P5P6 Math: Before and After (Starting Difference, Ending Fractional Comparison with Total)

This is a common MCQ question in Paper 1 where the difference between 2 values are given at first.

Each value is added with a different number and it ends with a fraction of total given, representing one of the values, at the end.

Such questions appears in P6 Paper 1 of Mid Year WA.

Calculator usage is not allowed.

Brett has $29 more than Aaron at first.

After Brett was given another $30 and Aaron was given $25,

the total amount of money Brett has is ³/₅ of the total amount of both boys.

How much did Aaron have at first?

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P6 Math: Fraction of Remainder with Addition and Ratio at the End

Fraction of remainder questions will be more complex at P6 level.

The following question type adds on to the difficulty by including an addition and provides the ratio comparing between the total at first and the total at the end.

Such questions usually appear in Paper 2.

Calculator usage is allowed.

Devinder has some money at first.

He spent ³/₈ of this money to buy a ruler and

²/₇ of the remaining money on a book.

After he was given $9.20 by his uncle, the ratio of his

money at the end to his total amount of money at first became 5:2.

How much did Devinder spend on his ruler?

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P5/P6 Math: Revisting Before and After Ratio ( Both Parties Change )

This question type is similar to the one posted here.

There are 2 values being compared using ratio and each of them undergo addition or subtraction and the ending ratio is also provided.

Such questions are common in Paper 2 of P6 exams.

Calculator usage is allowed.

Eric and Tyra were given money by their father in the ratio of 7:2. 

After Eric spent $165 and Tyra was given $210 more, 

the ratio of Eric to Tyra's money at the end became 2:7. 

How much did Tyra have at first?

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P5/P6 Math: Starting Total and Ending Ratio (Basic)

The question type below provides the student with the starting total between 2 parties and the ending ratio after each of them undergo some changes. One of the value will undergo a fractional decrease and the other will have some value added or subtracted.

Students will need to "start from the end" in order to solve. (aka working backwards)

Such questions are common in Paper 2 of P5 and P6 papers.

Calculator usage is allowed.

Similar questions of this type can also be found here.

Moorthi and Devi have a total of 1093 invitation cards to send out.

After Moorthi sent out ¹/₃ of his cards and Devi sent out 444 cards of her cards,

the ratio of Moorthi's to Devi's remaining cards was 4:5.

a) How many cards did Moorthi sent out?

b) How many cards did they have left altogether at the end?

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P6 Math: Patterns NOT of Constant Increment (Version 2)

Pattern questions that deals with constant increment can be solved using a certain "3-step method".

The pattern shown below, however, is not exactly showing a constant increment between every consecutive pattern.

Such questions are common in P6 Prelim Paper 2.
Calculator usage is allowed

Pattern	1	2	3	4	5	6	7
Tiles	25	26	28	29	31	32	34

a) How many tiles will there be in pattern 11?

b) In which pattern will there be 145 tiles?

Mosaic tiles commonly used in swimming pools

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P6 Math: Before and After Ratio (Expert)

A total of 3 ratios are given for this question type.

Starting ratio (before), ending ratio (after) and the ratio of change will be given for such questions.

Such questions will appear in Paper 2 of P6 Math exams.

Calculator usage is allowed.

Robin have a total of 384 grapes and berries in the ratio of 5:3 respectively.

He then gave away some grapes and bought more berries in the ratio of 2:1.

After that, the ratio of grapes to berries became 1:1.

How many grapes were given away?

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P5 Math: Average of 2 groups of items

The topic of Average requires students to find out each fair share.

The question type below provides 2 sub-totals, 
from which, students must be able to derive first the total before they can process the average [ aka fair share ].

Such questions can appear in both paper 1 and 2.

Calculator usage is allowed if in Paper 2.

A group of 3 boys have a total of 17 die-cast toy cars.

Another group of 5 boys have a total of 39 die-cast toy cars.

What is the average number of die-cast toy cars owned by each of these 8 boys?

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P3 Math: Comparison Model Drawing Exercise (More Than/Less Than)

The following is designed to help students visualise more than/less than questions by using comparison models.

These few questions may look identical 

but these numbers given are representing different parts of the model.

Draw the comparison models and fill up all the empty boxes in each model

Q1) 
Ali has $78. Ben has $30 more than Ali. How much do they have altogether?

Q2)
Ali has $78 more than Ben. Ben has $30. How much does Ali have?

Q3)
Ali has $30 less than Ben. Ben has $78. How much do they have altogether?

Q4) 
Ali and Ben have $78 altogether. Ali has $30 more than Ben. How much does Ben have?

