Extrapolating PSLE Mathematics 2018 into PSLE 2019 ......PSLE Math 2018 dissected - was the paper really challenging? Table 1 below shows the list of questions, their topics and mark

©BLACKBOXLEARNING APR’19 1|P a g e

BLACKBOX LEARNING Publication - PSLE Mathematics Apr 2019

Extrapolating PSLE Mathematics 2018 into PSLE 2019: Analysis & Strategies

By DIONE CHONG YUNJIA [email protected]

Edited by Lye Kok Leong [email protected]

The PSLE 2018 Surprise

Many candidates depended on mastery of these question models to score in the PSLE 2018 Math

paper: units and parts, repeated identity, remainder concept, or patterns, composite figures . None

appeared.

In particular, “units and parts* ” questions, an integral part of every candidate’s examination

preparations, have been absent from the PSLE since 2014.

Do the PSLE Math papers of the past few years disclose a discernible trend? We believe so.

Should it inform our strategy for candidate preparation? We believe so.

PSLE Math 2018 dissected - was the paper really challenging?

Table 1 below shows the list of questions, their topics and mark weightage of the 2018 PSLE

Mathematics Paper 2.

Included under each topic is a short description of the math skills needed to solve each question.

* Units and parts is a term that uses the same concept as simultaneous equation taught to Sec 2 students.


Table 1 – List of PSLE Questions in Paper 2

Question Mark Topic Tested

1

[2] each

Rate and Proportion

2 Speed (Finding Average Speed)

3 Algebra (Operations of Algebraic Expressions)

4 Composite Shapes (Area of Overlapping rectangles)

5 Whole Numbers (Model drawing)

6 [1], [2] Data Analysis, Fractions, Money (Bar Graph)

7 [1], [2] Fractions, Area (Expressing Whole in Parts) (Expressing Fractions in Unitary Form)

8 [3] Geometry (Properties of angles in shapes)

9 [3] Whole numbers (Guess and check: Induction Reasoning not to be confused with Assumption method)

10 [2], [1] Isometric Drawing, Counting cubes (Front & Side view),

11 [1], [1], [2] Data Analysis, Rate (Line Graph)

12 [3], [1] Geometry (Properties of angles in Trapezium & Parallelogram)

13 [2], [2] Data Analysis, Average (Bar Graph)

14 [1], [3] Ratio, Percentage and Fraction (Conversion of Cross-Topic Representations, Working Backwards)

15 [1], [3] Volume of Cuboids (Finding Height from V = Base Area x Height) (Common Height from Combine Base Srea)

16 [3], [2] Percentage (% Increase & Decrease from a given quantity)

17 [2], [3] Whole numbers, Grouping (Deductive Reasoning)

Most candidates had found Paper 2 “manageable” or “not that difficult”. The language framing the

problem in those 17 questions was simple and succinct. Textual/Visual comprehension was not an

issue for most candidates.

Roughly 40% of the questions in Paper 2 were “Recall Questions”. Figure 1 and 2 show both Question

6 from 2018 and 2014 respectively.

“Recall” questions test candidates for numerical and manipulative competency. Simply put, this is what

students learn in school, what they train for using practice papers and assessment books. Formulaic,

use-method-X-for-Y question types test candidates for speed and accuracy.


FIGURE 1: 2018 PSLE Paper 2 Q6 FIGURE 2: 2014 PSLE Paper 2 Q6

The differences between both questions:

• Instead of 4 types of object (2014), there are only 3 types of items (2018)

• Orientation of the bar graph

• Candidates are expected to convert cents to dollars (2018)

Circa 60% of the paper 2 comprised Higher Order Thinking (H.O.T) questions. These questions are

specifically crafted to defeat the ‘recall familiarity’ candidates have with ‘Recall’ questions. These

H.O.T require candidates to go beyond the mechanical application of algorithms and formulae and

be able to solve real-life problems represented visually or in textual form. The most-skilled

candidates will be able to reach out for the most efficient and effective manipulation methods in

their Mental Toolbox and apply them to solve the H.O.T question. H.O.T questions test the

adaptability of candidates to apply the ‘best’ (easiest and fastest) method to solve the question.

