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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P6 Math: Before and After (3 changes to percentage between 2 values)

This question type show the percentage changes at every step of the "internal transfer" that happens between 2 values.

Such questions are common in Paper 2 of P6 Prelim exams.

Calculator usage is allowed.

Shane and Kirsten have a total of $8640 at first.

Shane gave Kirsten some of his money and Kirsten's amount increased by 60%.

Kirsten then gave Shane some of her money and Shane's amount increased by 30%.

Then, Shane gave Kirsten some of his money and Kirsten's amount increased by 80%.

Both had equal amount of money in the end.

Find the percentage increase of the amount of Kirsten's money.

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: Before and After Ratio made Equal at the end

This question type starts with a ratio and after both values undergo some decrease, a new ratio is given.

Both values undergo another addition and that causes both values to become the same at the end.

Such questions are common in P6 Prelim Paper 2.

Calculator usage is allowed.

Benedict and Erica has erasers in the ratio of 5:7 respectively.

After Benedict gave away ³/₇ of his erasers and Erica sold some erasers,

the ratio of Benedict's to Erica's remaining erasers became 10:7.

Benedict then bought another 60 erasers and Erica bought 240 erasers.

Each have the same number of erasers at the end.

How many erasers does Erica 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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P6 Math: Equal Quantity after 2 Parties undergo Fractional Decrease

The question presents 2 different items, each of different value and quantity.
After each undergo a fractional decrease, both items have the same number remaining.

The unit value of each item and the total value of the remaining items are provided.

Such questions require students to make use of "Equal Value Fractions" in order to solve.

These type of questions will usually appear in Paper 2 of P6 exams.

Calculator usage is allowed.

Craig has a stack of $2 and $10 notes.

After using ²/₉ of the $2 notes and ³/₅ of the $10 notes to buy a figurine,

he has equal number of $2 and $10 notes remaining.

He has $672 left at the end.

How much money did Craig 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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P5P6 Math: Starting Difference Given with Both ending Equal at the End

This type of question begins with a value given(usually the difference between 2 parties).

Each of the value undergo fractional decrease and both ends up to be equal in the end.

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

Calculator usage is allowed.

Rachel has $105 more than Phoebe at first.

After Rachel spent ²/₃ of her money and Phoebe spent ¹/₄ of her money,

both girls have equal amount of money left.

How much did Rachel spend?

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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P4P5 Math: Before and After Start Multiples End Same

Such problem sums starts with 2 parties, one being a multiple of another at first.

Both parties undergo addition or subtraction and results in both having equal value at the end.

This type of problem sum will require student to use before and after models to represent visually the starting multiples of one another at the "Before" model and the "After" model to represent the changes and how both became "Equal".

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

Calculator usage is not allowed.

Chris have 3 times as many buttons as Bailey at first.

After Chris used 30 buttons making shirts and Bailey used 4 buttons for making pants,

they had the same number of buttons left.

How many buttons did Chris 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 Math: Uneven Ratio becomes Equal after Both Decrease

This question provides the ratio of 2 items at first.
After both undergo different decrease in value, both ends up being equal with one another.

Such questions are common in WA2(mid year) for P5.

Calculator usage may be allowed.

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

Alan and Rick each have pencils in the ratio of 5:8.

After Alan gave away 32 pencils and Rick sold 77 pencils.

They have equal number of pencils remaining.

How many pencils did Rick have 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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P4 Math: Before and After : Start with More, Ends with Equal

This question type is a "Before and After" comparison which starts with one party have more items than the other.

After one party undergo a decrease and the other having an increase, both parties ends up with the same items.

Students are required to use "before and after" comparison models to represent what they understand from the given values.

Such question often appear in Section C of P4 exams.

At first, Alan has thrice as much money as Ben.

After Alan spents $30 and Ben received $20 from his mum,

both boys have equal amount of money remaining.

How much did Alan 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. 

Copy below question down before making attempt.

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