Tuesday, February 4, 2014

Geometry: Study of Lines, Part One

Last week we began the study of lines with a presentation on points, lines, surfaces and solids.  The boys have continued to make progress on their study of lines.  First they learned about straight and curved lines.  We began with a sensorial experience of straight and curved lines by feeling the edges of square and circle from the geometric cabinet.

Next, they worked together on an exercise in which they sorted the perimeter cards (the thin outline cards) from the geometric cabinet.  I bet you thought you'd never use those again after primary!  I had to get ours out of the basement.  I made labels which state "figures limited by straight lines" and "figures limited by curved lines."

The boys sorted the figures in a kind of mad-dash fashion.  I was a little surprised and overwhelmed when it happened.  So, next I made them return the cards to me one at a time stating each time "The _______(name of shape) is limited by straight/curved lines" as appropriate.

 Next they needed to learn that a line has infinite length.  We do this with string.  I held blue yarn in my hands with extra yarn bunched up and hidden in both hands but with the visible yarn held taut.  I asked, "What am I making." The boys answered, "A line."  I showed them that I could continue to make the line longer and longer and stated that, "If I could stretch far enough the line could go on and on to infinity."

I held the taut yarn in many positions (over my head, under my rear end, horizontally, vertically, etc.,) and then the boys took a turn doing so.

I tossed the yarn onto the rug and we observed that the shape is now curved.  Then the boys took turns tossing the yarn.  We made a list of objects in our environment that are limited by straight and curved lines.

I drew them on the board.

The boys drew them on paper, labeled the lines, and then labeled the phrases with their grammar symbol stencils.  They store things like this in work binders we keep on a shelf in the school room.

Next we explored this idea with the box of sticks.  I let them each find a straight line and a curved line.  We changed the position of the lines on the table many times to observe that they remain straight or curved in all positions.

The next day we explored the parts of a straight line.  We started by reviewing the difference between straight and curved lines with the blue string.  The blue string has found its home in one of our geometry drawers so they can use this to explore at will.  Above they are demonstrating a straight line, below a curved line.

Above is a diagram of the rest of the lesson.  It is important to note that there is always extra yarn or string hidden in the hands so that you can show which ends can still be extended to infinity. 

I drew examples on the board to familiarize them with the written symbols for these parts of a line.  And, as with the previous lesson, they drew, labeled and drew grammar symbols for the new nomenclature.

We are continuing our studies this week with the three-positions of straight lines (vertical, horizontal, and oblique).


  1. Cool post. I am going to have to employ those work binders in our classroom. T's cubby looks like your typical lower el cubby...stuff pouring out everywhere! Where did you find this lesson?

  2. UGH. I can't stand the pouring out everywhere feature of young boys. The binders work well. Folders get out of control really fast. Now...If I could just do something about their desk and dresser drawers in their rooms....

    I'm using Mid America Montessori for Geometry, at least for now. I might transition into KotU or CD once we've transitioned as slowly and gradually as humanly possible I guess :)

    1. You did say that about the Mid America Geometry albums didn't you. Sorry. I've decided to "save" geometry for a little later in the spring after we regain some traction in the physical geography, history, and botany areas.

  3. I tried this comment earlier, and for some reason it didn't work. So I'll say first that I love the diagram - I was able to watch this presentation (from afar) in the lower el classroom and enjoyed seeing the interaction. Also, concerning the CD albums online - have you been able to access them from the site? I was going to look something up a couple days ago, and they were just....gone. Any ideas?

    1. I know I used the online CD albums within the last ten days (because the album content itself often shows up on a search), however I have checked back several times in the past few days since you posted and they have disappeared from his blog. I would recommend contacting him. He might not even know they are down. Possibly the site that was hosting the file expired.

    2. I did end up trying to both comment and send him a message. Thankfully, Abbie had very efficiently saved hers, unlike myself (who probably said in my HEAD to save them, and never did, and just remembered thinking to and considering it done - which may or may not have happened before!). I hope he is able to get them up, again, though because I am sure there are many people who depend on them! :) Loving your posts on geometry, by the way - another one of those subjects that isn't covered much in the early years of traditional school - at least not what we had used - so we will be having fun with geometry soon, and I will probably be piggy backing off your posts a little! :)