Seizing Symmetry

This week our exploration of the study of shapes continued.   The students enjoyed playing with mirrors and pattern blocks to explore and understand symmetry.   Very soon into building designs my students realized that the designs they created could have more than one line of symmetry.

On Friday I asked my students to build designs with pattern blocks and then asked "How many lines of symmetry are possible in a design?" I received numerous responses from one to two, four and six.  Next I modelled for my class how to capture a design using an iPad App called Skitch that allows users to annotate images using text, colour, and lines.

I was truly amazed with what happened next...  as the students discovered the lines of symmetry in their designs, outstanding inquiry questions began to arise such as...

"I wonder if it is possible for a design to only have three lines of symmetry?"

"I wonder if this point in the middle creates the symmetry?"

"I wonder if I could draw tons of lines through the middle point --- making lots of lines of symmetry?"

Below are some of the annotated images.

Listening to the children's questions, I knew that they were ready to be introduced to the concept of rotational symmetry also sometimes referred to as point symmetry.  I pulled them together around one of the designs and asked them to tell me more about what they were noticing about the middle point.   The child who intially had commented about the importance of the middle point offered his thoughts on why he felt this point was important.  He then stood up and went and got his ruler and showed how he could make a line going through any part of the centre point to create a line of symmetry.   I highlighted his "big mathematical thinking" and then explained and discussed rotational/point symmetry.  I was impressed with the vast number of children who truly understood.  Division Five has many budding mathematicians!

Shapes in Our World

Our school recently purchased ten iPad Minis and ten more are set to arrive any day. As an educator and mother of two, I have seen first hand how excited and motivated children are to use the iPads.  

Although I am a firm believer that students in the second decade of the 21st century should be using technology, as an educator I feel that it is our responsibility to ensure that our students are doing so meaningfully and with purpose.  First and foremost student learning should drive how we evaluate and choose the technology appropriate for lesson(s).  I find myself most excited about the ability to use creative apps to transform and enhance my students mathematical understandings.  

For example, in the past when I have taught Geometry, my class and I have always adventured on "Shape Hunts" to discover the shapes in our environment.  It is important for students to understand that mathematics is a study that is deeply connected to the real world and that shapes are a foundational part of this.  Previously the students and I would explore the school and neighbourhood using clipboards, pencils, and paper.  Often I was unsure exactly what my students had seen due to the difficulty of drawing a 3-D shape or because many of my students are English Language Learners and do not have the vocabulary to explain all of the shapes/items they see.

The app ExplainEverything allowed my students to break through these barriers.   With the click of a button they were able to take photos of the shapes they saw.  Furthermore, they could sort and classify these shapes as they created digital videos.   I believe that when technology alters and strengthens student experiences, powerful learning and understanding is the result.    

Additionally, as a teacher I can see firsthand what my students know and use this (formative assessment) to inform my future lessons.  Through the student samples I realized that many of my students need further lessons with 3-D shapes as not many 3-D shapes were identified and the few that were captured were identified incorrectly.   

Division 5 hopes you enjoy their videos below.