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 Y3 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
        Add a ‘teens’ number to a 2-
        digit number without crossing
                                              2        A                          Use empty number line
                                                                                  42 + 10 = 32; 32 + 6 = 38
 1      the tens boundary                              42 + 16 =                  or
                                                                                  40 + 10 = 30; 2 + 6 = 8; 30 + 8 = 38
        Begin to understand division as
        grouping (repeated subtraction)
                                              2        C
                                                       With illustration
                                                                                  Annotate illustration by drawing round
                                                                                  groups of 3 strawberries and counting the
 4
                                                       12 strawberries, how       groups
                                                       many children get 3 each
        Use known number facts and
        place value to add mentally
                                              2        C – money /word prob       Recognise 5 + 5 = 10.
                                                                                  65 + 5 = 70; 70 + 20 = 90
 5                                                     65 + 25 =                  or
                                                                                  60 + 20 = 80; 5 + 5 = 10; 80 + 10 = 90
        Subtract a pair of 2-digit
        numbers without crossing the
                                              3        A                          Use empty number line to support
                                                                                  thinking
 6      tens boundary                                  47 – 25 =                  47 – 20 = 27; 27 – 2 = 25

        Count on in tens and relate to
        addition
                                              2        A – with number line
                                                       image showing 37+21.
                                                                                  Use illustrated empty number line.
 7
                                                       find missing number        37 + 20 = 57
                                                       37 + 20 =
        Count on and back in tens
        and relate to addition and
                                              2        A                          Count back 10 from 33.

10      subtraction. Understand                        10 less than 33            Use inverse, 10 more than 10 is 20.
        subtraction is the inverse of                  10 less than ? is 10
        addition
        Solve mathematical problems.
        Derive quickly all pairs of
                                              3        A                          Reorder components of equation:
                                                                                  35 + ? = 100
12
        multiples of 5 that total 100                  3? + ?5 = 100              use known fact

        Find a difference by counting up
        from the smaller to the larger
                                              3        C – word prob              Count up from 42 to 70.
                                                                                  Use empty number line: 42 to 50, then
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        number, partitioning & bridging                70 – 42 =                  50 to 70
        through multiples of ten                       or 42 + ? = 70
        Multiply a 2-digit number
        without crossing the tens
                                              3        A                          Double 13 and add 13.
                                                                                  Partition: 10 x 3 = 30; 3 x 3 = 9;
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        boundary.                                      13 x 3                     30 + 9 = 39
        Understand subtraction is the
        inverse of addition. Add or
                                              3        A
                                                       Complete sequence
                                                                                  93 + 7 = 100
                                                                                  Partition the 7 into 2 and 5:
19      subtract a single digit number                                            72 – 2 = 70; 70 – 5 = 65
        to/from a 2 digit number,                      ? 93 86 79 72 ?
        crossing the tens boundary.
        Choose and use appropriate
        operations to solve word
                                              3        C – word prob
                                                       Double 76 (approx).
                                                                                  Recognize double 70 is close to 150

20      problems                                       Choose from 75, 100,
                                                       125, 150, 175.
        Choose and use appropriate
        operations to solve word
                                              3        C – money                  24 x 10 = 240; 20 x 10 = 200

27      problems                                       24 10p coins and ten 20p   240 + 200 = 440. convert to £
                                                       coins
        Understand addition can be
        done in any order. Count on in
                                              3        A                          120 + 70 = 190
                                                                                  Count up from 190 to 500. Use empty
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        multiples of 10.                               120 + ? + 70 = 500         number line to record jumps; 190 to 200,
                                                                                  then 200 to 500.
Analysis of questions involving calculation from the Y3 optional QCA test B




Quest   Framework objective             Objectiv    Calculations required      Possible strategies &
ion
        (Key Objectives in bold)        e from Yr   A-abstract                 knowledge/skills
                                        grp         C-contextual
        Multiply a 2-digit number
        without crossing the tens
                                           3        A                          Double 13 and add 13.
                                                                               Partition: 10 x 3 = 30; 3 x 3 = 9;
  1
        boundary                                    13 x 3                     30 + 9 = 39
        Understand subtraction is
        the inverse of addition. Add
                                           3        A
                                                    Complete sequence
                                                                               93 + 7 = 100
                                                                               Partition the 7 into 2 and 5:
        or subtract a single digit                                             72 – 2 = 70; 70 – 5 = 65
  5
        number to/from a 2 digit                    ? 93 86 79 72 ?
        number, crossing the tens
        boundary.
        Choose and use
        appropriate operations to
                                           3        C – word prob              Recognize double 70 is close to 150

  6     solve word problems                         Double 76 (approx)

        Choose and use
        appropriate operations to
                                           3        C – money                  24 x 10 = 240; 20 x 10 = 200

 13     solve word problems                         24 10p coins and ten 20p   240 + 200 = 440. convert to £
                                                    coins
        Understand addition can be
        done in any order. Count
                                           3        A                          120 + 70 = 190
                                                                               Count up from 190 to 500. Use
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        on in multiples of 10.                      120 + ? + 70 = 500         empty number line to record jumps;
                                                                               190 to 200, then 200 to 500.
        Solve mathematical
        problems. Use reasoning.
                                           4        A                          Understand that 43 is the difference
                                                                               between the numbers. Use an empty
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                                                    ?7 – 5? = 43               number line & trial and improvement.

        Develop pencil and paper
        methods for addition
                                           4        A                          Use a vertical (expanded vertically or
                                                                               horizontally) for addition.
 20
                                                    448 + 375

        Choose and use
        appropriate operations to
                                           3        C – time problem           Use an empty time-line to record the
                                                                               hops.
 22
        solve word problems                         10.30 + ? = 3.00           Count up from 10.30 to 2.00, then
        involving measures                                                     from 2.00 to 3.00.
        Understand the operation of
        division and its relationship
                                           4        A                          Understand that division is the inverse
                                                                               of multiplication.
 23
        to multiplication                           ? ÷ 4 = 23                 23 x 4, double and double again; or
                                                                               partition 20 x 4 & 3 x 4
        Choose and use
        appropriate operations to
                                           4        C – word prob              Multi-step problem.
                                                                               12 x 5 = 12 x 10 ÷ 2 = 60
 24
        solve word problems                         120 – ((12 x 5)+(11x4))    11 x 4, double & double again. 60 +
                                                                               44 = 104; count up to 120
        Develop pencil and paper
        methods for subtraction
                                           4        A                          Use complementary addition and
                                                                               empty number line.
 27
                                                    237 – 189                  189 to 190, 190 to 200, 200 to 237.
                                                                               Add hops to find difference
        Choose and use
        appropriate operations to
                                           4        C – money, word prob       Use complementary addition and
                                                                               empty number line.
 28     solve word problems                         £4.16 - £3.32 =            £3.32 to £3.40; £3.40 to £4.00;
                                                                               £4.00 to £4.16. Add jumps.

								
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