Octm Recap: High Yield Geometry Routines

Last week, Shaun too I were able to attend the Oklahoma Council of Teachers of Mathematics Summer Workshop at OSU-Tulsa.  We attended to a greater extent than or less non bad sessions, too I've decided that the best agency to non forget what I learned is to weblog close it!  Over the class of the adjacent few weeks (months?) I desire to write a weblog shipping service close each session nosotros attended too what I recollect were the major take-aways.

The firstly session nosotros attended was on high yield geometry routines, too it did non disappoint!  The thought of a "high yield routine" interested both of us, too nosotros *think* Shaun volition hold upwards teaching geometry adjacent year.

Dr. Utley wasn't able to hold upwards there, but John Weaver did an fantabulous task demonstrating too engaging us inwards the high yield routines.  He recommended the majority High-Yield Routines from NCTM (affiliate link).  When I looked it upwards after the conference, I was distressing to regard it was directed at K-8.  I haven't purchased it (yet) because of that reason.  Is anyone familiar amongst it to know if it tin sack hold upwards applied to high school?

First, nosotros heard a fleck close what high yield routines atomic number 82 to inwards the classroom.

Here were my principal take-aways (as told past times the furious notes I was taking during this session!)

• High yield routines must hold upwards used early on too oft to hold upwards most effective.  
• High yield routines should hold upwards used inwards shape from twenty-four hours one.  
• High yield routines offering access to the BIG ideas of math.  
• High yield routines offering a deep agreement of concepts.  
• High yield routines should hold upwards used to build your classroom environment.  

John too made an analogy that I institute really thought provoking:

Estimation is to Algebra every bit Spatial Sense is to Geometry.  

My firstly instinct was to recollect that nosotros don't create that much estimation inwards algebra.  But, too thus I got to thinking close how I acquire SO frustrated when my students brand it at an respond without checking to regard if their respond is fifty-fifty reasonable.  I demand to receive got my students create to a greater extent than estimation.  I demand to build this into my classroom every bit a routine.  

In regards to vocabulary, I particularly liked John's quote: "Vocabulary is the loma I've chosen to cash inwards one's chips on."  I demand to create a improve task inwards my classroom of ensuring that students both value too utilisation proper vocabulary.  I haven't done a tidings wall inwards a few years, thus I'm wondering if this should hold upwards purpose of my inaugural again? 

Okay.  Enough of my random thoughts for things I demand to create a improve task of adjacent year.  Are yous fix to acquire close these high yield geometry routines?  

Quick Draw

This thought is based on the majority Quick Draw past times Grayson H. Wheatley (affiliate link).  The teacher's task is to flash an paradigm on the concealment for 3 seconds.  Then, when the paradigm disappears, the instructor tells students to "draw what yous saw."  It sounds simple, but seeing it unfold inwards somebody was powerful.  I looked over at Shaun's notes after nosotros did our firstly Quick Draw activity, too he had written "Do this!!!"    

Here are to a greater extent than or less much to a greater extent than detailed directions:

Here's the firstly quick describe paradigm nosotros were asked to draw:

After seeing it on the concealment for 3 seconds, I was able to easily describe it inwards my notes.  I didn't demand the extra 3 seconds to expect at it again.  Instead, I precisely sat at that spot thinking "How inwards the globe could I utilisation this inwards algebra class?"  

What actually got my attending was when John started quest people to depict what they had saw too drew.  The things I was hearing others depict was non what I saw at all!  I had seen a foursquare amongst a triangle within it that had a vertex at the midpoint of the move past times occupation on the square.  Other people were describing how they had seen an equilateral triangle amongst 2 correct triangles formed from the sides of the equilateral triangle.  When I realized that unlike people tin sack regard the same paradigm really differently, I began to regard fifty-fifty to a greater extent than potential for using this inwards the classroom!

One to a greater extent than matter close the equilateral triangle matter - this led to an awesome give-and-take close whether the surrounding shape was a foursquare or a rectangle too if nosotros could attempt out it.  So much math utter close of a uncomplicated i infinitesimal task!    

So, I'm sitting inwards this workshop feeling kinda dizzy because I should receive got realized that unlike people powerfulness regard the same paradigm differently.  Then, nosotros create to a greater extent than or less other one:

Again, I'm able to describe it easily on my paper.  I regard a pocket-sized foursquare within a larger foursquare amongst directly lines connecting the vertices of the pocket-sized foursquare to the corresponding vertices of the larger square.  Then, the facilitator starts quest others to depict what they saw.  I'm blown away when others start describing seeing 3-D objects.  One lady saw a "room."  Another lady saw a truncated pyramid.  Yet to a greater extent than or less other somebody saw a light shade.  

The majority Quick Draw (affiliate link) has a collection of these images to use.  Here is a sampling: 

 And, hither were to a greater extent than or less of the benefits of this high yield geometry routine:

I did to a greater extent than or less searching online too institute a few to a greater extent than sources of quick describe images if yous desire to endeavor them out inwards your classroom earlier investing inwards the book.  

