures.                        2.25m – 75cm                 then 50 cm from 2.25m. Use empty
                                                                                     number line. Or use complementary
                                                                                     addition.
        Use all four operations to solve
        word problems in ‘real life’,
                                               4        C word problem, money        Use trial and improvement or listing to
                                                                                     find multiples of 20p and multiples of
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        using money or measures.                        (? x 20p) + (? x 50p) = £7   50p to total £7

        Subtract a pair of decimal
        fractions including crossing the
                                               5        A                            Use empty number line and
                                                                                     complementary addition.
24
        tens boundary                                   8.52 – 7.78                  7.78 + 0.22 = 8; 8 + 0.52 = 8.52
                                                                                     Total hops = 0.74

27
        Use all four operations to solve
        word problems in ‘real life’,
                                               5        C word problem, money        Halve and halve again. Half of £3 is
                                                                                     £1.50, half of 40p is 20p. Half of £1.70,
        using money or measures.                        £3.40 ÷ 4 =                  partition and recombine again.

								
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