Tuesday, December 4, 2018

Alijah is trying to mark the height of an aquarium. She also wants to mark different heights of the aquarium to ensure it holds enough water for her fish. She knows that when it is full, it holds 24 litres of water. She also knows that the base is 30 cm wide and 40 cm long.
(a) Find the height of Alijah’s aquarium.
(b) Using a piece of string, how can Alijah mark the heights when the aquarium is ¼, ½ and ¾ full?

Solution and Discussion:

This is a fairly typical fifth or sixth grade volume decomposition problem. It involves several concepts and skills:
● Conversion from cm to cubic cm to litre, and back again. 1 L = 1 000 cubic cm
● Area x height = volume, and the relationship of straight, square, and cubic units
● Understanding of volume as a part-part-part-whole problem, that is, length x width x height =        ghjkvolume, and any decomposition of that
● Measurements and fractions of measurements

(b) Alijah can place a piece of string from the base to the top of the aquarium. She can then fold the string in half to find the ½ full mark. Repeating the process again she can mark the ¼ full mark. Finally, by placing the ¼ length string at the ½ way mark, she can find the ¾ full mark.