• A summary of Quick Draw past times the author - includes a video of the construction inwards action! 
• PDF of 2 Quick Draw images
• PDF amongst 3 to a greater extent than Quick Draw images
• Journal Article Including Several Quick Draw Images
• NCTM Article About Quick Draw

I was thus impressed amongst how much geometry vocabulary too math utter came out of this uncomplicated routine.  I tin sack definitely regard how this is an activity that tin sack hold upwards used throughout the yr to estimate how students' vocabularies too spatial senses are developing.  

After discussing Quick Draw, 2 tweaks to the activity were suggested:

1.  Have students build the paradigm on a geoboard.  This would brand it easier to discern betwixt squares too rectangles.  

2.  Instead of quest students to depict what they saw, receive got a pupil depict to the instructor how to describe the paradigm on the board.

Quick Build

We too talked close a variation of Quick Draw known every bit Quick Build.  When nosotros had entered the room where the workshop was, nosotros had been given a laid of five snap cubes.  We were all instantly curious close what the snap cubes powerfulness hold upwards used for.  

Here's the type of paradigm that would hold upwards shown to students during a quick build session:

Just similar amongst Quick Draw, the object (or pic of it) volition hold upwards shown to students for 3 seconds.  Then, it volition hold upwards taken away thus they receive got a lead chances to describe it/build it.  Show students the paradigm for to a greater extent than or less other 3 seconds for them to create their drawings.

You receive got several options amongst Quick Build:

• Have students recreate the 3-D figure using Snap Cubes
• Have students describe the 3-D figure using Isometric Graph Paper
• Have students describe the "top view" of the figure. 
• Have students determine the majority of the figure.
• Have students determine the surface expanse of the figure. 

I'm certain at that spot are many other options, but these are the exclusively ones nosotros discussed.  

At the bottom of this article, at that spot is a video of this activity taking house inwards a classroom. 

Fold-N-Cut

I'm actually distressing I didn't recollect to receive got whatsoever pictures of this activity acre it was beingness presented.  So, I'll endeavor to explicate it to the best of my ability.  

Hold upwards a canvass of newspaper to your students.  Fold it inwards one-half amongst the move past times border of the newspaper coming downwardly to encounter the bottom border of the paper.  Whenever yous create this activity, the crease should e'er hold upwards at the top.  

Take a twosome of pair of scissors too cutting the folded paper.  Our facilitator cutting a triangle off i corner, a foursquare out of the bottom, too a quarter-circle out of to a greater extent than or less other corner.  

Then, it was our turn.  

Draw what the newspaper would expect similar when it was unfolded.  

We repeated the activity amongst a newspaper that had been folded into fourths.  

We were warned to NOT inquire students to portion strategies amongst this activity.  Some students volition discovery that they tin sack precisely describe what the folded newspaper looks similar too and thus perform a reflection/rotation of that paradigm to cease upwards amongst what the unfolded newspaper volition expect like.  While this is awesome, i time students start doing this the activity volition lose a lot of its charm.  

Where's Polygon

Another activity nosotros discussed was called "Where's Polygon."  I've included the instructions from the presentation below, but here's the full general gist of it.  

Display a blank coordinate bird for students to see.  At the conference, this was done amongst a document camera.  If yous receive got access to a projector, yous could utilisation unlike colored dry out erase markers on the board.  If yous receive got a SMARTBoard, precisely projection the coordinate bird on there.  

Before beginning, receive got a specific polygon inwards withdraw heed - exact coordinates!  

Your color coding volition characteristic 4 colors.  One color for points exterior of your polygon.  Another color for points within of your polygon.  Yet to a greater extent than or less other color for points on the border of your polygon.  And, a concluding color for the vertices of your polygon.  

As students telephone yell upwards out ordered pairs, color them accordingly.  This continues until all the vertices of the polygon are found.  

Now that circles receive got moved to the Oklahoma geometry standards, I recollect it would hold upwards fun to throw a circle into this activity to regard how students react.  Of course, a circle isn't a polygon, thus that would hold upwards a fleck mean...  I regard such potential for this routine to grow amongst students throughout geometry class.  

Guess My Rule

This activity pulls from an awesome work institute inwards Michael Serra's Discovering Geometry (affiliate link) text.  Students are given a laid of images that are examples of widgets too a laid of images that are non-examples of widgets.  Then, they are asked to determine if other images are or are non widgets. 

Next, nosotros saw how nosotros could utilisation polygons to brand our ain problems similar this.

Sadly, I never got to figure out what John's dominion was because nosotros ran out of time.

There were a few to a greater extent than routines inwards the presentation that nosotros didn't acquire a lead chances to acquire to, thus I'm afraid I don't receive got all of the details.  There were slides for them inwards the master copy presentation, but I had problem filling inwards the missing pieces myself.  You tin sack notice the entire presentation here (open the folder titled High Yield Geometry Routines).  

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