CCT-FEB 2020
Mathematics Literacy
Scoring Key
Context: Occupational
Content Category: Quantity
1.
n
|
Number of apple trees
|
Number of conifer trees
|
1
|
1
|
8
|
2
|
4
|
16
|
3
|
9
|
24
|
4
|
16
|
32
|
5
|
25
|
40
|
Full Credit: All 7 entries correct
No Credit: Two or more errors.
Correct entries for n=2,3,4, but BOTH cells for n=5 incorrect.
Both ‘25’ and ’40’ are incorrect; everything else is correct
Any other answer or missing answer
2.Full Credit: Responses with the correct answer, n=8, such as:
n2 = 8n
n2 – 8n = 0
n(n – 8)=0,
n = 0 & n = 8,
n= 0 is rejected, so n =8.
Responses including both the answers n=8 andn=0.
No Credit: Other responses, including just the response n=0.
• n2 = 8n (a repeat of the statement from the question)
• n2= 8.
• n=0. You can’t have the same number, because for every apple tree, there are 8 conifer trees.
3.Full Credit: -Correct response (apple trees) accompanied by a valid explanation. For
example:
• Apple trees = n X n and conifer trees = 8 X n both formulas have a factor n, but apple trees have another n which will get larger where the factor 8 stays the same. The number of apple trees increases more quickly.
• The number of apple trees increases faster because that number is being squared instead of multiplied by 8.
• Number of apple trees is quadratic. Number of conifer trees is linear. So apple trees will increase faster.
• Response uses graph to demonstrate that n2 exceeds 8n after n=8.
Partial Credit: -Correct response (apple trees) based on specific examples or based on extending the table.
• The number of apple trees will increase more quickly because, if we use the table, we find that the no. of apple trees increases faster than the no. of conifer trees. This happens especially after the no. of apple trees and the number of conifer trees are equivalent.
• The table shows that the number of apple trees increases faster
OR
Correct response (apple trees) with SOME evidence that the relationship between n2 and 8n is understood, but not very clearly expressed.
• Apple trees after n > 8
• After 8 rows, the number of apple trees will increase more quickly than conifer trees.
• Conifer trees until you get to 8 rows, then there will be more apple trees.
No Credit: -Correct response (apple trees) with no, insufficient or wrong explanation.
• Apple trees.
• Apple trees because they are populating the inside which is bigger than just the perimeter.
• Apples trees because they are surrounded by conifer trees.
-Other Responses:
• Conifer trees
• Conifer trees because for every additional row of apple trees, you need lots of conifer trees.
• Conifer trees. Because for every apple tree there are 8 conifer trees.
• I don’t know.
Any other answer or missing answer
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
Cognitive Demand
|
1
|
Employing mathematical concepts, facts, procedures and reasoning
|
Fixed Response(Open)
|
Easy
|
2
|
Formulating, applying and evaluating mathematical outcomes
|
Fixed Response(Open)
|
Average
|
3
|
Interpreting, applying and evaluating mathematical outcomes
|
Open constructed
|
High
|
UNIT 02: SKATEBOARD
Context: Personal
Content & Category: Quantity
4.Full Credit:Both the minimum (80) and the maximum (137) correct.
Partial Credit: Only the minimum (80) correct or only the maximum (137) correct.
No Credit: Any other answer or missing answer
5Full Credit: Option (D). 12
No Credit: Any other answer or missing answer
6Full Credit: 65 zeds on a deck, 14 on wheels, 16 on trucks and 20 on hardware.
No Credit: Any other answer or missing answer
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
CognitiveDemand
|
4
|
Employing mathematical concepts, facts, procedures and reasoning
|
Fixed Response
(Open)
|
Easy
|
5
|
Interpreting, applying and evaluating mathematical outcomes
|
MCQ
|
Average
|
6
|
Formulating, applying and evaluating mathematical outcomes
|
Fixed Response
(Open)
|
Average
|
UNIT 03: SPEED OF RACING CAR
Context: Personal
Content Category: Change and Relationship
7.Full Credit: option (B) 1.5 km
No Credit: Any other answer or missing answer
8.Full Credit:option (C) at about 1.3 km
No Credit: Any other answer or missing answer
9. Full Credit:option (B) The speed of the car is increasing.
No Credit: Any other answer or missing answer
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
Cognitive Demand
|
7
|
Formulating, applying and evaluating mathematical outcomes
|
MCQ
|
Average
|
8
|
Employing mathematical concepts, facts, procedures and reasoning
|
MCQ
|
Average
|
9
|
Employing mathematical concepts, facts, procedures and reasoning
|
MCQ
|
Average
|
Context: Personal
Content Category: Space and Shape
10.Full Credit: Top row (1 5 4) Bottom Row (2 6 5). Equivalent answer shown as dice
faces is also acceptable.
1
|
5
|
4
|
2
|
6
|
5
|
No Credit: Any other answer or missing answer
11.Full Credit: No, Yes, Yes, No, in that order.
