P4P5 Reverse Model Drawing (Before and After Fractional Change)

This exercise below aims to help students better understand before and after models by having them look at the already completed models and have them fill in the blanks to the original problem sum description.

While these are not exam questions, they help students to structure their thinking process for the formation of the equations(number sentences) needed to solve such questions.

Given the before and after model above, 
fill in the blanks.

Luke has ___ times as many toy cars as Marvin at first.

After Luke gave away __/__ of his toy cars.

He now has equal number of toy cars as Marvin.

Luke have 13 toy cars at the end.

They have ___ toy cars altogether at first. 

If the above question is easy, try to do the more challenging question below. 

The question below will randomize with different numbers every hour. 

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P5P6 Math: Value and Multiples and Differences

This is a question type that will provide 4 of the listed information below for 2 different items of different quantities,

1. Total value of 2 items
   
   
2. Difference between 2 item's totals
   
   
3. Unit Difference between 2 items
   
   
4. Multiples of 1 item compared with another 

Similar questions using ratio to represent the multiples can also be found here and here.

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

Calculator usage is allowed

Samy bought thrice as many books as pens.

He spent a total of $3850 on all the books and pens.

Each book cost $5 more than each pen.

He paid $2030 more for all the books than for all the pens.

How many books did Samy buy?

If the above question is easy, try to do the more challenging question below. 

The question below will randomize with different numbers every hour. 

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P5P6 Math: Before and After (One Party Change) Fractional Comparison

Such questions are very similar to before and after "ratio" comparison where only one of the values changed, but the ratios are expressed using fractions. 

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

Calculator usage is allowed.

Similar Ratio (One Party Change) questions can be found here.

Ben and Lenny each have some baseball cards.

At first, Ben has ²/₅ as many cards as Lenny.

After Ben bought 36 more cards,

Ben has ²/₃ as many cards as Lenny.

How many cards did both boys have altogether at first?

If the above question is easy, try to do the more challenging question below. 

The question below will randomize with different numbers every hour. 

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P4P5 : Internal Transfer Multiples (More Became Less)

This question type is very similar to the one with external transfer where the one with more became the one with less.

This one, however, is internal transfer, where the larger value gives away to the smaller value until the smaller value becomes the bigger one.

Such questions will appear in Section C of P4 exams and Paper 1 of P5 exams.

Calculator usage is not allowed.

Kieran has thrice as many marbles as Irwin at first.

After Kieran gave Irwin 75 marbles,

Irwin now has twice as many marbles as Kieran.

How many marbles did Kieran have at first?

If the above question is easy, try to do the more challenging question below. 

The question below will randomize with different numbers every hour. 

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P4P5 Math: Before and After Multiples (More became Less)

This type of question is a "Before and After" where the one with more, became the one with less after an external transfer.

This question requires students to draw "before and after" comparison models in order to visualize the problem sum.

Such questions are common in Section C of P4 exams and also Paper 1 of P5 exams.

Calculator usage is not allowed

Another one of more difficulty that deals with "internal transfer"

Jenny has twice as much money as Kelly.

After Jenny spent $36 on a durian, 

Kelly now has twice as much as Jenny.

How much did both girls have altogether at first?

If the above question is easy, try to do the more challenging question below. 

The question below will randomize with different numbers every hour. 

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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?

If the above question is easy, try to do the more challenging question below. 

The question below will randomize with different numbers every hour. 

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P3/P4 Before and After One Party Unchanged (Start Multiples, End Difference)

Such questions presents 2 values to be multiples of each other at first.

One of the value undergo a change(addition/subtraction) and the resulting difference is given after the chance.

Such questions require students to use "Before and After Comparison Models" to visualize the changes and to also be aware that one of the values "did not change".

These questions are common in Section C of P3 and P4 exam papers.

There were thrice as many boys as girls whom were in the school hall at first.

After 15 boys left the school hall to go toilet, 

there were still 17 more boys than girls remaining in the hall.

How many students were there altogether in the school hall at first?

If the above question is easy, try to do the more challenging question below.

The question below will randomize with different numbers every hour. 

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P6 Math: 3 Parties Before and After with Uneven Ratio at the End

A total of 3 parties are given at first.
Each of the party undergo increase or decrease and the end ratio is given.

Some of the increase/decrease are fractional and some are numerical.

Such questions are common in Paper 2 of P6 exams

Calculator usage is allowed.

An easier version of this question can be found here.

Elizabeth, Wendy and Lindy had a total of $483 at first.

Elizabeth was given more money by her parents and had double of what she had at first.

Wendy spent $67 on a pair of ballet shoes and Lindy's brother gave her another $94.

In the end, the ratio of remaining money of Elizabeth to Wendy to Lindy was 5:4:2.

How much did Lindy have at first?

If the above question is easy, try to do the more challenging question below.

The question below will randomize with different numbers every hour. 

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P5/P6 Math: Before and After with Percentage and Fractional Decrease

This question type begins with the total of 2 values given at first.

One of the value undergo percentage decrease and the other a fractional decrease.

Both values become equal at the end.

Students will need to work backwards in order to solve such questions.

These questions are common in Paper 2 of P5 and P6 exams.

Calculator usage is allowed.

Mr Tan and Mr Lee had a total of $418 at first.

After Mr Tan spent 75% of his money on a gift and Mr Lee spent ¹/₃ of his money on lunch, both men had equal amount of money remaining.

How much did each have remaining at the end?

If the above question is easy, try to do the more challenging question below.

The question below will randomize with different numbers every hour. 

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P5/P6 Math : 3 Parties Before and After with Equal Amounts at the End

This Before and After problem sum starts with the total of 3 parties given.

Each party undergo either numerical increase, numerical decrease and/or fractional decrease. The problem sum ends with each party having equal ratio in the end.

Such questions are common in P5 and P6 Paper 2.

Calculator usage is allowed.

Ben, Carl and Dave have a total of 1021 marbles at first.

After Ben halved his number of marbles by giving some away, 

Carl bought 118 more marbles and Dave threw away ¹/₅ of his marbles,

each boy have the same number of marbles left.

How many marbles did Dave have at first?

If the above question is easy, try to do the more challenging question below.

The question below will randomize with different numbers every hour. 

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