Mathematics

Primary 5 / 6

15 February 2019

PSLE Examination Format 2019 - SMA

Paper Booklet Item Type Number of questions

Number of marks per question

Weighting Duration

1A

Multiple-choicequestions

10 1 10%

1 hour5 2 10%

BShort -answer

5 1 5%

10 2 20%

2Short-answer 5 2 10%

1 h 30 minStructured/Long-answer 12 3, 4, 5 45%

Total 47 100% 2h 30 min

- Students are allowed to use calculator for Paper 2 only. - There will be a break in between Paper 1 and Paper 2.

PSLE Examination Format 2019 - FMAPaper Booklet Item Type Number of

questionsNumber of marks per question

Weighting Duration

1A

Multiple-choiceQuestions

10 1 10%

1 hour10 2 20%

BShort-answer questions

10 2 20%

2Short-answer questions

10 2 20%1 hour

Structured/Long-answer questions

6 3 , 4 20%

Total 46 90% 2 hours

- Students are allowed to use calculator for Paper 2 only. - There will be a break in between Paper 1 and Paper 2.

2

11

6

9

6

5

6

4

6

5

3

2

Do not stop at improper fraction unless it is instructed

Common Error

Addition & Subtraction of Fractions

• Always leave final answer in simplest form

Multiplication of Fractions

• Don’t need to find common denominator for multiplication of fractions

Division of Fractions

4

3

8

6

8

5

5

6

8

5

6

5

• Incorrect inverting of the dividend instead of divisor

3

11

3

4

6

8

5

8

6

5

8

5

6

5

• Keep the first fraction

• Flip(Invert) the second fraction (find the reciprocal)

• Change the operation sign ( ÷ to x )

Division of Fractions

25

231

25

48

5

8

5

6

8

5

6

5

• Incorrect inverting of both the dividend and divisor

3

11

3

4

6

8

5

8

6

5

8

5

6

5

• Keep the first fraction

• Flip(Invert) the second fraction (find the reciprocal)

• Change the operation sign ( ÷ to x )

Equivalent Fractions

20

155

4

3

• Should multiply both numerator and denominator with the same factor

20

15

4

3

5

5

Word Problems involving fractions

Take note of the following. Do not misread the questions.

• I had 2 kg of flour. I used 𝟏

𝟓kg of it to bake a cake. How

much flour had I left in the end?

• I had 2 kg of flour. I used 𝟏

𝟓of it to bake a cake. How much

flour had I left in the end?

2 −1

5= 1

4

5

2 ×1

5=2

52 −

2

5= 1

3

5

Unknown Angles

• Wrong assumptions thinking that it is isosceles triangle which is not stated in question

∠𝑐 + ∠d -----------

∠𝑎 + ∠b -----------

Unknown AnglesABCD is a parallelogram. EG = EF and GF is parallel to AB and DC.

Find ∠x and ∠y.

• Wrong assumptions thinking that ∠ADE and ∠EDC are equal

Unknown Angles

• No reference of angles obtained in the solution

No method mark will be awarded

Unknown Angles

• Angles obtained are shown clearly in the diagram

70°

70°

Method mark will be awarded accordingly even though the final answer is incorrect as there is clear indication shown in the diagram

Unknown Angles

• Angles obtained are labelled clearly in the diagram

Inappropriate Presentation

Errors involving Units

•Money ‘$’• $12.9 (x)

• Must have 2 decimal places

• $12.90 ()

• $54 – 90¢ = $53.10 (correct presentation)

• 54 – 90 = 53.10 (incorrect presentation due to missing units)

• Change all numbers to the same units in the equation

• This also applies to mass, length, time etc. which involve different set of units

•Percentage ‘%’• 50% % (incorrect as there is a change in value, 50% % = 0.5%)

Errors involving Units

Misuse of Equal Sign

•10% = 50 (inappropriate presentation as value is different)

•10% ---- 50 (appropriate presentation)

•2

3+ 5

6=

4

6=

4

6+ 5

6=

9

6= 1

3

6= 1

1

2(x)

•2

3+ 5

6=

4

6+ 5

6=

9

6= 1

3

6= 1

1

2()

• 4 + 3 x 9 = 4 + 27

= 31

Inappropriatepresentation

Appropriatepresentation

Misuse of Equal Sign

Inappropriatepresentation

Appropriatepresentation

Transfer Error / Misread

12 NOON / 12 MIDNIGHT

• Using “a.m.” and “p.m.” correctly

NOON

Solving Word Problems Involving Time

Use of Timeline

• Drawing a time line to find start time, end time and

duration

Use of Timeline

–

Heuristics

Understand the word problem

Decide an approach

Go through ‘Decision Guide’

Solve the word problem using selected approach

Understand the word problemNot OK

END

OK

SPAR framework

See

Plan

Act

Reflect

Decision guide

Easily represented using model/ diagram?