No Credit: Any other answer or missing answer
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
Cognitive Demand
|
10
|
Employing mathematical concepts, facts, procedures and reasoning
|
Fixed Response
(Open)
|
Easy
|
11
|
Formulating, applying and evaluating mathematical outcomes
|
Binary Choice
|
Average
|
UNIT 05: FARMS
Context: Personal
Content Category: Space and Shape
12.Full Credit: 144 (unit already given)
No Credit: Any other answer or missing answer
13.Full Credit: 6 (unit already given)
No Credit: Any other answer or missing answer
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
CognitiveDemand
|
12
|
Employing mathematical concepts, facts, procedures and reasoning
|
Fixed Response
(Open)
|
Easy
|
13
|
Formulating, applying and evaluating mathematical outcomes
|
Fixed Response
(Open)
|
Average
|
Context: Personal
Content Category: Change and Relationship
14.Full Credit:12 600 ZAR (unit not required).
No Credit: Any other answer or missing answer
15. Full Credit: 975 SGD (unit not required).
No Credit: Any other answer or missing answer
16. Full Credit: -‘Yes’, with adequate explanation.
• Yes, by the lower exchange rate (for 1 SGD) Myra will get more Singapore dollars for her South African rand.
• Yes, 4.2 ZAR for one dollar would have resulted in 929 ZAR.s [Note: student wrote ZAR instead of SGD, but clearly the correct calculation and comparison have been carried out and this error can be ignored]
• Yes, because she received 4.2 ZAR for 1 SGD, and now she has to pay only 4.0s ZAR to get 1 SGD.
• Yes, because it is 0.2 ZAR cheaper for every SGD
• Yes, because when you divide by 4.2 the outcome is smaller than when you divide by 4.
• Yes, it was in her favor because if it didn’t go down she would have got about $50 less.
No Credit: -‘Yes’, with no explanation or with inadequate explanation.
• Yes, a lower exchange rate is better.
• Yes it was in Myra’s favor, because if the ZAR goes down, then she will haves more money to exchange into SGD.
• Yes it was in Myra’s favor
• Any other answer or missing answer
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
CognitiveDemand
|
14
|
Employing mathematical concepts, facts, procedures and reasoning
|
Fixed Response
(Open)
|
Average
|
15
|
Employing mathematical concepts, facts, procedures and reasoning
|
Fixed Response
(Open)
|
Average
|
16
|
Interpreting, applying and evaluating mathematical outcomes
|
Open constructed
|
High
|
UNIT 07: LICHEN
Context: Scientific
Content Category: Quantity
17. Full Credit: 14mm (units not required). Full credit should be given as long as the correct answer is 14 whether working out is shown or not.
d=7.0× 14mm
d= 14
d=7.0×(Note that here the calculations are all correct, but the
d=7.0× unit is wrong. We will assume for now that it is the
d= 14 yearsslip of the pen)
Partial Credit: -Partial responses including:
• Correct substitution of value in the formula but incorrect answer Or
missing answer.
• Incomplete answers (eg, 7√4).
d=7.0×(wrong answer but correct substitution)
d= 16 years
d=7.0×(complete answer)
d=7
No Credit: Any other answer or missing answer
18Full Credit: 37 years (unit not required) whether working out is shown or not.
35=7× 35÷7=5
5= 7×5=7×
25=t−12=7×
t =37=7×37
⸫ 37years
35/7=5(Strictly incorrect algebraic representation, but we know
52 =25 what the student is trying to do)
25+12=37
t = 15 d = 12.1 (Note that here the answer 37 is embedded in an equation
t = 25 d = 25.2 that is correct)
t = 40 d = 37.0
t = 35 d = 33.6
t = 37 d = 35
So 37 years after the ice disappeared
756 = 35 = 7 × = 7 ×√25 = 7× 5 = 35
Partial Credit: Correct substitution of values in the formula but incorrect answer or missing answer.
OR
36 years or 38 years. (Students may arrive at these answers using the trial and error method)
35=7.0 35=7.0× 35=7.0×
352 = 72× t-125= 5=
49t = 123725=t2-1225= -
t=25t=13Too hard!
No Credit: Any other answer or missing answer
35=7.0
28=
784 = t-12
t= 796
40 years
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
Cognitive Demand
|
17
|
Employing mathematical concepts, facts, procedures and reasoning
|
Fixed Response
(Open)
|
Average
|
18
|
Formulating, applying and evaluating mathematical outcomes
|
Fixed Response
(Open)
|
Average
|
UNIT 08: CHOICES
Context: Personal
Content & Category: Quantity
19.Full Credit: 6.
No Credit: Any other answer or missing answer
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
CognitiveDemand
|
19
|
Formulating, applying and evaluating mathematical outcomes
|
Fixed Response
(Open)
|
Average
|
UNIT 09: EARTHQUAKE
Context: Scientific
Content & Category: Uncertainty and Data
20.Full Credit: option (C) The likelihood that there will be an earthquake in Zed City at sometime during the next 20 years is higher than the likelihood of no
earthquake.
No Credit: Any other answer or missing answer
Classification of Test Item:
Item No
|
Process category
|
Item Format
|
CognitiveDemand
|
20
|
Interpreting, applying and evaluating mathematical outcomes
|
MCQ
|
Average
|
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