Investigation Frustration!

I've been trying to do more investigation/discovery activities with my geometry students.  Right triangles easily lend themselves to these types of activities, so I thought this unit would be a great place to start.  I knew that my kids lack persistence when solving problems, but I had no idea how bad it was.

Activity 1

The first activity I tried was for 45-45-90 triangles.
45-45-90 Special Right Triangles Investigation - trying to teach students persistence  |

I used it as a long warm up before I taught the lesson.  They were supposed to work with their partner.  I asked them to write all of their answers and explanations in complete sentences.  I read all of the questions aloud before letting them work.  I could tell we were in for a world of hurt when they started freaking out over #3.

"Write the Pythagorean theorem.  Write an equation in terms of x and h by substituting the side lengths in the formula."

After several painstaking minutes of them whining asking questions, I finally wrote it on the board.  Maybe that was a mistake…I don't know.  Then, when they read #4 about half of them put their head down and gave up, while the other half of them whined like 4 year-olds.  I gave them hints.  I made them squirm.  They never got what I wanted them to get out of it.  I ended up moving on to the notes.

I'm having a hard pinpointing exactly what went wrong.  First, I think that my kids weren't willing to slow down and actually read what #3 was asking them to do.  Since it wasn't totally obvious, they gave up.  I reinforced that behavior by leading them along.  However, I didn't know what to do to get them moving.  The only part that I thought could have been a little tricky was #4, but they wouldn't even write anything down.  It's not like it was just a few kids, it was the whole class.  I made them turn in what they had written.  When I read them later I got irritated when I read conclusions like "I hate math" and "This was ridiculously hard".

Activity 2

A colleague made a GeoGebra applet for the next investigation (30-60-90 special right triangles).

30-60-90 Special Right Triangles Investigation - geogebra applet and download - trying to teach students persistence  |

30-60-90 Special Right Triangles Investigation - geogebra applet and download - trying to teach students persistence  |

Again, I used it as a long warmup.

The students did a better job with this investigation, but they still didn't do great.  Even when their work was ok, their conclusions were terrible.


I think I need to model how to write good conclusions.  As much as these activities frustrated me, I think I need to do more of them in class.  Having them work in partners helped, but I think next time we should try one as a class.  That way, I can model exactly what to do.  If you know of a way that I can fix this or do a better job, please let me know!!


  1. I love your blog and activities on Teachers Pay Teachers. I too, teach geometry and find a lot of students struggle with writing complete responses. We have a template for stumper problems that helps students really BREAK DOWN the problem solving process. We thought this would help. Nope, just more fragmented sentences with just an answer, not an explanation. To tackle this, I posted the next day someone's response "5" and asked my students if they knew what this was about. We slowly built on this meager answer by quickly rewriting and rewriting and rewriting (yes, I was glad to have my English supplement/minor at that point!) to create an acceptable and strong argument/support for their answer. This has helped, however I am curious to see if students actually apply this to their stumper problem due tomorrow. Time will tell. Overall, this modeling/revising took maybe 7-10 minutes and the students really seemed to respond.
    :) Michelle Eby

  2. That is a good idea! I have never thought about working backwards. I'll have to try this next time. Thanks for sharing!

  3. I like to go FROM specific examples TO the general rules, so here I would start with a bunch of different triangles each with one angle and one side marked and have them find the missing pieces and make observations how it works with all the triangles that are isosceles and have a right angle. Once they write up this observation in complete sentences and recognize the pattern, then move on to having the sides marked with x.


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