Working out the weight of photocopy paper

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

14 February 2021

“Is it true that if you divide Sh47 billion equally among the 47 million Kenyans, each person will get one million shillings?” I get these kinds of questions a few times and it makes me wonder whether those asking don’t trust their own calculations. Of course, the answer is no! And if you don’t believe me, work it out for yourself.

Such questions indicate to me that there is a major problem in the way teaching is done in our educational institutions. It appears that learners are not encouraged to test and figure out their own answers. Thankfully, the new Competency Based Curriculum (CBC) is attempting to solve this problem.

Recently, grade 3 children in a school in Nairobi were asked by their teacher to count the stars in the sky. Luckily, it was a cloudless January night with fairly good visibility. The child with the highest count in the entire class had counted only 32 stars!

This exercise was for a religious education lesson – the star of Bethlehem. I wonder how the teacher will tackle the part where God tells Abraham that he will have as many decedents as the stars in the sky. From what the children observed, that’s not a very large number!

Any way, a more interesting question came from George Wafula: “Photocopy papers are labeled 80gsm. What does this mean?” The quick answer is “80 grammes per square meter”.

However, I anticipate a follow-up: so, I will attempt to answer it. What is the mass of one sheet of A4 paper? To find out, we need to understand the meaning of the size A4. As explained here in 2011, the A-series of paper sizes starts from A0 which is exactly one square metre in area.

The next size is A1 which is half of A0; followed by A2 (half of A1); then A3 (half of A2) and A4 (half of A3). The series continues that way up the smallest paper which is A10.

Clearly, A4 is a half of a half of a half of a half of a square metre. In other words, it is one-sixteenth of a square metre. Therefore, if the mass of A0 (one square metre) is 80 grammes, it turns out that the mass of one A4 photocopy paper is 80g divided by 16; that is, 5g.

We can test this quite easily. A rim of paper has 500 sheets. Therefore, it should weigh 5g x 500 = 2,500g = 2.5kg. I weighed such a rim and it came to exactly 2.5kg. Case closed!