Purposeful Play In Math

 

When we think of using play in the classroom, we automatically think about the elementary classrooms since that is where most of it seems to happen.  That may be because much of the research shows that student learn well when using play in the early years to develop literacy and numeracy skills. In addition, students tend to be more involved when they are able to "play" as a way of finding solutions to problems on their own. 

Furthermore, play can help students use the creative part of the brain to come up with solutions to problems and they can discover new concepts and ideas at the same time.  In addition, integrating play into the classroom motivates students to want to learn math because it's fun and they are then engaged.  

One of the all round toys to use in all grades from kindergarten to twelfth is Legos.  Legos can be used to build things while letting students learn more about math skills.  I've seen fractions taught using different sizes to represent fractions such as the block that is 2 by 4 is designated the whole, a 2 by 2 is considered a half, the 1 by 2 represents a fourth, and a one by one is the visual for an eighth but this way tends to restrict the fractions that can actually be used.  

A different way of using Legos is to use different colored blocks to show the fractions.  For instance, if you want to show 3/5, you would have say one blue 2 x 4 block, a other blue 1 by 4 block and one red 2 by 4 block so that you have 5 rows of blocks and 3 are shown in one color to represent the 3/5th's.  This method of representation allows students to find ways of showing more fractions with many different denominators.  It also opens the way for a discussion of 2/5th being needed to make a whole. 

Legos blocks can also be used to help students visualize prime numbers.  If we think of the numbers representing the total area and the factors as the sides, we arrange the factors to create either rectangles or squares.  If the number is prime, there is only one way to arrange the legos into a rectangular shape and that is 1 by the number.  Composite numbers can be arranged in more than one way.  An example would be 8 where it can be arranged as 8 by 1, and 4 by 2.  

These blocks can also be used for questions like how many ways can you get an area of 64 feet squared, or  what is the biggest area you can get from using a certain number of blocks.  In addition, students can figure out the perimeter of visuals such as the perimeter of a rectangle that is 4 by 2. The same exercise can be used with students to work on their multiplication tables since multiplication is represented using the area shape.  

Speaking of multiplication, if you designate the 2 by 1 as X and the single 1 by 1's as ones, you can show binomial multiplication or use the 2 by 2 to represent X^2 and create trinomials for students to factor using a square.  

Finally for geometry, they can use Legos to create three dimensional shapes for geometry so students can work on volume and surface area of rectangular prisms, and cubes. 

I've discovered that middle school and high school students don't mind using Legos to create visuals of the concepts because they don't see these as manipulatives, especially if you allow them to build what they want at the end.  Let me know what you think, I'd love to hear.  Have a great day.