This is a level 4 measurement strand activity from the Figure It Out series.
A PDF of the student activity is included.
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solve problems involving mass and volume
calculator, ruler
access to a bath
FIO, Level 4, Measurement, Book One, Weighty Water, pages 12-13
The previous activity was designed to help students gain a sense of area, measured in hectares. This activity is designed to give them a feel for volumes and the mass of water. It also reinforces the processes for calculating volume and mass.
The students need to be given time to find out the volume of a (standard) bath. This could be done as a home activity the night before. Given that any bath has a sculpted shape, this involves rather more than simply finding the bath’s external dimensions. The students could be challenged to come up with a method and asked to report back next day on both the volume and the method used to estimate it. Clarify the fact that in this case, we are using the bath simply as a unit of measurement, so they are to imagine it filled to the rim.
Students who come from homes where the bath is a corner bath or a spa bath can still find its volume, but when they do question 1, they should use the approximate volume of a standard bath, as worked out by their classmates.
Two ways of estimating the volume of a bath are:
The vital connections here should be learned by heart and never forgotten:
These relationships are so precise and convenient because the metric system was designed to be simple and sensible.
Question 2 asks the students to make a comparison between the mass of the water in the waterbed and the mass of a car. It is surprisingly difficult to find the mass of cars, but the Internet is a useful resource. Question 3 applies the same principles of volume and mass to a larger situation.
Question 4 is a more complex scenario, involving rates, and you should work through it before giving it to your students so that you are familiar with the issues. One approach to part a is as follows:
Social Studies
Students could investigate the legal and moral responsibilities of the owner of the leaky pool, along with a consideration of good neighbour protocols. Newspapers and consumer advocate television programmes often have stories about such issues involving neighbours.
Demonstrate knowledge and understandings of:
1. Answers will vary, taking into account the shape of the bath. A reasonable estimate for a standard bath, filled 3 times, is 700–800 L.
The internal volume of the bath in cubic metres can be estimated by multiplying average length, breadth, and depth. The following measurements are typical
for a standard bath: 0.585 x 1.4 x 0.32 = 0.26 m3
(approximately 1/4 m3 ).
There are 1 000 litres in 1 cubic metre, so 0.26 m3 = 260 L. 3 x 260 = 780 L
2. a. Answers will depend on the answer given to question 1.
1 litre of water has a mass of 1 kg. 780 L has a mass of 780 kg. That is 0.78 tonne (just over tonne).
b. 0.78 tonne is similar to the mass of a small car (or a large bull or 20 bags of cement).
3. a. 8 x 20 x 1.2 = 192 m3
b. The mass of the water is 192 tonnes.
c. If the pool were to burst, the force of the water could cause serious damage to the property below. Even if this did not happen, the seepage of so much water could undermine the foundations of the neighbours’ house.
4. a. 1 280 L. (0.8 x 800 x 2 000 ÷ 1 000. The water is falling 0.8 cm per day. The dimensions of the pool have been converted to centimetres. )
b. 112 days (rounded up). (89 ÷ 0.8 = 111.25)
c. Answers will vary.
Possible reasons for increased time include:
A possible reason for decreased time is that the crack in the pool may get bigger, leading to a greater rate of flow.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/weighty-water at 10:31pm on the 26th February 2024