Describe the differences and similarities between volume and capacity, and apply the relationship between millilitres (mL) and cubic centimetres (cm^{3}) to solve problems.

Solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another.

Show that 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.

Context

Whole-class discussion followed by teacher-led demonstrations and group work.

Students should have prior experience 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 about their prior knowledge of water displacement:

What happens to the water in a bathtub when you get in/out?

Imagine I was to get into a bathtub filled to the very brim and dunk myself completely under the water. What would happen to the water in the tub?

Now imagine I could somehow collect every drop of water that spilled out of the bathtub. What would this amount of water be equal to? Have students discuss this question in pairs and then come back together to share ideas.

Fill a clear tank halfway with water. With the students, measure the length, width, and depth of the water in the tank and calculate its volume.

Mark the water level outside of the tank with a dry-erase marker.

Pick an object to measure its volume and drop it into the tank. Watch the water level rise.

Emphasize that small changes to one dimension of a rectangular prism can lead to a HUGE difference in volume.

Ask students to think about how this information may be used to calculate the volume of the object. Have students discuss in pairs and then return to share ideas.

Students will recognize that the volume of the item being placed in the water is equal to the volume of the water being displaced by the object.

When students are in pairs, give them clear tanks and allow them to repeat the demonstration on their own with different objects around the room.

Bring students back together to share discoveries and check their understanding through their examples.

Ask students: 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 students to consider what information they need to solve this problem (e.g., 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 (see Appendix for calculations). Instruct them to show their work on the chart paper and decide if this change in water level is noticeable.

Look Fors

Are students able to calculate the volume of the rectangular prism?

How are students expressing their understanding of displacement? Are students able to explain the relationship between the volume of the water displaced and the volume of the item being placed in the water?

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?

Extension

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. You can ask: If we took all the fish out of the ocean, how much would the water level drop?