Mr Gan ordered 45 pots of plants to decorate the corridor for a school concert. They were to be placed in a straight row from one end to the other end of the corridor at an equal spacing of 1.2m apart.
On the day of the concert, Mr Gan was short of 11 pots of plants. As a result, the remaining pots of plants had to be placed from one end to the other end of the corridor at a new equal spacing.
What was the new spacing between the 2 pots of plants?
How would you interpret the the underlined phrase above (“short of 11 pots of plants“)?
We found that most students would interpret it as either one of the two scenarios below-
There was some initial miscalculation on Mr Gan’s part and he ordered 11 pots less than what he should. With this train of thought, the student will deduce that 45 + 11 = 56 pots of plants were actually needed to make up the length of the corridor with a spacing of 1.2m between them. The answer derived from this scenario will be 1.5m (new spacing between 2 pots of plants) based on the following workings.
Number of spaces between 56 pots of plants
= 56 – 1 = 55
Length of corridor = 55 x 1.2m = 66m
With only 45 pots of plants, there would be 44 spaces between them.
New spacing = Length of corridor ÷ 44 spaces = 66m ÷ 44 = 1.5m
45 pots of plants were needed to make up the length of the corridor with a spacing of 1.2m between them. Something went wrong with the delivery of the plants, so only 45 – 11 = 34 pots of plants were delivered. The new spacing calculated will then be 1.6m, which is actually the “correct” answer provided by the school.
Number of spaces between 45 pots of plants
= 45 – 1 = 44
Length of corridor = 44 x 1.2m = 52.8m
With only 34 pots of plants, there would be 33 spaces between them.
New spacing = Length of corridor ÷ 33 spaces = 52.8m ÷ 33 = 1.6m
Another issue with this question is that students had to make a presumption that the pots take up negligible space/length, which is not true.
How do you feel about this question? Do you think it can be better phrased to prevent any misunderstanding by students?
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