Does It Make A Difference?

Whenever I am helping Princess with her school work, I am always digging for old memories of my studying years to better understand what she is going through. But, to my dismay and her frustration, what she is going through right now has little semblance of what we had gone through then. What we did previously perhaps makes up only 5-10% of what is still existing in her curriculum.

During our time, a standard Primary 4 Math exam would include questions like this:

Q: What is the L.C.M. of 15 and 18?

Q: What is the H.C.F of 5 and 8?

In case you have forgotten all about your primary school work, L.C.M. refers to Lowest Common Multiple and H.C.F. refers to Highest Common Multiple.

Today, the question looks something like this:

Question from Popular Primary School #1:

A shopkeeper has more than 50 sweets. If he puts them in packets of 7, he has 5 sweets left. If he puts them in packets of 9, he has 6 sweets left. How many sweets does the shopkeeper have?

Question from Popular Primary School #2:

Don has some stamps. If he packs 5 stamps into each bag, he will have 2 extra stamps. If he packs 8 stamps into each bag, he will need 3 more stamps. What is the least number of stamps Don has?

Question from a popular enrichment book:

A tailor has a bag of buttons and has to sew a certain number of jackets. If he sews 8 button on each jacket, he will have 8 buttons left. If he sews 10 buttons on each jacket, he will need 4 more.

(a) How many jackets did he have to sew?

(b) How many button did he have?

All 3 questions test the application of the concepts of L.C.M. and H.C.F.. At first glance, one might think that these 3 questions looked similar and the method of solving is perhaps the same. Well, if you think so, then you are both right and wrong.

Solution to Question from Popular Primary School #1:

So the shopkeeper has 96 sweets.

Solution to Question from Popular Primary School #2:

Don has 37 stamps.

Solution to Question from a popular enrichment book:

(a) He had to sew 6 jackets.

(b) He had 56 buttons.

According to the answer keys provided, the above answers are all correct solutions to the questions but the workings are all mine, particularly the last solution because instead of a table, the enrichment book provided a formula to solve such questions.

By now you would have noticed the difference between the first two questions and the third. The first two school test questions are just merely testing the kids’ ability to list multiples accurately and match the numbers quickly. Period. However, these two questions fail to consider that there are multiple answers. Don’t believe? Look at the solutions again below.

Solution (expanded) to Question from Popular Primary School #1:

So should it be 96 or 159?

Solution (expanded) to Question from Popular Primary School #2:

37 or 157?

However, you don’t have such ambiguity from the question from the enrichment book because there is a definite multiple (i.e. one answer only). Such questions has a very real life application. I remember I found myself in this situation while packing goodie bags for Princess’s birthday party in kindergarten. The number of students in her class is a definite number.

What were the teachers who set those questions thinking? Or were they even thinking at all? Maybe they were, and they thought that under exam conditions, kids will not be crazy enough to attempt any multiples beyond 10. And they might be just right. However, is it right to set such questions with multiple answers in exams and testing the kids for merely listing the multiples really teaching them its applications in the real world?