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Maths;; Before And After Concept This concept is relatively easy - as long as you pick up the technique of drawing models. I have noticed that quite a number of pupils from our class don't really like to draw models, especially the weaker ones, but ratio method is also acceptable. But, in this post, I'm only going to demostrate the model method. Model Method The main focus is to draw our case 2 model first, followed by case 1. Let's take an example below. Salleh's money was three Case 1 is in blue while case 2 is in red. Let's draw the model for Case 1 first.  The grey shaded part represents 1 unit. As Salleh has 3 and a half units while her brother has 1 unit, I decided to cut up each unit into 2 so that all of the units in the above model are equal. Now, Salleh has 7 units while her brother has 2 units.Now, from our first model, we bring it down and draw the model for Case 1.  Let's call each unit in case one as parts. Now, you can see that 1 unit (case2) is equals to 2 parts plus $90 dollars. Stuck ? That's the problem! We drew Case 1 first. Hehe. Now let's start back to the top, this time, Case 2 first.  Once again, the shaded part represents one unit. Take note that instead of adding the moeny, we remove, because we are working backwards. Now, we move on to Case 1 ^^. But first of all, how are we going to deal with 3 1/2 units? Well, we multiply 3 1/2 by 2, which is also 7. And, not forgetting to multiply 1 by 2, which equals to 2. Be fair mar! Finally, Salleh has 7 units while her brother has 2.
In case 1, the shaded parts represents that the unit has been removed ;) The 7 units and 2 units are now changed to parts. Now, I want to divide the 7 parts by 2, because Salleh has at first 2 units and I want to find how many parts are there in 1 unit. So, in order to divide without any remainder, we multiply 7 by 2 and 2(brother) by 2 too. So, Salleh has 14 units while her brother has 4. This part is utterly confusing. Dijested ther information already? Now let's continue. Now, since 2 units (Salleh) is equals to 14 parts plus $30, we divide 14 and 30 by 2 in order to find what is in 1 unit. 14 / 2 = 7 (Parts) $30 / 2 = $15 Thus, we know that one unit consists of 7 parts and $15. But, remember that we multpied by 2 for all the parts and money for Salleh, we do not have to divide by 2 for him as he already have 1 unit at first. Finally, for Salleh's case, 1 unit is equals to 7parts + $15 while for her brothers case, 1 unit is equals to 2parts + $90. Saw something? Yes! But if you didn't, here is a model to show what exactly happens. This is a little like simultaneous.  So we know that 7 parts - 2 parts = $90 - $15. The answer is 5 parts = $75. Now we find 1 part, which is $75 divided by 5, and the answer is $15. The question is: How much did Salleh had at first? This is referring to Case 1. And the total parts for Salleh in Case 1 is 14. 14 x $15 = $350 |
