GAUTENG DEPARTMENT OF EDUCATION

PROVINCIAL EXAMINATION

NOVEMBER 2016

GRADE 6

MATHEMATICS

MEMORANDUM

10 pages
memorandum / MATHEMATICS
GRADE 6
GAUTENG DEPARTMENT OF EDUCATION
PROVINCIAL EXAMINATION
MATHEMATICS

General marking note:

1.  Give full marks for answers only, unless stated otherwise.

2.  Accept any alternative correct solution that is not included in the memorandum.

3.  CA refers to consistent accuracy. See clarification in Question 3.3.

QUESTION / EXPECTED ANSWER / CLARIFICATION / MARK / TOTAL
1 / 1.1 / Cü / 1 / 10
1.2 / Dü / 1
1.3 / Aü / 1
1.4 / Cü / 1
1.5 / Aü / 1
1.6 / Cü / 1
1.7 / Aü / 1
1.8 / Bü / 1
1.9 / Bü / 1
1.10 / Dü / 1
2 / 2.1 / 879 500ü / 1 / 5
2.2 / 3ü : 5ü / 5: 1 mark
3: 1 mark
No marks if the learner included any other numbers / 2
2.3 / 154ü / 1
2.4 / 0ü / 1
3 / 3.1 / 5 4 8 3 1 2
+ 3 6 7 4 8 6
9 1 5 7 9 8
ü ü / Correct answer: 2 marks
915: 1 mark
798: 1 mark
Accept any other alternative correct method. / 2
3.2 / 4 2 0 9 9 5
− 1 9 5 7 2 4
2 2 5 2 7 1
ü ü / Correct answer:
2 marks
225: 1 mark
271: 1 mark
Accept any other alternative correct method. / 2
3.3 / 4 1 3 2
× 5 0 2
8 2 6 4 ü
0 0 0 0 0
+ 2 0 6 6 0 0 0 ü
2 0 7 4 2 6 4 ü
Example of CA:
4 1 3 2
× 5 0 2
8 2 6 8 x
0 0 0 0 0
+ 2 0 6 6 0 0 0 ü
2 0 7 4 2 6 8 ü / Correct answer:
3 marks
8264: 1 mark
2066000: 1 mark
Correctly adding steps: 1 mark
Any other alternative correct method including Napier’ s Bones method
Apply CA / 3
3.4 / 41ü rem 103
223) 9 2 4 6
− 8 9 2 ü
3 2 6
− 2 2 3
1 0 3ü / Correct answer
3 marks
41: 1 mark
103: 1 mark
Correct calculation: 1mark
Apply CA
Accept any other alternative correct method. / 3
3.5 / = 4 × 5ü +3
= 20 + 3 ü
= 23 ü / Correct answer: 3 marks
Calculating bracket first: 1 mark
Multiplying before adding: 1 mark
Correct addition: 1mark
Apply CA / 3
3.6 /
15 = 10 ü / 2: 1 mark / 1
3.7 / = 5 + 69 + 29 ü
= ü5 89ü
OR
= 113 + 209 ü
= 339 + 209 ü
= 539ü / Correct answer: 3marks
Converting so that fractions have common denominator: 1 mark
Adding fractions correctly: 1 mark
589 or 539: 1 mark
Accept any other alternative correct method, and any answer that is equivalent.
Apply CA / 3
3.8 / = 365 – 175 ü
= 195 ü OR 3 45 / Correct answer 2 marks
Relevant calculation: 1 mark
= 195 ü OR 3 45: 1mark
Accept any other alternative correct method, and any answer that is equivalent.
Apply CA. / 2
3.9 / 1 1 , 0 3
0 , 5 ü
1 1 , 5 3 ü / Correct answer:
2 marks
Correct place value:
1 mark
11,53 : 1 mark
No marks to be awarded for the final answer if there is no comma. / 2 / 23
3.10 / 80 × 750 ü
100
= 8 × 75
= 600 ü
OR
750 × 80 ÷ 100 ü
= 600 ü / Correct answer:
2 marks
Relevant calculation:
1 mark
600: 1 mark
Accept any alternative correct method. / 2
4 / Children:
112 × 18 = 9 + 18 = 27ü
OR 32 × 18 = 542 = 27
Adults: 7 × 2 = 14ü
Total: 27 + 14 = 41ü
OR
112 + 112 +112 +112 +112 + … =
18 + 9ü
2 × 7 = 14 ü
18 + 9 + 14 = 41 ü / Correct answer: 3 marks
Calculating doughnuts for children: 9 +18 = 27
1 mark
Calculating doughnuts for adults:
7 × 2 = 14: 1 mark
Adding doughnuts for adults and children:
27 + 14 = 41:
1 mark
Accept any alternative correct method.
Apply CA / 3
5 / 1 kg = R50

