Enriched Activities
20:30:00Sesame Street. Counting Bats [film]. Retrieved from www.sesamestreet.org
Congratulations on making it to October, everyone. Please enjoy this appropriately spooky, mathematical, and charmingly nostalgic gif of Sesame Street's Count.
Speaking of The Count (I love a good segue - this isn't one), how many possible responses can you count for answering this question:
WHICH ONE DOESN'T BELONG?
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| Bourassa, Isabella (2013).WODB Shapes [image]. Retrieved from http://wodb.ca/shapes.html |
My initial reaction was to conclude that there was one answer; it was obviously the star that did not belong, because it was the only shape that was not outlined in red.
However, this is hardly the case. There are quite a few ways one can approach this question, and my count for possible answers continues to increase, the longer I consider the image.
If you were to show students this image, they could provide a plethora of unique answers including
- The heart does not belong because it is the only shape with round sides
- The dodecagon does not belong because it is the only shape not filled with a solid colour
- The bottom left object does not belong because it is made up of more than one recognizable shape
- The star does not belong because it does not have an outline like the others
- The dodecagon does not belong because it has more than one line of symmetry
- The dodecagon does not belong because it cannot represent more than a simple shape, whereas the heart can represent love, the star can represent the cosmos/magic, the triangle-rectangle can represent a house, etc
The number of responses is endless because they are only limited by students' creativity. This activity is great for implementing differentiation in the classroom because each answer is as unique as the mind of each student.
Which One Doesn't Belong also provides opportunity for implementing Rich Math Tasks. A rich task generally is engaging, has a mathematical focus, is grounded in problem solving, provides opportunities for connections, is multi-representational, differentiable, and promotes a positive attitude. Engaging the class in a quick session of WODB helps to foster a rich-task mindset. It provides students with a positive environment in which they have the opportunity to share their different points of view and become accustomed to the fact that there is almost always more than one way to solve a Math problem.
This week we were challenged to explain how to solve the equation of 18x5.
For me, this was a matter of relating the equation to Mathematical components with which I was already familiar. Having worked in retail for several years, I am quite familiar with counting bills and quickly determining sums of money. I know my 20 times tables by heart, up to 50 (that's when you bundle the $20 and start over again - the bank doesn't like counting deposits with stacks over $1000). So I instantly felt comfortable solving 20x5, rather than 18x5. Since I knew that 20x5=100, I then had to subtract 5 twice, to account for the two 5 dollar bills that I didn't need in my 18x5 stack, leaving me with $90.
Or such was the monetary-themed process in my head.
But more simply, I solved 18x5 by converting it to (20x5)-(5+5). It could also be written as (20x5)-(5x2), and neither is more correct than the other, because DIFFERENTIATION IS GREAT.
Within my own method, there are multiple ways of looking at the process for arriving at 90. Within a classroom, there are countless unique methods for solving the equation. After lurking the forums, I found three other methods that I really liked.
A very popular approach was to solve (8x5) + (10x5). This method seems a lot cleaner on paper, and perhaps less convoluted than my method, but again, neither is more correct.
James mentioned that he solves 18x5 by doubling. He first determined that 18x10 = 180, and then divided the sum by 2, since 5 is half of 10, leading him to solve 180/2 = 90. This method would not work for me personally, but again, it is still just as correct as any other method, and goes to show how creative and varied others' approaches can be when solving the same equation.
A less popular, but very innovative way to solve 18x5 is to redistribute the numbers. Matt approached the equation by first reducing 18 to a smaller number (by dividing it by 2) and then solving (9x2)5, redistributing the brackets, to form 9(2x5)=9(10)=90. I had never even considered solving an equation this way, but I like how this method breaks everything down into single digits, which are for some reason far less intimidating than those spooky two-digiters.
When we provide our students with Rich Math Tasks, differentiation will be at the root of all problem solving. Students will have multiple ways to approach the problem and should be given opportunities to work collaboratively so that unique and creative approaches can be shared amongst peers. Once again, we are reminded that each of our students is unique, and in order to support these unique, young minds, we must offer Mathematics that reflects individual ways of seeing the world. Most importantly, we must remind our students that Math isn't rigid or set in stone.
2 comments
Hi Erika,
ReplyDeleteI agree that we must provide students with opportunities that reflect multiple ways of learning and understanding. I also like how you put emphasis on the fact that each student is unique. As teachers it is very important that we keep this in mind in order to help our students be successful.
Hi Erika,
ReplyDeleteI really enjoy the Which One Doesn't Belong math task! I didn't realize that there were so many possible answers. Do you think that there are even more if we look hard enough? I wonder. It's interesting to see how you initially determined WODB. I actually started with ruling out the heart as it was the only shape with curved edges. It's awesome to see how differently minds can work while they're doing math!
I like that you say that none of the 18x5 solutions are more correct than any of the others. I was intrigued when I looked at Matt's solution; I had forgotten that you could rearrange math equations like that. It was very innovative and makes me want to try using that strategy when the opportunity presents itself. The way my brain works with larger numbers is to break them down into more manageable numbers, usually by separating the ones and tens columns and then adding up the results. Now it's so clear to see that great minds don't necessarily think alike!