Started teaching topic and pupils find this topic tough. This is partly due to pupils being weak in Mensuration and they do not like to do questions that are very wordly (one characteristics of NA pupils - language). To help them tackle questions on Rate of Change, I taught them to identify information from keywords in the questions, write them down in mathematical notations and how to piece them together with the help of Chain rule.
For example, the question will always have one rate of change given, say "the rate at which x is increasing is 5 cm/s". Then pupils will write this as "dx/dt = 5". Next, they will have to identify what the question wants them to find, say "find the rate of increasing of the volume". Then pupils will have to write down "dV/dt = ?". They will then write down using Chain Rule a relationship between dV/dt and dx/dt : dV/dt = dV/dx*dx/dt ---(1). From this eqn, they will see that they need to find dV/dx as dx/dt is already given. So to find dV/dx, they need a formula relating V and x which is normally a formula they already know or given in the question. After getting the formula, they will get their dV/dx and then substitute it into (1) and BINGO they have answered the question.
Normally after showing one to two examples, the pupils and I will write down the essential general steps to solving similar question on the topic taught so that they have some basic steps to follow as they do other similar questions as practice.
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Yes, these are mathematical steps that can be checked along the way.
ReplyDeleteI believe, in fact, all mathematics can be scaffolded into steps this way.
Drill these steps with them :)