Thanks for your detailed info.


The question is from Math Olympiad for P3 and P4, as I mentioned in a followup message. The correct answer from the book indicates inclusion of 12 noon and 11pm. This confuses me and my child as well. I would like to suggest teachers 9especially those who create exam papers) to use something like \"from 12 noon to 11pm\" if the markers or boundaries are expected to be included.

mathsguru:

itro:

Hi,

I have a question on understanding \"between\" when it is used in Math questions. Sometimes, \"between An and B\" does not include A and B, but sometimes it does. When we say a number between 10 an 20, the number should not be 10 nor 20. Could you please advise whether I should include 12 noon and 11 o'clock at night when solving the following problem and why?

The grandfather's clock chimes once when it is 1 o'clock, chimes twice when it is 2 o'clock, chimes thrice when it is 3 o'clock and so forth. How many times will it chime between 12 noon and 11 o'clock at night?

Hi Itro,

In the above question, I would take it to exclude 12 noon and 11pm. So, actually, the question is asking for 1 + 2 + 3 + 4 + 5 + ... + 9 + 10.
It's testing students the summation of numbers. Answer should be 55 times.

I guess when the word \"between\" is used, we have to \"analyse\" and see if it's used figuratively or literally.

Figuratively when it's used to describe a scenario. For instance, share 100 marbles between A & B. A task is shared between 2 workers. In such cases, we usually divide the total by 2 (or according to how they portion the items/task). The word \"between\" is used for 2 people/items while the word \"among\" is used for more than 2 people/items.

Literally when it's used to indicate the no. of things/distance/intervals/etc between 2 objects/places/persons/markers/etc. Basically, we can \"literally\" count the no. of things/distance/intervals/etc which exist or are placed between the 2 objects/places/persons/markers/etc. Hence, it makes sense for us to not include the 2 objects/places/persons/markers/etc, unless the question specifically mentions so.

In the above question, it is the \"literal\" interpretation --> the no. of chimes between 12 noon and 11pm. 12 noon and 11 pm are used as markers and they should not be included.

As for Coffeecat's suggestion to include the chimes of 12 noon (which will logically still take place seconds after 12 noon), I think we can interpret it simply. This is because the question did not mention how long each chime will take, so I don't think the question is expecting us to go so deep into that level.

Just my 2 cent's worth based on my experience so far...


MathsGuru

Thanks for your kind reply. The question I quoted is from book \"Math Olympiad for beginner\" by Terry Chew, P25.


Your explanation sounds ok for me and it is probably the only reasonable explanation, but it may not be easy for a P3 pupil to understand.

Sometimes the usage is confusing. For example, \"between you and me\" definitely includes both you and me. But in Math, it does not include.

CoffeeCat:

Hmm this is an interesting but rare question so i will present my opinion. It will be cool if you can get back to us when you got the answer.
Ok yes usually between means not including A and B but notice that what is commonly dealt with are termed \"discrete\" or countable quantity.
Time on the other hand is what we called a continuous quantity.
Measurements like Mass, Weight all belong to continuous quantity.
When the clock chimes 12 times at 12 noon, it must take a few seconds to chime 12 times, so it doesn't make sense for us to define the time between 12noon and 11 o clock as starting only after the clock finishes its chimes.
So my guess is 12noon is included, probably because it is what we called a continuous quantity.
May i know where you get this question from?

Hi,


I have a question on understanding "between" when it is used in Math questions. Sometimes, "between An and B" does not include A and B, but sometimes it does. When we say a number between 10 an 20, the number should not be 10 nor 20. Could you please advise whether I should include 12 noon and 11 o’clock at night when solving the following problem and why?

The grandfather’s clock chimes once when it is 1 o’clock, chimes twice when it is 2 o’clock, chimes thrice when it is 3 o’clock and so forth. How many times will it chime between 12 noon and 11 o’clock at night?