The volume of a bathtub

Curriculum Goals

Grade 6 – Measurement

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

Context

  • Students understand how to calculate the volume of a rectangular prism
  • Prior classroom experiences included measuring water volume inside differently-sized tanks

Goal:

  • Have students extend their thinking about volume by examining water displacement
  • Students will measure the volume of irregular-sized objects submerged in water

Materials

  • Clear tanks/bins (rectangular prisms)
  • Objects of a variety of sizes (that will sink)
  • Rulers
  • Dry-erase markers

Introduction

Activate students’ prior knowledge with an example of water displacement.

Ask the following:

  • How many people have ever taken a bath? What happens to the water in the bath tub when you get in or out of the bath? (The water level rises and falls)
  • Imagine I were to fill a bathtub up to the very brim, and then I get into the bath tub and I dunk myself completely under the water. What would happen to the water in the tub? (It would overflow)
  • Now imagine I could somehow collect every drop of water that spilled out of the bath tub. What would this amount of water be equal to? Have students discuss this question in pairs or small group, then come back together to share ideas

Lesson

  • Fill a clear tank about halfway with water
  • Pick an object to measure the volume of
  • With the students, measure the length, width, and depth of the water in the tank and calculate the volume of water
    • You can use the dry-erase markers to mark the water level of the outside of the tank
  • Drop the object into the tank of water and watch the water level rise – use a larger object to make sure students can clearly see the rise in water level
  • Ask students to think about how this information may be used to calculate the volume of the object. Discuss in pairs or small groups and then share all together
  • Students may see that calculating the volume of the object is possible by finding the difference between the water tank at time 1 (without the object) and time 2 (with the object)
  • Give groups of students or individual students clear tanks, shaped like rectangular prisms, and allow them to fill them with water about half way
  • Students’ task is to find different objects around the room and calculate volume
  • Instruct students to record all of their measurements to later share with the class

Closure

  • Bring students back together and share discoveries
  • Ensure student understanding through their examples