More often than not, students do not lack practice
questions, but the techniques on HOW to analyse and sieve out the "gems" behind each clue given in the problem sums. While it is important to guide the students the correct way to solve a question, they need to know why certain methods are wrong and not applicable too. For example, to learn why a particular solid is called a pyramid, one has to know why the other solids are not called a pyramid. This is what we call the non-examples.
In my blog, other than showing the different ways to solve a question, I will also include the common misconceptions that tend to arise or careless mistakes that students tend to make.
Are you ready? Here we go... :)
Example 1:
There are 50 questions in a quiz. 5 points are rewarded for
each question answered correctly and 2 points are deducted for each question
answered incorrectly. Jowe answered all the questions and scored a total of 194
points. How many questions did he answer correctly?
50 x 5 = 250
250 - 194 = 56
5 + 2 = 7
56 ÷ 7 = 8
50 - 8 = 42
He answered 42 questions correctly.
Common error(s):
50 x 5 = 250
250 - 194 = 56
56 ÷ 2 = 28
50 - 28 = 22
Discussion between the student and Miss Liew:
Student: Why not dividing 56 by 2? The question said 2
points are deducted, which means Jowe lost 2 points if he answered wrongly.
Right?
Miss Liew: No.. He lost 7 points if he answered wrongly.
Student: What.....?
Miss Liew: First of all, he lost 5 points that he could have
earned if the answer was correct. Then, he got deducted another 2 points for
the wrong answer. So, he lost a total of 7 points for each question!
(More help: If students still cannot get this, ask them if
they get the 5 points if they answer the question wrongly. After they agree
that they did not get 5 points and still lose another 2 points, students will
sense the loss as 7 points.)
Student: Is the 5 points what we call the.............?
Miss Liew: Yes, that 5 points is what we call the
opportunity cost.
Student: Ah, now I understand!
Let's extend the problem:
Scenario 1: Instead of 2 points, what if 3 points are deducted for every wrong answer? How will this affect your working?
Scenario 2: What if, instead of deducting points, no points
were given for wrong answers? How will this affect your working?
Scenario 3: What if only 1 point was given for each wrong
answer? How will this affect your working?
(This scenario is rare but well... for practice purpose.)
Student: Miss Liew, is it true that this 'opportunity cost'
concept is only applicable to questions involving correct and wrong answers?
Miss Liew: Of course not. Do you want to try setting a
question that is related to delivering vases and involves the 'opportunity
cost' concept?
Student: What? I can set a question by myself?
Miss Liew: Of course you can. Everyone is an innovator.
Student: Ok! Let me try!
Words to the readers:
Thanks for reading.
Have you encountered this type of questions before?
What other difficulties do you face when coaching your
child/student this type of question?
Let's share, exchange ideas and support one another.
(to be continued...)
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