Developing Perimeter

I recently was in a grade 3 class and tried this activity with them to help them understand that perimeter is the sum of all the sides of a shape. To help with this, I cut five lengths from stir sticks with these measurements:

3cm, 4cm, 4cm, 5cm, 8cm

I used stir sticks as I wanted something thin so the students focus on the length of the segment and not its width (or even height). I also wanted to see how well these students were meeting the overall expectation: 'estimate, measure and record length, perimeter... using standard units'.

I started by asking the students to order the sticks from shortest to longest:

I then asked them to pick up the longest stick and asked them to estimate how many centimetres it was. I would say that about half the class had a reasonable estimate. To help them refine their answer, I gave them two benchmarks: firstly, that the width of their finger is about a centimetre; and secondly I held up a ruler and showed them what 10cm looked like. This helped all students refine their estimates and was worthwhile doing.
Then, each student was given a ruler and asked to measure and record the lengths of the five sticks. What particularly impressed me with this class was that every student used the ruler correctly i.e. by lining up the zero on the ruler with one end of the stick. It was clear that there teacher has done some fantastic work on this already.
I asked the students to round their  measurements to the closest centimetre (which helped cover the fact that sometimes my cutting was not as accurate as it should have been!)

I then set the students a challenge: 

Create as many triangles as you can using only three sticks and find the perimeter of each triangle.

Before they did this, I demonstrated (using longer sticks) how I wanted them to carefully place the sticks end-to-end.
For the next fifteen minutes, they worked really well on finding as many triangle as possible. I was really impressed as to how much care they took in putting the sticks end-to-end and also how well they recorded their results.

I had carefully chosen the lengths of the sticks to limit the number of possible triangles as well as to create situations where a triangle was impossible. When I realised that they have pretty much found all the possibilities, we recorded our results as a group. As I wrote these down, some students were able to explain why one triangle had the largest perimeter and another had the least perimeter. Some also made the point that some sticks didn't form a triangle so I gave them some time to think about why this was:

This is getting at a big math concept which I think often is not mentioned: the triangle inequality i.e. that two sides of a triangle always sum to more than the third side. Having the sticks in front of them made it easier for me to show them why this is true.
Now some students had earlier tried using four sticks to create a triangle so I gave them one final challenge: 

Create a rectangle with all five sticks and find its perimeter.

Most were able to do this but in the future, I would make it more accessible by asking them to create any shape using all five sticks and to work out its perimeter.

I was really pleased how well the students took to this. It is so important that they have this CONCRETE understanding of what perimeter is before they move on to more diagrammatic and abstract questions and, hopefully, will help them avoid misconceptions as outlined in this earlier post.