This month we are working on classifying quadrilaterals. Creating these overlapping hierarchies is always a challenge. Relationships that work one way, don’t work the other way, and there is a lot of specific vocabulary that needs to be learned and applied in novel situations.
It’s a little like this: everyone who lives in Olympia lives in Washington, but not everyone who lives in Washington lives in Olympia. Bringing it back to the shapes – all squares are rectangles, but not all rectangles are squares.
To do this work, we need to know the defining characteristics of the quadrilaterals that we are classifying – and here we run into yet another difficulty… mathematicians don’t always agree on these! But the work of classification goes on. We just learn the specific characteristics and create the relationships accordingly. Here is a table that tries to communicate these overlapping relationships.
Under the inclusive definition of trapezoids, all six shapes a the top of this post are trapezoids, under the exclusive definition only three of them are… can you spot them?
We were playing this game in math class today called “I have, You need” during which the number ninety-ten came to my attention.
The game is pretty simple – one person thinks of a number between 1 and 99 and the other person comes up with the number that will add to that number to make 100. Warming up we start with numbers like 30, 45, 75 etc. Then we move on to more difficult numbers like 37. Many students will think first that 73 is the matching pair. This is because they want to make 100 and they know that 30 and 70 go together. When I explained ninety-ten, the problem became much easier. They were now trying to make nine tens, so 63 was immediately identified.
Sometimes we need to think about numbers a little differently. From place value to working from left to right, there is much more freedom in math than we’ve been led to believe. Create something new!