‘Higher order thinking” questions are not only confined to 4/5 mark questions, but also appear as 2

mark questions that are crafted to holistically assess Mathematical disposition skills and conceptual

knowledge of candidates. These questions are increasingly the new norm.

3 H.O.T question types in the PSLE Mathematics 2018 paper.

1. Beyond computation and procedural knowledgeFigure 3 is an algebraic question that is adapted from the 2018 PSLE Paper. This question goes beyond

the operations of algebra computation. Unlike its predecessors (see Figure 4), Figure 3 is an option

question and the first its kind to appear in a PSLE paper.


FIGURE 3: 2018 PSLE Paper 2 Q3 (modified)

FIGURE 4: 2014 PSLE Paper 2 Q3 (modified)

The question requires the candidate to have an in-depth understanding of the topic apart from the ability

to perform computations. Unassuming candidates could have neglected to consider that the value of

variable 𝑎 ranges from 1 to infinity and it would be impossible to tell if Rajiv or Nasri has more. This

failure would have cost them 2 marks.

2. Interweaving Concepts from 2 or more topics.

H.O.T questions require candidates to use 2 or more concepts from different topics simultaneously to

solve the question.

An example is shown in Figure 5. Candidates need to recall the ‘fraction concept’: Parts of the whole

must be equal to be expressed as a fraction. Thereafter, candidates must possess the applicational

competence to link the ‘fraction concept’ to the ‘area topical concept’ by using the answer in a) to

solve b).


FIGURE 5: Source, 2018 PSLE Paper 2 Q7

Solution for 7a)

Since AF=FE and AE=ED, we cut square ABCD into equal and identical parts shown below.

Fraction of Tile ABCD shaded = "#"$

A

B

C

D

E F


FIGURE 6: Source, 2018 PSLE Paper 2 Q17

Solutions for 7b) using the answer from 7a)

Since #"$

of a single tile is not shaded, then #"$

of 4 identical tiles is not shaded too.

#"$

of 4 tiles (Unshaded) = 81 cm2

""$

of 4 tiles = 81 cm2 ÷ 3 = 27 cm2 "#"$

of 4 tiles (Shaded) = 27 cm2 × 13 = 351 cm2

Without applicational adaptability, candidates may have to resort to inefficient methods to solve

question 7 (e.g. cutting Figure Y into 64 parts and counting the unshaded parts). This method invariably

requires more time as candidates need to count parts individually.

Time is of the essence. Candidates with the strategic competence and in-depth knowledge of the topic

“see” the fastest and simplest way to solve the problem.

3. Questions for the Adaptive Solver

Apart from operational and conceptual knowledge, candidates’ mathematical proficiency is also

dependent on his/her ability to be an “Adaptive Solver”. Adaptive solvers are able to:

- Analyze the question though keywords and their context

- Organise the information by choosing the appropriate visual representation (model)

- Identify the key concept the question is assessing.

- Connect (synthesize) this information to solve the question

Question 17 from the 2018 PSLE Math Paper 2 in Figure 6 exemplifies a problem that

requires candidates to exhibit their Mathematical disposition capacity as Adaptive Solvers.

user

Highlight


From the first sentence in the question, candidates must deduce that the candles are only sold in boxes

of 7 (short) or boxes of 5 (long) and use the “Grouping*” Concept.

*“Grouping” uses the concept of multiplication that is first taught at P2 and subsequently in P4 as

multiples and factors. At P5 and P6, students may revisit this concept under Whole Numbers.

Candidates that fail to deduce this reasoning would try to find the per piece price of each type of

candle.

