Question 1 focuses on recognising, describing, extending, explaining patterns in different settings.
1.1 The given sequence consists of regular polygons staring with a 3-sided regular polygon (triangle), then a 4-sided regular polygon (square) and then a 5-sided regular polygon (a pentagon). Different choices are given, but the learner is not limited to one choice. If a learner selects:
A: The learner is not extending the given pattern, but he recognises that the next shape needs to have 6 sides.
B: The learner recognises the pattern, he can extend the sequence correctly, and he understands that the shapes are all regular.
C: The learner knows that the next shape in the sequence must have six sides, but he does not understand regular shapes.
D: The learner cannot extend the sequence; he does not recognise the pattern.
1.2 The given sequence consists of an unfamiliar combination sequence: 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, ….
Different choices are given, but the learner is not limited to one choice. If a learner chooses: A: He recognises the linear or arithmetic part of the sequence only.
B: He recognises the linear or arithmetic part of the sequence and realises there must be a one in the sequence.
C: He recognises the combination sequence and extends the pattern correctly. D: He does not recognise the pattern, he cannot extend it.
1.3 In the open sequence: 1, 2, 4, … the learner has the opportunity to:
A: He recognises a quadratic sequence, even though he might not know that it is called a quadratic pattern, he still recognises that there is a pattern that emerges with the first differences.
B: Recognise an exponential pattern, even though he might not know that it is called an exponential/geometric pattern, he still recognises that there is a pattern that emerges when you multiply by a constant value.
C: No pattern. The learner cannot extend this sequence, which means he cannot relate to forming any next term.
D: No pattern. The learner cannot extend this sequence, which means he cannot relate to forming the next term.
1.4 The following sequence bids quite a challenge. 1, 3, 5, 7, 5, 3, 1, 3, … The learner has four options to try and describe the pattern. If he chooses:
A: He recognises the first part of the sequence that is adding three each time. He does not apply this recursive rule to the second part of the sequence.
B: He recognises the second part of the sequence that is subtracting three each time. He does not apply this recursive rule to the first part of the sequence.
C: He cannot see a constant pattern, so the learner decides not to attempt his own description.
D: The learner attempts his own description for the pattern he sees. He might even attempt to extend the pattern.
1.5 In this question, a sequence is given, and a learner needs to select the correct rule which will work for each term. This question attempts to assess whether a learner can relate a rule to a sequence. If he chooses:
A: He only applied the rule for the first term.
B: Could apply the rule for the first two terms only. This means that the learner did not test the rule for all the terms.
C: He could test the rule for each term successfully.
D: He does not understand how to relate the rule to the sequence.
1.6 This question does not involve extending or recognising or even describing a pattern. During the modelling problems it is important for a learner to apply the correct operation rules, this question will assess if learners can use the BODMAS (brackets of division, multiplication, addition and subtraction) from left to right.
Question 2 focuses on recognising, describing, extending and explaining patterns with different properties. This question is an open question with the aim to assess the knowledge of patterns that learners have. Learners need to construct any linear number pattern, describe it by giving the
first few terms and explaining how they would find more terms. This will clearly show if a learner knows that there is a constant first difference between two consecutive terms.
In the second part of this question, the learner needs to construct any quadratic number pattern, describe it by giving the first few terms and explaining how they would find more terms. Even though they might not know what a quadratic number pattern looks like, the question hints that there is a constant second difference. A learner might use a simple sequence such as 1, 4, 9, 16, … and can at least explore the possibility of getting a second difference to be constant.
In the third part of the question, learners have the opportunity to construct any sequence other than a linear or quadratic. This question will give the teacher a clear understanding of the learner when he describes different sequences. He might describe and extend a cubic, a geometric sequence or a Fibonacci sequence. This accounts for the learner thinking of patterns and relationships between numbers.
Question 3 assesses the use of the In-Out table or diagram. The In-Out table shows the functional relationship of a pattern clearly (see Section 3.4.2). During the modelling problems, learners can choose to use the tables as a model building tool to represent the real problem as a mathematical problem. Once again, the learner needs to recognise patterns that are represented in a different way. This question is constructed so that the level of pattern recognition can be established. Question 3.1 involves a straight-forward sequence. Terms are given in order, so the learner might look at the Out column to find a relationship between the patterns. Learners need to fill in the missing terms in the sequence. In 3.2 the terms are not given in any order, and learners are forced to find a general rule to represent the Out values in terms of the In values in order to fill in the missing values. In the last question (3.3), information is given in no specific order, and is presented in a table. Learners need to find a general rule to represent the Out values in terms of the In values in order to fill in the missing values.