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?

To help visualise, the children had access to cubic cm:

**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?

**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.

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