Seeing the Big Picture in Mensuration Questions

In Mathematics, the topic that uses much of creativity is that of Mensuration. When encountered in lower primary, pupils are just introduced to shapes and simple properties of shapes. Then comes primary 4 where they are introduced to composite figures and pupils are required to find the area and perimeter of such figures. Progressing on to primary 5 and 6, pupils are faced with that of triangles and circles. With such a 'variety' of shapes and composite figures, the challenge that most pupils face is that of 'Oh, I know how to do this question, but it's going to be many steps'. Next, they set themselves to work out the problem. One method would be to step back and analyse the figure before attempting to solve it right away. No doubt, a question on a straightforward composite figure may seem pretty obvious to most pupils, yet I would suggest they hold back computing the answer right away. Instead, spend about 30 seconds writing down the 'big picture' of how exactly to go about solving the problem.


Let's take the question below for example: (Source: Ai Tong School SA1, 2010)

Instead of delving into solving and computing the answer for the question, a big picture written at the top of your working space would be:
Area of shaded figure = Area of circle of radius 7cm + (Area of rectangle 7cm by 7cm - Area of Circle of radius 7cm)
                                 = Area of rectangle 14cm by 14cm
                                 = 198 square cm
This enables the pupil to see the question more clearly before solving it and preventing the pupil from making any unnecessary careless mistakes along the way. In the case of the above, it can also help the pupil see that, actually finding the area of circle of radius 7cm is redundant. :)


Try it! You would be surprised that it takes you less time as compared to having to remember all the steps in this big picture in your mind and slowly work it out.


~ Learning, like teaching, is a work of heart ~