Each short candle = $3.20 ÷ 5 = $0.64

Each long candle = $2.50 ÷ 7 = $0.35714… (long decimal)

Having done so, candidates would get a long decimated number, triggering instant panic. Anxiety in

the mind of a candidate invariably affects his performance in all subsequent problems.

Solution for 17(a) Boxes of short candles = 19 ÷ 7 = 2.714…. ≈ 3 boxes of 5 candles Boxes of Long candles = 3 ÷ 5 = 0.6. ≈ 1 box of 7 candles Total cost = 3 x $2.50 + $3.20 = $10.70

At first glance, most candidates would presume that 17b) would be a guess-and-check question and try

to use the Supposition/Assumption method. Clueless candidates would take a shot in the dark and

choose a random number (e.g. 30 long candles) and use it to complete the sum.

Candidates who are Adaptive Solvers would deduce that Eva can only buy complete boxes of long and

short candles. He/she could simply make a list of multiples of 7 and 5 to compare and find the difference

of “21” to solve the sums.

Solution for 17(b) Long candles 5 10 15 20 25 30 35 40

Short candles 7 14 21 28

Difference = 35 -14 = 21 35 long candles = 7 boxes of long candles 14 short candles = 2 boxes of short candles Total cost = 7 x $3.20 + 2 x $2.50 = $27.40

A candidate who has not been explicitly taught the “Making a list” technique would not naturally be

able to think of it – certainly not during an examination.


Preparing candidates for PSLE Math 2019?

Yes, H.O.T questions are increasingly prominent. Candidates aiming for A/A* must possess more than

the basic procedural and computational competencies for “recall familiarity”-type Standard Model

questions. They need Adaptive Solvers strategies and skills to solve H.O.T. questions quickly and

efficiently.

How to be an Adaptive Solver?

We have developed the 5-step S.U.R.F.S. process to help students become Adaptive Solvers. This

technique serves as a step-by-step guide for students to tackle different types of problem sums, including

H.O.T sums.

Outline of the S.U.R.F.S Approach.

Table 2 – 5 Step S.U.R.F.S Approach

Scan Scan through the sum to identify - Topics

(Whole No, Fraction, Percentage, Area and Perimeter, Algebra, Data Analysis, Speed,

Measurement, Geometry) - Keywords, numbers, values

* Key words that students often fail to recognise:- “Only, Each, Some, Left (verb), Remained..”

Understand Understand the keywords and the context of the sum to- Recall the key concept behind the problem sum

“Is it Comparison, Change or Grouping” - Question the effect or logical consequence of each keyword,

number or clue

Represent From the identified Key Concept + Topic, choose an appropriateRepresentation technique to map out the information.

Common types of representation are: - Model drawing - Ratio/unit - Proportion statements - Process Flow - List

For shapes and angles, write the measurements, properties of angles with equal sides.

**Make sure to represent ALL the numbers provided in the question


Find Finding and Matching sub-goals to the sequential steps of solving multi-step problems. Map out the problem-solving strategy:

- Work towards finding that “1 unit ” - Organise information from the question - Offload the working memory - Receive method marks for shown working

Solve Read the final question to check what the question requires you to express. E.g. “Shaded or unshaded” parts or “Area vs Perimeter”

To be Adaptive Solvers and to apply the S.U.R.F.S technique successfully, candidates need to have a

good foundational grasp of the concepts for specific topical areas like speed, time and volume.

The SURFS technique is a structured approach to problem-solving. It helps candidates to bridge the

gaps within the problem-operation-solution triangle by guiding them in accessing and selecting the right

‘tools’ form their mental toolbox.

Today, For Tomorrow.

For information about our programmes, please see: https://bboxlearning.com/programmes/academic/mathematics

About the Author https://bboxlearning.com/practitioners/dione-chong-yunjia

Whatsapp Dione @ 81382956 Kok Leong @ 9062 0068

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Extrapolating PSLE Mathematics 2018 into PSLE 2019 ......PSLE Math 2018 dissected - was the paper really challenging? Table 1 below shows the list of questions, their topics and mark