P4 Math: Listing Multiples with Remainders

This question type requires students to list out multiples between 2 numbers and also to consider another condition when selecting the common number that appears in both lists.

Such questions are common in P4 exams in Section C.

Heather has some lollipops to pack.

If she packs the lollipops into bags of 5, there will be no remainder.

If she packs the lollipops into bags of 7, there will be only 2 lollipops in the last bag.

What is the least number of lollipops that Heather could have?

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P6 Math: Bill shared by 3 people but one of them paid first

A bill is shared equally by 3 people whom have different amounts of money at first.

This is a very unique question that requires students to make use of "Total Unchanged" to visualize the models between all 3 parties.

Such questions usually appear in Paper 2 of P6 exams.

Calculator usage is allowed.

Mary, Roger and Ken shared the cost of a gift for their father equally.

If Mary paid for the gift first, the amount she have remaining will 

be ⁴/₉ of the amount of what Roger have at first. 

If Roger paid first, the amount he have remaining will 

be ¹¹/₁₅ of the amount of what Mary have at first.

If Ken paid first, he'd have no money remaining.

If Roger had $126 more than Mary at first,

how much did the gift cost?

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P3/P4 Math: Fitting Equal Quantities into Containers with Remainder

The following question requires basic division so as to find out how many containers can be fitted with equal quantities but there will be some remainder after performing the division.

Such questions are common in P4 exams in Section A or B.

Mrs Lim is planning an excursion for her 60 students.

She needs to ferry the students and herself to the Science Center.

A mini-bus can sit up to 12 people.

What is the least number of mini-buses needed 

to ferry the students and herself to the Science Center?

Typical 12-seater mini-bus

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P5/P6 Math: Percentage of Remaining

The question first presents a "percentage of a total" used.

Followed by another "percentage of remaining" used.

A value is given for the amount "left"

Such questions are similar to "fraction of remaining" and 

usually appear in Paper 2 of P5 or P6 exams.

Calculator usage is allowed.

Wendy has a a full tank of petrol in her car at first.

30% of the petrol was used when she drove from home to her aunt's place.

She used 20% of the remaining petrol to ferry her aunt to the city.

She has has 28 litres of fuel remaining in the car.

How much fuel did she have at first?

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P4/P5 Math: Fraction of Total remaining

"Fraction of total" and "Fraction of remaining" are common Fraction problem sums in P5 and P6 Math.

While the word remaining is used here, it is not representing the "fraction of remaining".

A value and fraction of total was used and what remains is a fraction of the total.

Simple model drawing can be used to solve this fraction problem sum.

Such questions usually appear in Paper 1 of P5 papers or Section C of P4 papers.

Calculator usage is not allowed.

Sally read 60 pages of a book on Thursday and read ¹/₈ of the book on Friday.

She completed reading the remaining ¹/₄ of the book over the weekend.

How many pages has this book got?

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P4 Math: First fraction of total given

Questions like these require students to be able to draw model to represent the first fraction of total before processing the rest of the numerical values to represent the remainder.

A part whole model will allow students to be able to process the remaining using the given numerical values.

Such questions often appear in Section C of P4 exam papers.

Gianna drank ¹/₅ of the milk in the carton.

Her father drank 115ml and her brother finished drinking the remaining 81ml.

What is the volume of milk in the carton at first in millilitres?

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P6 Math: Starting Ratio and Ending Fraction and Ending Value

This question begins with a ratio between 2 parties.

Both will share to spend on an item [ unequal shares ].

One of the parties will have a fraction of its amount left and the other party will have a certain value remaining after the spending.

Matt and his brother has money in the ratio of 5:3 at first.

They shared to buy a handbag for their mother.

Matt paid for 60% of the handbag and his brother paid for the rest.

After paying for the handbag, Matt has ¹/₄ of his money left and his brother has $316 left.

How much was the handbag?

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P5/P6 Math: Before and After Fractional Change with Starting Difference (Advanced)

The question below require students to be able to split up 2 different quantities with the starting difference given.

Each unknown quantity is needed to split up to its corresponding fractions.
The difference between the 2 quantities at the end is given.

A similar variation of this question can also be found "here".

Such questions will appear in P5 SA2 and P6 Paper 2.
Calculator usage is allowed.

Harry has 45 more pencils than Matthew at first.

After Harry sold ¹/₃ of his pencils and Matthew gave ¹/₂ of his pencils away,

Harry has 80 more pencils than Matthew at the end.

How many pencils did both have altogether at first?

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P5/P6 Math: Before and After Fractional Change with Starting Difference (Basic)

The question below require students to be able to split up 2 different quantities with the starting difference given.

Each unknown quantity is needed to split up to its corresponding fractions.
The total of what both have left is given at the end.

A similar variation of this question can also be found "here".

Such questions will appear in P5 SA2 and P6 Paper 2
Calculator usage is allowed.

Fergie had 54 more instagram photos than Lionel at first.
After Fergie deleted ¹/₂ of her instagram photos
and Lionel deleted ¹/₃ of his instagram photos, 

both had 69 instagram photos left altogether.

How many instagram photos did both have altogether at first?

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P3 Math : Total Given with Partial Division

The question type below requires P3 students to understand and draw part/whole models.

Part of the total will be deducted and the remaining will be split to equal parts.

(Multiplication and Division)

Such questions often appear in P3 WA1 or SA1 during May and usually appear in the first few questions of section C.

At first, there are 517 mangoes.

After 152 rotten mangoes are thrown away,

the rest of the mangoes are packed into bags of 5.

How many bags will be needed?

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P6 Math: Decreasing sets with remaining

The question type below deals with decreasing sets

The starting ratio is given and each time, a set of 2 different values is deducted.

Such questions often appear in P6 mid year and prelim papers.

This is a paper 2 question so calculator is allowed.

Miss Teo had ¹/₃ as many chocolates as sweets.

After she gave each of her students 4 chocolates and 3 sweets.

she had 6 chocolates and 180 sweets left.
How many students does she have?

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Students may find these question types to be similar.

P5/P6 Math: Fraction of Remaining (Basic)

Questions that deals with fraction of total followed by "fraction of remaining" will usually appear in P5 mid year exams.

Such questions will appear in Paper 2.

Calculator usage is allowed.

Alan gave ¹/₂ of his marbles to Ben.

He gave ¹/₄ of the remaining marbles to David.

Alan has now 12 marbles left.

a) How many marbles did he give Ben?

b) How many marbles did Alan have at first?

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