Bridging the Gap- Modeling and Methods in Maths(Part 1)

Learning Maths
Learning Maths

Maths is a subject which requires a lot of practice in order to be familiar with it. There are many different concepts which one need to master and formulas to memorise in order to complete the array of questions within the given time.

In the last post I gave an overview of the components tested in a Math’s paper.  In this post I will be showing how Long Answer Questions can be solved using different methods.

**These are actual questions which are taken from the homework worksheets that Monkey boy has brought  home and  I have worked through together with him.

Maths Question
Maths Question

My first inclination was to see if it was possible to draw a model to analyse the question.  After pondering on it for a while both of us found it more complicated to explain if we drew a model for it and eliminated it from the ” potential way to solve the question” list.

We decided to use the Guess/List and check method as there were two different unknowns which had to be identified.

Square to rectangle
Square to rectangle


We worked through the possible  chance of  what the two different lengths of the rectangle could be given ( X and Y) given that the square was of a certain length for each side.

Length of Side Area

X (at 75%)

Y at ( +2)

Area of Rectangle



10-2 = 8

10 + 2 = 12

8 x 12 = 94 cm²



8- 2 = 6

8 +3 = 10

6 x 10= 60 cm²




6=2= 8

4.5 x 8 = 36cm²

As shown above I assumed that each side of the square was 10cm so the area of the square would be 100 cm2. 

Using the projections that ” one side had to be decreased by 25%”  the possibility of 1 side of the rectangle would  be 10-2 = 8 cm.

Following through on the part ” increase the length of the other side by 2cm” I added 2 to 10 to get 12cm.  However when you multiplied both sides to find the area of the rectangle I got 8 x 12 = 94 cm2. 

This is not correct as there has been a change in the total area from 100cm2.    to  94 cm2. 

I slowly moved down the list of possible numbers till I got to 6 cm as the length of the side of the square  and that the area of the square was equal to the area of the rectangle.

That was how we found the answer for this particular question.


Multiple Part Long Answer Question
Multiple Part Long Answer Question

If you are anything like me you too may draw a blank after reading through the whole question. I had to re-read through it a couple of times just to process what the questions was asking.  I found the question really complicated.

I seriously don’t remember having to attempt such complex questions when I was in Primary 5 back then. The difficultly level of questions attempted in Maths has certainly increased a lot!!

To solve this sum we had to use the Working backward method.

We start off from the sentence

” David paid $3 back to Cali”

If we divide the amount David should have paid in 2 parts

The amount Cali paid : The amount  Aini and Bala paid = 2u: 5u

Therefore if all the kids paid  and equal proportion of the present  each

2 u (x4) : 5 u (x4)

8 u : 20 u

Cost of the present = 28u

Each child would have to pay 7 u. However Calia paid  1u more as she paid part of David share so

8u- 7u = 1 u

1 u = $3

28 u = $3 x 28

= $84

a) The price of the present is $84

The amount of money Aini and Bala paid in total = 20 u ($60)

Based on the fact that Aini paid $10 more then Bala we find the amount the Aini paid by doing the following.  (60 + 10) / 2 = $35

Bala pays $10 lesser

$35 – $10 = $25

(Checking – $25 + $35 = $60)

Since each person originally needed to pay 7 u = $21

David had to return $25-$21 = $4 to Bala  and $35-$21 = $14 to Aini

b) David returns $4 to Bala

c) David returns $14 to Aini.

In the next post I will go through the remaining two methods- Modelling and Looking at a pattern to show how they can be applied in problem solving.


 Bridging the GAP

Post in this series

1) Bridging the Gap- An Introduction

2) Bridging the Gap-  Identifying the Gap in Chinese Language ( P4 to P5 )

3) Bridging the Gap- Reinforcing the Learning of Chinese

4)Bridging the Gap- Identifying the Gap between P4 and P5 English.

5)Bridging the Gap- Learning of English in Upper Primary

6) Bridging the Gap- Identifying the Gap between P4 and P5 Maths

7) Bridging the Gap –  Modelling and Methods  in Maths (Part 1) 

Highlights of August 2015

Monkey Boy and me
Monkey Boy and me

August was a really happy month for me. R flew down and took time off from work to spend time with me and the kids. We managed to  spend quality time as a family and as a couple.

The kids and us in the park cycling
The kids and us in the park cycling

Now that Tiger girl is 4 she is able to ride her own bike and we can go riding as a family when R is in town.  She doesn’t need to be excluded from any group activities as everyone can participate in it.

R and me
R and me.

We manage to catch up and have some couple time during my birthday week and am working towards a renewed growth for our marriage.

Light purple blooms
Light purple blooms

I shared photos of the flowers that I took when I visited the Flower Dome  a few months back during the last school holidays.  I’m hoping that I have time for a trip to the National Orchid garden one of these days so that I can capture the blooms housed there too.

Single yellow/white bloom
Single yellow/white bloom

I love spotting unusual flowers and was able to capture a few  unique single blooms during that outing with the kids.

Gift wrapping Workshop with Jane Means
Gift wrapping Workshop with Jane Means

August was also a month of many firsts for me. It was the first time that I attended a  Gift wrapping class.  I’ve always been curious on how to package a gift properly and it was really fun to learn how to do the simple designs that Jane taught in the lesson.

What's is your mindset?
What’s is your mindset?

I had an eye opening talk about NLP and both R and I learned quite a bit about how one’s mindset can affect one’s outlook on life. Everything starts from the mind – If you think you can do it you will find ways to do it.

Attending the Make Me Beautiful Workshop
Attending the Make Me Beautiful Workshop

August was also the month I attended my first beauty workshop by Mas a Makeup Guru who is with Mary Kay. She too started off with not much knowledge about Make up 5 years ago and look where she is today. She has her own Makeup Artist school and does beauty and other makeup for others using our Mary Kay products.

R and the kids when they were younger
R and the kids when they were younger

Planning for the future is very important. R and I have been considering about our finances a lot this year and it was really interesting to know that nowadays they have plans like the Family Advantage by AXA which makes financial planning easier for young families.

My Purple Winged Fairy
My Purple Winged Fairy

I’ve cut back further on my blogging and online commitments to spend more time with the kids as they will be having the SA2 exams soon. I’m also doing more homeschooling with Tiger girl to prepare her for K2 next year.

How was your month of August like?

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