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Squares and Square Roots – Taking It Outside

September 25, 2012

One of the first math concepts we explored this year is square roots and their relationship to squares. Last year I tried to address this in the classroom through drawings and sketches on the board. While I think this was somewhat effective, this year we decided to combine the three classes of grade 8 students and take the learning outside to the field.

To start the lesson we had students divided into groups. Each group was given a number from one to eight and a position on the field. One team member from each group was asked to come forward for instructions and necessary materials for the task. Instructions were stated simply as:

1) Using 4 tent pegs and a metre stick create a square which has an area in square meters equal to your group number (e.g. Group one – 1 square metre, Group two – 2 square metres, etc.)

2) After outlining the square with the tent pegs determine the amount of string necessary to enclose your square.

3) The group leader can then obtain the exact amount of string and make the square. To make this a bit more of a challenge we asked them to consider the amount of string to tie a knot.

After about 10 minutes the first group came up to get the string. This was a little bit of a surprise as I thought the groups with perfect squares (1 and 4 square metres) would be completed much sooner. Debate however, occurred in each group and it was easy for the three teachers present to see students testing assumptions, questioning prior knowledge and misconceptions with a quick walk around each group.

Some of the highlights of this activity for me were

  • It emphasized the importance of understanding the problem. To my surprise one of the groups actually thought that 1 metre of string would enclose one square metre of space. The group assured me that they did not listen all that well to their group leader.
  • The importance of examining prior knowledge. Some students had misconceptions about area and perimeter.
  • How to work in groups. Determining the course of action among a group can be difficult at any age.
  • The relationship between area and side length of a square. Some students were able to figure out the side lengths especially those with areas which were perfect squares. Those with non-perfect square numbers found this a bit more difficult.
  • The importance of estimation and metal math. One group with an area of 3 square metres was sure that each side had to be 1.5 metres. They added the numbers rather than multiply. To their credit they realized the mistake.
  • Developing the relationship between squares and square roots. The week that has followed has allowed me many opportunities to draw upon this experience and I will admit students remember it much better than they did last year.
  • Place based learning works. Having completed this activity in a location outside of the math classroom gives me a chance to say, “do you remember when we were out on the field …”
  • Each square provided a referent for talking about square areas of measure. Students developing these referents are useful for later study. Many students did not realize the size of one square metre.
  • Combining classes provided a chance to further develop our grade 8 math learning community as a resource for each other over the course of the year.

Next year I would improve the lesson by nesting the areas so students have a better sense of the impact of doubling area on side length. I am sure that there are many other things that could have been done to improve the lesson. If you have ideas feel free to include them in the comments section below.

3 Comments leave one →
  1. September 26, 2012 8:33 am

    Wow… I like it 🙂 a challenging task — I’d have considered starting with perfect squares amounts for those predictable misconceptions about area and perimeter. Good point about “place based learning,” too.

    • September 26, 2012 10:09 pm


      Let me know if you try it. I am sure there are some things that will make it go even better. ALways nice to get some refinements.


  1. Squares – Conceptual Understanding of Square Roots | Math in the Middle

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