# 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
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
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
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
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
14
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;
16
boundary.                                      13 x 3                     30 + 9 = 39
Understand subtraction is the
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
done in any order. Count on in
3        A                          120 + 70 = 190
Count up from 190 to 500. Use empty
29
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
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
done in any order. Count
3        A                          120 + 70 = 190
Count up from 190 to 500. Use
15
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
18
?7 – 5? = 43               number line & trial and improvement.

Develop pencil and paper
4        A                          Use a vertical (expanded vertically or
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.