Volume Line Up

Task 227 ... Years 2 - 10

Summary

This task provides experience with estimating, measuring, ordering and comparing volumes (capacities). It is offered to students as an invitation to explore and discover relationships likely to determine the volume of an object. Keeping notes of experiments and preparing a report are key elements that link the task to the work of a mathematician. The task represents the type of experience likely to make textbook exercises more meaningful.
 

Materials

  • At least 7 objects
    (The card says 7, but more may have been included.)
  • A container of rice
  • A measuring cup / medicine glass marked in millilitres

Content

  • estimating fractions
  • estimating number
  • estimating volume/capacity
  • measurement, area
  • measurement, length
  • measurement, perimeter
  • measurement, volume
  • recording mathematics
  • sorting, classifying, ordering
  • spatial perception, 2D or 3D
Volume Line Up

Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
   

Containers supplied with this task will vary from the photo depending on availability. However, the card questions are equally relevant regardless of the equipment included. Therefore we are not providing specific answers to the card questions.

What we would like to do is publish student reports which you get excited about, along with a photo of the equipment your students were using at the time.

  • What criteria do students use to decided most and least?
  • What criteria do they use to guess the order of the objects?
  • How does their guessed order relate to the resulted measured with rice ...water?
Where possible, some containers of the same height have been included. In these cases do the students come to any conclusion about the effect of base area if the height is constant?

Extension

  1. Choose three containers and use a small piece of masking tape to mark one third of the volume of each container. The top edge of the tape is used to mark the guess. Explain why you put the tape where you did.
    1. Find a way to check your estimate. How close where you?
    2. Can you check your estimate another way?
  2. The classroom is a container and its volume would normally be measured by cubes with 1 metre sides. Ask the students to estimate, then calculate the volume of the room.
  3. Students might like to explore a volume problem faced by engineers in industries which have to store toxic liquid chemicals, for example, oil, petroleum or raw materials to make paint. The problem is to contain the spread of the chemical in the event of the storage cylinder leaking

    One way to do this is to first dig a rectangular hole and then place the cylinders in it. If they leak the chemical is contained by the hole. Suppose a company has two cylinders each of which holds 1000 litres and they build them inside a rectangular hole. What could the dimensions of the hole be so that the worst case scenario of both cylinders simultaneously leaking all their fluid would be controlled by the flow into the rectangular hole?

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.
   

To convert this task to a whole class investigation you will need a set of containers for each group. If groups of three are used and each student is asked to bring two different containers no taller than (say) 7cm and no wider than (say) 7cm, then each group would have six containers to explore.

Look around the house and try to make your containers as interesting as possible. They have to able to have water poured into them.
Containers of rice are easy to make in advance for each group and medicine cups are easily obtainable. The card provides a clear direction for the lesson and the notes above offer an interesting and valuable extension. The report writing might be a little more imaginative than a written report. It could be a PowerPoint, poster, or video presented as a television news item or perhaps in the style of a children's science show.

An alterative whole class use is at task work station in unit of work on measurement. Related tasks could be Task 20, Pack The Box, Task 193, Surface Area With Tricubes, Task 226, Playing With Objects. Other volume and capacity activities can be found in most curriculum documents.These could be the basis of other work stations. You could also consider the whole class investigation section of Task 63, Fried Rice, which begins with a classic volume problem used in a Die Hard film and develops into an investigation in prime numbers.

At this stage, Volume Line Up does not have a matching lesson on Maths300, but Lesson 80, Cylinder Volumes, and Lesson 81, Biggest Volume, are related. Together with the tasks they could form the basis of a Mixed Media Unit.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
   

The Volume Line Up task is an integral part of:

  • MWA Chance & Measurement Years 5 & 6

Green Line
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