Q5)
Ben has $78 more than Ali. Ali has $30. How much do they have altogether?

Q6) Ali has $30 more than Ben. Ben has $78. How much money do they have altogether?

Q7) Ali and Ben have $78 altogether. Ben has $30. How much more money does Ali have than Ben?

Q8) Ali has $78. Ben has $30 How much more money does Ali have than Ben?

Draw this model for each question and
fill up the blanks with information from the question

P3 Math: Part/Whole Model Drawing Exercise

The following is designed to help students visualise subtraction and addition by using part/whole models.

These few questions may look identical 

but these numbers given are representing different parts of the model.

Draw the part/whole models and fill up all the empty boxes in each model

Q1) 
Bella has $100. She bought a book and had $15 left. How much was the book?

Q2)
Bella spent $15 to buy a magazine and has $100 left. How much did she have at first?

Q3)
Bella has some money at first. She received $15 from her father and now she has $100. How much money did Bella have at first?

Q4) 
Bella wanted to buy a bag that costs $15. How much change would she get if she gave the cashier a $100 note?

Q5)
Bella paid for the pair of shoes with $100 and received $15 change. How much did the pair of shoes cost?

Q6) Bella bought a chair that costs $15. She also bought a table that costs $100. How much did she pay for the 2 items altogether?

Draw this above model for each question and
fill up the blanks with information from the question

P4/P5 Math: Before and After: Start Same but End with Multiples

The following question is a P4 and P5 question that does not require a calculator.

This is a "before and after" model drawing exercise where both parties starts with the same amount but after each add or subtract different amounts from their total, the story ends with one being a multiple of another.

Derek and Becky baked the same number of loaves of bread at first.

After Derek sold 20 loaves and Becky gave away 80 loaves,

Derek now has 4 times as many loaves of bread left as Becky.

How many loaves of bread did both bake altogether at first?

How does yeast help make bread?

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P3 Math: Total Given After Subtraction and Addition

This question type is a simple before and after question that requires students to be able to comprehend what 2 mathematical functions (subtraction or addition) must be performed to get the total that was given at first(aka before).

Such questions usually will appear in Section B or C of P3 exam papers.

The train left Ang Mo Kio station with some passengers.

When the train reached Bishan station,

433 passengers alighted.

When the train reached Braddell station,

100 passengers boarded the train.

There were 645 passengers altogether on the train 

after the Braddell station passengers boarded

How many passengers were there on the train 

when the train left Ang Mo Kio station?

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P6 Math: Patterns NOT of Constant Increment

This question below is a very demanding P6 Pattern question.
Mostly seen in Prelim Papers and PSLE itself.

Usually appear in the last few questions of Paper 2 so calculator usage is required.

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Are you able to see the square and triangles in this question?

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P3 Math: Part Whole Model with Total Height(or Length) given

The question type below tests the ability of P3 students to draw and label a Part Whole model with the information included.

Height/Length is given in both m and cm to ensure that they are able to perform such conversions between metres and centimetres effectively

With the heights(lengths) information given, students must piece together the information to construct a part whole model that conforms with the information presented in the question.

Such questions often appear in P3 WA2 or SA2 and will appear in Section C of the P3 Exam paper

Larry had 4m 2cm of ribbon at first.
He used 80cm of the ribbon to tie a present.
He gave 2m 43cm of the ribbon to Eddie.

What length of the ribbon did Larry have left now?

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P3 Math: Comparison Models with Total Mass given

The question type below tests the ability of P3 students to draw and label a comparison model with the information included.

Mass is given in both kg and g to ensure that they are able to perform such conversions between g and kg effectively

With the comparison sentence given, students must piece together the information to construct a comparison model that conforms with the information presented in the question.

Such questions often appear in P3 WA2 or SA2 and will appear in Section C of the P3 Exam paper

Sherlyn have 1kg20g of fruits more than Peter.
The two children has a total 5kg400g of fruits altogether.

What is the mass of the fruits that Sherlyn have?

Top 20 edibles that are richest in Vitamin C

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P5/P6 Math: Ratio: Both Parties Change

The question below deals with the ratio, where both parties undergoing changes via addition or subtraction. Both the starting ratio and ending ratio will be given.

Such questions will appear in exams once after ratio techniques are taught in P5.

Calculator usage is allowed.

A similar version of this question can also be found here.

Jason and Alan each bought some flowers

in the ratio of 1:3 respectively.

Jason gave away 12 flowers and Alan gave away 18 flowers.

The ratio of Jason's flowers to Alan's flowers became 2:9.

How many flowers did they buy altogether at first?

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