Comparing capacities

Note: Volume is the measure of space taken up by a three-dimensional object. The space within a container is known as its capacity. As the thickness of many containers is negligible, it has become acceptable to refer to the space inside as volume too. You might frame the purpose for finding capacity within a context that is relevant to your students' interests, cultural backgrounds, and to learning from other curriculum areas.

1. Put out two of the cut-down water bottles, a distance apart. Discuss the capacities of the containers. Look for students to directly compare the containers by bringing them together and comparing heights. Some students might raise the possibility that the width of the container might also be important.
   I am thirsty. Which container will hold the most water?
   How do you know the taller container holds the most water?
   Is it always true that tall containers hold more than short containers? 
    
2. Compare the capacities of the two cut-down water bottles with the third bottle, and ask the students to order the three containers by capacity.
   Why do you think these containers hold different amounts of water?
   Let’s check to see if we are right by pouring water from one container to another.
    
3. Fill the largest container. Ask a student to pour from the largest container to the next largest.
   What should happen if you are right?
   Students should say that the second container will get filled and there will be water left over. Follow similar steps to check the middle container holds more than the smallest container.
    
4. Compare the three containers with the same height but different cross-sectional areas. Begin with two containers then progress to ordering all three. Pour from one container to another to check that the order created by visual comparison matches the true order.          
   Why is it that these containers are the same height but hold different amounts of water?

• Look for students to comment that the cross-sections are different. Wide containers hold more than narrow containers.
   

5. Carry out ordering with the three containers that vary by both height and cross-section. Let students order the containers by perception and explain the order they choose. Look for them to consider both height and cross-sectional area.

• Pour between containers to confirm the order by capacity.
  What advice would you give someone who is trying to find out which container holds the most?
• Students might come up with an algorithm for comparing containers by capacity. If the cross-sections have similar area, then the height predicts the capacity. If one container, has a greater cross-section but heights are similar them width predicts the capacity order. If both height and cross section are different, then they need to be balanced to order the containers. A tall container may not hold the most, nor a wide container.

Next steps

1. Provide students with experiences where the containers are not cylindrical. Household containers such as shampoo bottles and fruit juice bottles come in a variety of shapes. Give the students as much experience as possible with predicting the capacity order then comparing the containers by pouring from one to another.
    
2. Look at the measurements on containers. 
   Discuss the size of a 1 litre bottle and how millilitres relate to litres (1000 mL = 1 L).
   Record the capacities of containers using metric units. Increase students’ estimation strategies, especially related to benchmarks like 500 mL. Provide opportunities for students to explore these capacities using a variety of actions and expressions.
   Pour water from the containers into a measuring jug or cylinder and read the capacities on the measurement scale.