## Thursday, 28 April 2016

### Open-Ended Tasks: Volume of Cuboids / Rectangular Prisms

Open-ended tasks are a great way to differentiate learning and provoke deep thinking.

They are also a wonderful way for children to deep or formulate new understandings of a maths concept.

Good open-ended tasks generate a natural state of enquiry and student-driven theories which they test out for themselves. They challenge each child at a level that they are comfortable with to expand upon.

Additionally, every child is made to feel successful provided they know they put in their best effort.

Today, two open-ended tasks were presented for the children to select from which I found in this brilliant book which I highly recommend every primary teacher has:

We used the think-pair-share routine and after sharing our ideas together, wrote and shared our reflections on patterns or types of thinking we found interesting from the learning experience.

Open-Ended 1:

The end of a rectangular prism looks like this.

What might the volume of the box be?

Discoveries shared:

° the base area of a prism plays a really important role in measuring the volume

° a pattern of multiples of 6 existed

° some had created and tested their own theories seeing if they changed the base area, would other multiple patterns exist- they do!

° This could go infinitely.

Open-Ended 2:

How many possible volumes for this shape can you think of?

Visualising option, creating strategies and theories to test out:

Discoveries shared:

° There are SOOOOO many possibilities.

° I had a theory that is if just add 1 to each dimension, a pattern will form. It did- so then a tested by adding 6 to all the dimensions and found a different pattern.

° I decided to measure its volume using cubic cm and then in cubic mm. I thought there might be a connection, but I couldn't see one.

° There are quite a few different strategies to measure the volume.

Doing open-ended tasks allow for a much broader range and depth of thinking parameters that typical question-answer maths learning can never achieve.