More Interesting question

A figure is made up of a square and a rectangle overlapped each other as shown below. The ratio of the area of the square to the ratio of the are of the rectangle is 3:2. The shaded area of the rectangle is 3/8 of the area of the rectangle. The total unshaded area is 42cm² . What is the area of the rectangle?

It is relative common for MOE to set a typical question like this. Firstly ratio is provided between the area of the square & area of the rectangle. Then the fraction of shaded area of the rectangle is provided. Finally, the area of the unshaded is provided so that you can determine the area of rectangle.

In order to compare the item properly, we can compare the items in units as below :-

Since the shaded area of the rectangle is 3/8. We can represent the shaded portion of the rectangle as 3 units and the unshaded portion as 5 units. As the area of the rectangle take up 2 parts, which is 8 units in total, we can simply said that 1 parts is equal to 4 units. Since the rectangle is 2 parts then the square is 3 parts, which will take up 12 units. The interlapped took up 3 units, hence the unshaded portion of the square will be 9 units (12units - 3 units). The unshaded portion make up by unshaded rectangle portion (5 units) and the unshaded square portion ( 9 units), so the total unshaded area is 14 units.

14 units     42cm²

1 units       42/ 14 = 3cm²

         

Since the area of rectangle is made up of 8 units

8 units      3cm² X 8 = 24cm²

Interesting word problem - Remainder Concept

I saw this interesting word problem posted in one of the thread in Kiasu parents forum (http://www.kiasuparents.com) the question look something like this :-

Question :

Kumar spent $1729 on a set of encyclopedia. He spend 1/4 of the remainder on a a camera and still had 2/5 of his money left. Find the total amount of money he had at first.

This is a typical question based on remainder concept. While it is relatively easily for experienced teacher to solve the question. However, in teaching, it is not how much you know, but rather how easy you make it for the children to understand. You have to approach it from the mentality of your students. There are a few points which you have to specially take note as below :-

1. The amount given $1729 is a relatively odd number and some students will perceive it as tough to calculate.

2. 3/4 of the remainder which makeup the Final fraction of 2/5 is not very clear cut to some students who are not fast learner. (as you need to further divide the 2/5 to 6/15 so that the 3/4 of the remainder fit nicely into the subunit. You could split the 1/4 & 3/4 of the remainder properly into the subunits nicely.)

3. After further divide the final fraction into 15 equal parts, it will not be easy for your students or your kids to work on as they have to be careful visually as well as when they carry out the computing.

4. For students that you have not introduce the remainder concept, you will need to guide and train them to identify why this question belong to the remainder concept. This question also give you to opportunity to train them how to think.

Let approach it from the model method

From the question we can draw the model below

We know that Kumar had spent the money on the encyclopedia and camera are left with 2/5 of the total amount. We know the amount spent on the encyclopedia but not the final fraction (We could immediately calculate the total amount if we know the final fraction of the encyclopedia. We know the final fraction left but not the actual money left. The great clue is the money left is 2/5 of the total and it is also 3/4 of the remainder after buying the encyclopedia and camera. So trying to relate the amount left which is 3/4 of the remainder to the final fraction we have to compare as below

We had to split the each 1/5 to 3 equal units so each 1/4 will make up 2/15 of the final fraction and 3/4 will make up 6/15 of the final fraction as indicated below

Hence we can find out the final fraction of the encyclopedia by substract 2 units (camera) and 6 units (left) from the total 15 units. Hence the encyclopedia is 7 units as shown below:-

Therefore the total amount is as work out as below

                            7 units  1729

                            15 units1729 / 7 * 15 = 3705  

Word Problem - Fraction

Question :

XiuLi has $459 and YuLi has $1560. After both of them spent equal amount of money, XiuLi has 1/4 as many money as YuLi. So how much money has YuLi spent ?

Model Methods

Different at beginning = Different after spent

So 3 units $1560 - $459 = $1101

1 unit $1101 /3 = $367

YuLi spent = XiuLi spent = $459 - $367 = $92

                                                                                              ANS : $92

Word Problem - Whole Number

Question :

At first Ali has 20 marbles more than John. After John give Ali 5 marbles, then Ali has 3 times as many marble as John. How many marbles do Ali & John has at first ?

Model Method

2 units   5 + 20 + 5 = 30

1 unit15

At first Ali has 3 x 15 -5 = 40 marbles

and John has 15 + 5 = 20 marbles

                                          ANS :  Ali has 40 marbles John has 20 marbles

Word Problem - Ratio

Question   :

A farmer has equal number of chickens and ducks. After he sold 10 chickens and 36 ducks, The ratio of chickens he has to the ratio of duck he has became 3:1. How many chickens do he had at first?

Model Methods

Different remaining = Difference sold

               

                 2 units         26

                 1 unit  13

At first the farmer had 3 x 13 + 10 = 49 chickens

Alternate Methods

Make sure both the final quantities (3 parts and 1 part) are equal. Multiply the entire column by the same number

then we have the following table

As both the chickens and ducks are having the same final quantities, we can find out the below

2 units108 - 10   =   98

1 unit  49

                                                                                                             ANS :       49 chickens