Project Day: Visualizing in Math!

One thing that I have noticed over my many many many years of teaching is that some things that seem so obvious to many of us are NOT obvious to some students–especially struggling ones.  We have worked over the years to get students better at visualizing when they read (“See it like a movie in your mind!”) because that is not natural or innate for some kids.

I also believe strongly that we must be explicitly teaching students how to visualize in math–whether that be imagining in their minds the actions in a word problem (“If Cara has 24 candies and she shares them with 2 other friends–what does that look like in your mind?”) or visualizing situations to check for reasonableness (“If you know that a ruler is 1 foot long, is it reasonable that our classroom door is 8 of those tall?”) or with more spatial topics such as geometry or fractions–we have to help students become more aware of how important visualizing is.

To have a little fun with it, I had the kids do a fun mosaic project.  I told the students that their job was to try to keep in their mind what they THOUGHT the project was going to turn out like as they were working and to adjust their thinking as their work unfolded.

It started with me introducing the word “quadrant” and modeling how I used 1 inch squares of paper to create a design in the upper left quadrant.  I talked as I worked and explained how being able to “see” math and patterns can be so helpful as the math gets harder through the years.  They offered me suggestions as to what colors would be interesting (I used all winter colors–though last year I blogged about this project and used fall colors and focused more on the symmetry aspect of the project).  Click here to see a slide show of last year’s project and how it unfolded…

Sorry for blurry photos…UGH.  I need to slow down!
After creating the first quadrant, I asked the students to imagine in their minds what my design would look like if I could “flip” (then introduced the word “reflect”) over the line.  I clarified by explaining that I meant that the square next to the line would flip right over and be right next door.  We talked about my design as I quickly build the second quadrant.  
NOTE:  Because I couldn’t very well take photos of my own work, I tried to grab a few shots of the students as they built theirs…
What next?  Of course!  Trying to imagine the final square once the top two quadrants are reflected over the axis.  Students were chatting like crazy about what designs were going to form and so on…I heard comments like “I think the purple part is going to reflect and make a square in the middle.” and “Hey–my diagonals turned into a square at the end!” so they really were working to notice what was happening visually.  

They had a great time, and I can’t wait to hang these up from our clips this week!  I did make the copies of the grid paper on cardstock to give the a little more weight–but I think they will winterize our room quite nicely!  I will be referring back to “visualizing” a TON as we move into our fraction unit next.  Have a great Sunday!