 # Displacement in large volumes of water

#### Curriculum Goals

• Estimate and calculate the surface area and volume of triangular and rectangular prisms
• Convert large and small metric units (e.g., metres to centimetres, kilograms to grams, litres to millilitres)

#### Context

Students can already calculate the following:

• volume of a rectangular prism
• length, width, and height of an object if volume and two other measurements are known
• calculate the volume of an irregular object by having it displace a larger body of water
• calculate the time it will take to fill a large object (e.g. tank) by calculating the time it takes to fill a smaller object

#### Goal

Understand that displacement in large volumes of water is difficult to visually identify, but does occur, regardless of the object’s size.

#### Materials

• Large tank filled with water and many small, sinkable objects (representing bodies in a swimming pool)
• Large pieces of paper for group work
• Pencils #### Lesson

##### 1. Introduction

Ask the students, “When there are a lot of people in the pool and they all get out, why doesn’t the water level drop?”

##### 2. Anticipate students’ responses:
• filters, drains, etc.
• It drops, but you cannot see it
##### If they do NOT realize it drops

Pose the following question: What if this pool has no filters or drains or anything like that? If there are 100 people in the pool, will the water level drop when they get out?”

##### 3. If they DO realize it drops

Pose the following question: “How much does the water level drop?”

• 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 estimations
• What kind of information do we need to solve this problem?
• The dimensions of an average sized (or Olympic-sized) swimming pool
• The volume of an average person
• See Appendix for these calculations
##### 5. Consolidate student thinking

As individuals, pairs, or small groups, ask the students to come up with a good estimate for this problem. They should use the large paper to show their thinking.

##### 6. Closure (or next class)
1. Have each group explain the thinking behind their solution
2. Ask the students, “Is this (the increase in water level) a noticeable increase? If all 100 people got out of the pool at the same time, would you be able to see a difference in water level?
3. As a final demonstration, use the large fish tank filled with water and the small plastic people to demonstrate the SMALL water level rise when the people are added – show again with a small plastic bin compared to the large fish tank
4. These rectangular prisms may not look like they are that different in size, but there is a HUGE difference in the amount of water that they each hold. Compared to the small volume of these people, the difference is even larger.
5. The larger the volume of water, the larger the object(s) must be to create a noticeable rise in water level!

#### Extensions:

Students can choose more difficult or simpler numbers depending on their comfort level, for example:

• Estimating that the volume of an average person is 70L versus 73L
• Choosing to include the average volume of both adults AND children in the pool (70L for an adult, 35L for a child) and the number of adults versus children in the pool (possibly 50:50, 65:35, etc.)

Students who need more of a challenge can be asked, How many people would it actually take to make the drop in water level visible to us?” These students will need to determine what a “visible” drop in water level would be and solve this problem in a different order to determine the number of people, rather than the measurement of the water drop

Students can also choose to simply answer the question, or take their thinking further in relation to this problem. For example, “If we took all of the fish out of the ocean, how much would the water level drop?”