Table or series of numbers/ diagrams?

Two or more quantities (unknowns) linked in more than one way?

Stated range or multiples? (“How many ways of arranging…”)

Has a result or relationship?(“First this… Then this…”)

No

No

No

No

H1 – Model/ Diagram

H2 – Find a pattern

H3 – Substitution

H4 – Make-a-list

H6 – Working Backwards

H5 – Guess and Check

Yes

Yes

Yes

Yes

YesNo

H1: Model Drawing

Relate the word

problem with the model

diagram to help students

visualize the question

better.

[ PSLE 2015 Paper 2 Q7 ]

At first, Ben had $90 and Chandra had $48. Each bought a shirt at the same price. The amounts of money Ben and Chandra had left were in the ratio 4 : 1. How much did the shirt cost?

3u = 90 – 48 = 42

1u = 42 ÷ 3= 14

48 – 14 = 34

Ans: $34

H1: Model Drawing

[ PSLE 2017 Paper 2 Q3 ]

Mrs Lee had a bottle of orange juice. She drank 600 ml of the juice in the morning

and 1

6of the remaining juice in the afternoon. After that, there was

1

2a bottle of

juice left. How much of the juice did she drink in the afternoon?

4u = 600

1u = 600 ÷ 4= 150

Ans: 150 ml

half amt left

600 ml

half amt drank

remaining

Sets of 4 digits

H2: Finding a Pattern

4 , 0 , 1 , 2 , 4 , 0 , 1 , 2 , 4 , 0 , 1 , 2 , 4 , 0 , 1

[ PSLE 2017 Paper 2 Q8 ]

The first 15 numbers of a number pattern are given below.

4 , 0 , 1 , 2 , 4 , 0 , 1 , 2 , 4 , 0 , 1 , 2 , 4 , 0 , 1 , …1st 15th

Find the 626th number. Find the sum of the first 627 numbers.

627 ÷ 4 = 156 r 3

4 + 0 + 1 + 2 = 7 (sum of a set)

156 x 7 = 1092

1092 + 4 + 0 + 1 = 1097

Ans: 1097

626 ÷ 4 = 156 r 2

Ans: 0sets

pattern starts again

pattern starts again

H2: Finding a Pattern

Relate the solution with respect to the

pattern no.

[ PSLE 2016 Paper 2 Q18 ]

Yasmin uses triangles and circles to form figures that follow a pattern as shown below.

A figure in the pattern has a total of 100 triangles and circles. What is the figure number?

Fig. No. 1 2 3 4

No. of 2 5 9 14

No. of 2 4 7 11

Total no. 4 9 16 25

Another figure in the pattern has 50 more triangles than circles. What is the total number of triangles and circles in this figure?

Total no. 42 x 2

93 x 3

164 x 4

255 x 5

Fig. No. 1 2 3 4100 = 10 x 10 10 – 1 = 9 (Figure No.)

Fig. No. 1 2 3 4

No. of 2 5 9 14

No. of 2 4 7 11

Find difference2 – 2 = 05 – 4 = 19 – 7 = 214 – 11 = 3

Diff = 50Fig – 50 + 1 = 51Total = 52 x 52

= 2704

Relate the solution with respect to the

pattern no.

H3: SubstitutionAt a bakery, Jen paid $12.40 for a banana cake and 4 egg tarts. Shan paid $25.20 for a

banana cake and 20 egg tarts. Rani bought 5 banana cakes. How much did she pay?

[ PSLE 2013 Paper 2 Q9 ]

1 C + 20 T = 25.21 C + 4 T = 12.4---------------------------------

16 T = 25.2 – 12.4= 12.8

4 T = 12.8 ÷ 4= 3.2

1 C = 12.4 – 3.2= 9.2

5 C = 9.2 x 5= 46

Ans: $46

H3: SubstitutionYulin wants to make 14 small identical stars and 20 large identical stars using wire. She has made 12 small stars and 7 large ones using 960 cm of wire. The length of wire she used for 3 large stars is the same as that for 4 small stars.

[ PSLE 2014 Paper 2 Q17 ]

4s --- 3L12s -- 9L

× 3

12s + 7L = 9609L + 7L = 960

16L = 960

L = 960 ÷ 16= 60

How many large stars can be made with the same length of wire used to make 12 small stars?

What is the length of wire she needs to make the remaining stars?

13L = 60 × 13= 780

3L = 60 × 3= 180

2s = 180 ÷ 2= 90

4s --- 3L

780 + 90 = 870

Ans: 870 cm

H4: Make-a-list

Multiples of 8Multiples of 8

+ 2Multiples of 9 Multiples of 9

- 2

170 ÷ 8 = 21 R 2

Try 22 × 8 = 176

176 178

184 186

192 194

200 202

170 ÷ 9= 18 R 8

Try 19 × 9 = 171

171 169

180 178

BINGO !!!We have a

match! Ans: 178

Catherine has a bag containing between 170 to 200 coins. When she arranged them into stacks of 8, she has 2 coins extra. When she arranged them into stacks of 9, she has 2 coins short. How many coins are there in the bag?

