Sunday, March 4, 2012

Geometry in Grade 7!

YESSSS! I am excited, because soon I will get to introduce basic Geometry to my 7th-graders! yay. I've never done this before. I have some ideas based on having taught Grade 9 Geometry a few times now, but how to translate that to the correct middle-school level and to meet my students' interests and spatial understanding is never quite so straight forward.

Here are my ideas so far. I'd love to hear what you think!

* I am going to start with introducing the idea of non-square quadrilaterals. I found and modified a nifty activity that asks students to find as many different quadrilaterals as possible within a 2-by-2 grid. I will start with that, to encourage them to think of Geometry as a discipline of math that requires creative thinking. Following coming up with their own quadrilaterals, they will be introduced to the idea of area being "counting the squares contained" and be asked to find as many areas as they can, for those quadrilaterals. I want the first day to just be a day to gauge their creativity and problem-solving, and if some of them manage to come up with some cool (insightful) area reasoning, I will have kids share them with the class.

* Then, we will move on to area of triangles. Typically I introduce this concept to my 9th-graders by letting them play with the Geoboard, so this year I will do the same for my 7th-graders. They will build triangles within rectangles, to see why area is always 1/2 of the rectangle. From there, we will discuss shearing of triangles (using hands-on cutting/pasting of strips of area), in order to understand how to construct a "nice" triangle that has equivalent area to a sheared triangle. They will then do some triangle mixed practice.

* Then, we will talk about Pythagorean Theorem from a historical perspective, because Pythagorus was such a badass cult leader! Following which, they'll obviously need some mixed practice for a few days, blah blah.

* Based on how the kids do with these introductory topics, I will decide where to go next... I think in the standard Grade 7 curriculum at the school, they just have to be able to do basic area and perimeter, so we'll almost certainly have to cover circles to some extent. (I am less excited about this, as you can tell, because I still need to think about how to teach the formulas not-so-rotely.) But to me, I don't really see why they cannot start working on composite areas relatively soon after that! OR to jump ahead to doing some fun visualization exercises in the 3-D space. :)

* For extra hands-on fun, I am definitely planning to have my students use toothpicks and marshmallows to build tetrahedrons and cubes, to explore/explain why triangular structures are used commonly by architects! Maybe they can even build a toothpick bridge as a nearing-end-of-year project...

Do you have any killer ideas for introductory Geometry activities that are good for 7th-graders? I would LOOOOVE to hear them.


  1. I love the 'Geometry Begins With Play' article by Van Hiele in Teaching Children Mathematics for thinking about beginning geometry. I think you want to focus on those van Hiele level transitions: from visual identification to thinking about properties, from properties to thinking about conjectures and arguments. Sounds like a fun line up of activities. Lots of opportunities to consider 'what do you notice,' 'how would you sort these,' 'what could we measure,' and 'what's the same/different.'

  2. For area of a circle, I like to cut a circle up into a lot of pie pieces and then assemble them into a quasi-rectangle. It's fun to show younger students some parts of proof like that and also neat to introduce the concept of a limit.

  3. Ooh, thanks for the suggestions! I'll think about them as I pull together more stuff for this upcoming unit...