Describe the differences and similarities between volume and capacity, and apply the relationship between millilitres (mL) and cubic centimetres (cm3) to solve problems.
Solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another.
Demonstrate the volume of a prism or cylinder can be determined by multiplying the area of its base by its height, and apply this relationship to find the area of the base, volume, and height of prisms and cylinders when given two of the three measurements.
Whole-class discussion followed by group work and teacher-led demos.
Students should have previous experience with calculating the following:
Volume of a rectangular prism
Length, width, and height of an object if volume and two other measurements are known
Volume of an irregular object by having it displace a larger body of water
Time to fill a large object (e.g., tank) by calculating the time to fill a smaller object
Ask students the following: When there are a lot of people in the pool and they all get out, why doesn’t the water level drop?
If they do NOT realize it drops, pose the following question: What if this pool has no filters, drains, or anything like that? If there are 100 people in the pool, will the water level drop when they get out?
If they DO realize it drops, pose the following question: How much does the water level drop?
Ask the students to consider the following:
Can the problem be solved by looking at it as a Fermi (a question or problem that is difficult to solve with direct measurements and requires accurate estimation)?
What kind of information do we need to solve this problem? See Appendix for calculations.
The dimensions and volume of an average-sized (or Olympic-sized) swimming pool
The volume of an average person
Have students work in groups to provide an estimate for how much the water level will drop. Instruct them to show their work on the chart paper and decide if this change in water level is noticeable.
Fill the large fish tank with water and demonstrate the SMALL water level rise when the people are added. Try again with the small plastic bin.
Emphasize that small changes to one dimension of a rectangular prism can lead to a HUGE difference in volume. Compared to the small volume of these people, the difference is even larger.
Do students recognize that the greater the volume of water, the larger the object(s) must be to create a noticeable rise in water level?
Students can choose simpler or more difficult numbers depending on their comfort level. For example:
Estimate the volume of an average person as 70L vs. 73L
Considering the volume of adults AND children in the pool (70L for an adult, 35L for a child), as well as the number of adults and children in the pool (possibly 50:50, 65:35, etc.)
Students can be asked the following: How many people would it actually take to make the drop in water level visible? They will need to determine what a “visible” drop would be and solve this problem in a different order.
Students can take their thinking further. For example, If we took all the fish out of the ocean, how much would the water level drop?