H6: Working BackwardsA bus left an interchange carrying some passengers with it.

At the first stop, ¼ of the people in it alighted and 5 people boarded it.

At the 2nd stop, ½ of the people in it alighted and 20 people boarded the bus.

When it left the 2nd stop, there were 60 passengers in it.How many passengers were there in the bus when it left the interchange?[ http://www.singaporemathguru.com/blog/working-backwards-with-fractions/ ]

@ Interchange

@ 1st Bus Stop

@ 2nd Bus Stop

5

20

?

Working backwards from the 2nd Bus Stop

60

60 – 20 = 40

40 × 2 = 80

80 – 5 = 75

75 ÷ 3 = 25

25 × 4 = 100

Ans: 100

H5: Guess-and-check

Meng sold a total of 368 large and small durians at the prices shown below and collected $2760. How many large durians did Meng sell?

[ PSLE 2013 Paper 2 Q15 ]

No. of Large No. of Small Total ($) / ×

184 184 184 x 9 + 184 x 5 = 2576 x

2760 – 2576 = 184 (difference in amt)9 – 5 = 4 (diff bet. 1 L and 1 S durian184 ÷ 4 = 46 (need to top up 46 L)

230 138 230 x 9 + 138 x 5 = 2760

Assumption Method (Alternative solution)Assume all small durians

368 x 5 = 18402760 – 1840 = 920

920 ÷ 4 = 230

Assume all large durians368 x 9 = 3312

3312 – 2760 = 552552 ÷ 4 = 138

368 – 138 = 230

Examination Time Management Strategy for PSLE Math Paper 1- Time Allocation

• Total duration: 1 hour

Paper 1- Booklet A- MCQ: 10 qns- 10 min

5 qns-10 min

Booklet B- Short Answer qns: 5 qns- 5 min

10 qns- 20 min

Total time taken- 45-50 min

Checking- 10-15 min

Rule of thumb :

1 mark qn - 1 min

2 mark qn - 2min

Highlighting of Keywords

Revision Tips

•Important things to take note

Revision Tips

•Important things to take note • Spelling of words eg. forty, ninety, million• Use of hyphen for numbers like twenty-one, fifty-nine etc.• Order of operations • Area and perimeter of square and rectangle• Area of triangle• Average• Properties of 4-sided figures• Speed• Volume• Area and Circumference of Circles• Multiplication tables of 2 to 9

Revision Tips

•Use calculator only when you see

•Do remind your child to write down every step clearly.

•All workings/equations/steps are essential.

•Your child’s final answer may be incorrect, but he/she can still obtain some marks for showing the correct workings/equations/steps.

•Ensure that your child has cultivated the habit of checking the reasonableness of their answers.

Revision Tips

•Ensure your child has exposure to questions on all the topics to be tested.

•Run mock examinations at home and time him/her.

•As PSLE approaches, your child should be revising instead of learning new concepts.

Revision Tips

•As the saying goes, “Practice makes perfect!”, encourage your child to practise consistently for the PSLE.

• Learn from the mistakes made and try out the problems again to build confidence.

•Taking short breaks in between the study sessions is crucial.

Examination Tips – Multiple Choice Questions

•Highlight the keywords / key information

• Look for the ‘negative’ keywords in the questions • not or incorrect

•Do the calculation and working for easy checking later

•Write down the options selected in the booklet before shading

• Shade the OAS carefully with the answers matching the respective questions

• Eliminate any impossible answers

• Substitute the options chosen into the questions to check for reasonableness

• Circle the question number if decide to skip first

Examination Tips – Short/Long Answer Questions

•Highlight the keywords / key information•Questions involve Geometry, mark the necessary

information in the diagram shown• Angles• Length

•Plan and organise the solutions for easy checking later•Draw model to help visualise the questions•Apply any of the heuristics skills learnt• Guess & Check / Working Backward

•Transfer the numbers/digits correctly from the questions and throughout the steps•Minimise transfer error/misread

•Circle the question number if decide to skip first

Examination Tips – Short/Long Answer Questions

•Perform the operation (add/subtract/multiply/divide) carefully•Write in complete equations and be consistent in the

units•Answers given in fractions/ratios must be in the

simplest form•Check if rounding (1 or 2 d.p.) is required when

answers are in decimals•Work backwards with the answers obtained to check if

they satisfy the conditions given in the questions•Provide with a standard unit of measurement at the

final answer line unless the unit is already been given• Avoid 19% %