DESMOS : Les angles remarquables

While scrolling through Twitter posts, I saw one from @DESMOS and @mr_stadel. Andrew Stadel created a DESMOS activity that allows students to explore special right triangles through familiar triangles.  It is an activity that is still in the works and I decided to translate it and test it with my students in order to provide feedback to Andrew Stadel and DESMOS before this activity saw its final draft.

The activity goes like this : 

1. Starts with a square, that is then cut in half.
2. This creates the special right triangle 45-45-90.
3. With the use of animation, the student can then think about the relationship between the length of the sides and the hypotenuse.
4. Next is the equilateral triangle, that is cut in half by its height.
5. This creates the special right triangle 30-60-90.
6. Again the use of animation, the student explores the relationship between the long leg and the short leg, as well as the hypotenuse.

J’ai traduit l’activité et vous pouvez suivre ce lien pour pouvoir l’utiliser et/ou faire des changements.

J’ai utilisé l’activité en classe ce qui m’a permis d’animer plusieurs différentes discussions.  Je voulais noter la réaction des élèves aux différentes questions afin de pouvoir analyser les questionnement de l’activité, la suite des questions et si l’activité atteint son but.

Here is a summary of the different student responses given during the activity.

This is the feedback I sent to Andrew Stadel and the team at DESMOS.  First, referring to the 45-45-90 triangle :

I believe this was successful.  It created a thinking classroom, it made for great discussion and I liked how the students were able to describe the relationship using prior knowledge.  However, I wanted to transfer this to the unit circle for a 45 degree angle and I think I went too fast there.  I should have presented this before the unit circle and will try that next time around.  I felt that a few students were a bit overwhelmed when we started transferring this to trig ratios.  I will split this up into 2 days next time around.

Next, the 30-60-90 triangle :

I realize that I should have intervened sooner regarding the equilateral triangle and the fact that the students were not seeing it as such.  I wonder why they didn’t.  Is it the image?  Do they think that the “sommet” of the triangle should be (0,6) meaning they think a diagonal that measures 6 units should reach that point.   I am going to come back to this again after a small review of types of triangles and lengths of diagonals.  I wonder if there should be another image, another slide, something that allows them to confirm that it is equilateral before moving on to the other slides.

Même avec ces petites difficultés, j’ai été contente de pouvoir faire des liens avec le théorème de Pythagore et les rapports entre les longueurs de côtés suite à cette activité de DESMOS.  Voici des images de nos discussions ici :

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