Root 2

The other day, I posted this Vine:  

[Note: I just started using Vine last week.  I know I'm late to the party with Vine but it's not too late to state that it's an awesome way for students to document and share their ideas and creations.  Doesn't require any video editing skills.  Just a steady(ish) hand and a smartphone or tablet]

Root 2

You can figure out the relationships between the green, white, yellow, red and grey rods from the Vine using a bit of geometry.  Its a nice exercise that really makes you realize how smart the inventors of K'NEX were.  It also becomes obvious why I titled the Vine 'Root 2'.

There are actually hundreds of math questions that you can generate from the Vine.  Questions involving shapes, proportion, angles, colours, similarity, scale, pattern recognition, length, measurement, area, parallel and perpendicular lines, special triangles, manipulating root expressions, polar coordinates and more.  These topics cover every grade and even some university stuff.  K'NEX is a great tool for teaching a wide variety of math to students of any level or ability.  I can't believe I didn't use it for one of my lesson or unit planning assignments for OISE.

Extend...

Once you figure out the relationships between the lengths of the rods, you can start to ask some more interesting questions.  For example:

• What lengths can be made by combining the pieces and what lengths can't be made
• Is it possible to construct a 3-4-5 triangle with K'NEX?  The math gets interesting because you have to mix rational and irrational numbers.  
• How about this question: Is there a piece or combination of pieces that will perfectly join two opposite corners of this cube (below)?  Prove it.  With math.  Even if you had a piece that was the correct length, would you be able to connect it? 

Answers and more K'NEX to come...