Measurement

Minds On

This week we began our class with a minds on activity called "I have... who has?"
We have played this game as class before for a colleague's presentation, so we were all familiar with the expectations before we had even begun. We knew we would all need to be paying attention and we had the chance to collaborate as a table to make sure we all understood our mathematical terms before we began!

I think this is an excellent way to begin a lesson as it is a good way to ensure student's are familiar with terms and gives them a chance to activate prior knowledge. I can definitely see the advantages of using it in a music classroom to reinforce that students are familiar with important musical symbols!

Here is a resource I found with various pre-made decks! I have.. who has?

Of course, with pre-made resources, you will need to make sure that the terminology is being used properly and that it is relevant to what you are teaching!

A disadvantage to this game is that the students whose cards come up first may quickly lose interest as they no longer have an incentive for paying attention. Once a student has answered once, they could pick up a second or third card to make sure they have a motive to stay engaged. Because our group was working collaboratively, as were many others, I noticed we did not do this. We made sure to pay attention to help our classmates not miss their opportunity to answer!

Activities

Next we worked together in pairs on a quest to find shapes with the same perimeter, but a difference in area of 6. Pat suggested that we track our attempts in a column to see what we could learn from them.

We were fairly lucky in discovering a solution that worked right off the top, but then we struggled to find another solution. We did notice that odd numbers would not work but I couldn't find any clear formula in my head as to why some of my attempts were working and some were not!

On page 502 of Making Math Meaningful the writer states that students are often surprised to discover that shapes with the same area can have different perimeters. By creating different rectangular shapes and comparing their area and perimeters, students may discover that " the perimeter of a shape increases as the are is stretched out and decreases as the parts are pushed together or become more like a circle."

My favourite part of each chapter is always the common errors and misconceptions students may have. I think this is such an important resource to consult because we can prepare prior to a lesson how to avoid these common mistakes with our students and ensure a deep understanding of material through practice.

Guided Inquiry 

The next activity we moved into was a guided inquiry activity where we helped to produce giant metal columns for our school.


We used paper rolls as our models, knowing that the actual columns would 10 times the size (the ratio given was 1:10). We were given stamps, string, scissors and a ruler to help us in our quest to determine the surface area and perimeter of the cylinder.

I remember being surprised when I was younger to discover how many shapes are so alike. When you unroll a cylinder you can easily see why you are using the formula you do to determine it's surface area. The circumference x height is essentially the same as length x width used to find the surface area of a parallelogram. By having students cut open the cone into a diamond they can then contextualize why the formula was developed and this gives them a deeper relational understanding that they can fall back on when trying to retrieve this formula in the future.

This is the magic of inquiry based discovery. Even though a concept may be challenging, giving students a chance to explore and reason how to complete a problem means that there will be greater consolidation (hopefully) of the concepts that they are hoping to learn in class! This is especially true if the problem is well developed, Pat is always careful to point out to us why she uses the examples and numbers that she does when creating her problems.