1000 g = R50
ü
100 g = R5
R5 × 9 = R45 ü / Correct answer: 2 marks
Converting to grams, or calculating Rands per gram, or any other relevant calculation:
1 mark
Multiplying by number of grams:
1 mark
Accept any alternative correct method.
Apply CA / 2
6 / (4 × 4) + (2 × 8) = 32 ü
4 cows and 8 chickens
There are 8 chickens ü / Trying combinations that add up to 32, or trying to draw a picture, or a table or diagram:
1 mark
8: 1 mark / 2
7 / 7.1 / Hexagon ü / 1 / 2
7.2 / Obtuse ü / 1
8 / Triangular ü pyramid ü
OR
Triangleü based pyramid ü
OR
Tetrahedronü / Triangular / triangle: 1 mark
Pyramid: 1 mark
OR
Tetrahedron: 2marks / 2 / 2
9 / 9.1 / Reflection ü or flip / 1 / 1
10 /
ü / Do not penalize the learner for not using a ruler or not drawing the blocks with equal sides. / 1 / 1
11 / 11.1 / D5 ü or 5D / 1 / 2
11.2 / Screen
7
6
5
4
3
2 / X
1
A / B / C / D / E / F / G / H / I
ü / “X” in block F2:
1 mark / 1
12 / 12 ü cm / Do not penalize the learner for not writing the unit. / 1
13 / 4 ü / The mark can also be awarded if the learner correctly draws the lines of symmetry on the square instead of writing the number. / 1
14 / 14.1 / 3550 g – 2300 g ü
= 1250 g ü
OR
3,55ükg – 2,3 kg
= 1,25 kgü / Correct answer 2 marks
Converting to grams or kilograms: 1 mark
1,25 kg OR 1250 g:
1 mark / 2
15 / 15.1 / 14056 mm ü / 1 / 2
15.2 / 7 500 l ü / 1
16 / 16.1 / 21ü square centimetres / Do not penalize for not including unit, or for wrong unit. / 1 / 2
16.2 / 28ü centimetres / 1
17 / Double the length and height:
4 × 4 × 2 ü
= 32 cubes ü
OR
8 cubes (original) + 8 (double length) + 16 (double height) ü
= 32 cubes ü / Correct answer: 2 marks
Calculating volume using new dimensions, or adding extra boxes, or drawing the enlarged box:
1 mark
32: 1 mark / 2
18 / 7:45 to 08:00 = 15 minutes
08:00 – 21:00 = 13 hours ü
21:00 – 21:30 = 30 minutes
Total: 13 hours 45 minutesü / Correct answer: 2 marks
Converting both times to 12 hour or 24 hour time, or counting to 9 in the evening:
1 mark
13 hours 45 minutes:
1 mark / 2
19 / × 3ü / × 3 : 1 mark
Learner must include the operation to get the mark. / 1
20 / 5th / 19th
9ü / 37ü
/ 9: 1 mark
37: 1 mark / 2
21 / 12 × ▲ = 60ü
▲ = 5ü
OR
12 × (5) – 10 = 50 ü
▲ = 5 ü / Correct answer: 2 marks
Any attempt at trial and improvement or inspection:
1 mark
5: 1 mark / 2
22 / 22.1 / Chocolate Tally Frequency
Bar One IIII II 7ü
Rolo IIII IIII ü 9
/ 7: 1 mark
IIII IIII : 1 mark / 2 / 3
22.2 / Rolo ü / 1
23 / 23.1 / Anke ü / 1 / 2
23.2 / Sifiwe ü / 1
TOTAL: / 75

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