Pythagorean Theorem…Take 2.

Math No Comments »

This week I begin Pythagorean Theorem with my grade 8 students. I intend to use many of the same applets as last year (see Fun with Applets), with a few new additions.

Illuminations Proof without Words – This is similar to Puzzle 1 from the National Library of Virtual Manipulatives. The difference here is that this applet runs for you and asks you to figure out the proof from what you see. In the NLVM applet, you manipulate the pieces yourself. I still prefer the NLVM applet, but this is a nice alternative.

IES Applet – This is similar to their applet that I shared last year. In this applet, one of the squares gets transferred whole, while the other one is broken into pieces. The whole square and the pieces must fit into square “c”.

Learning Math – This site from learner.org has some features that I like. In Part A, students are led through some inquiries and then the theorem is explained. Part B then leads students through a few different proofs. Part C and the Homework section have some interesting questions to solve.

Wolfram Math World – This site has some of the proofs already mentioned on other applets and sites, they are all just put together in the same place.

I plan on showing my students a few of the proofs, and then providing them with the websites so that they can explore. They will need to choose one that makes sense to them, and then find a way to display it with reference to a real-world problem of their choosing. In the past, students have used foam board or bristle board and made pieces that they could move around and fit with Velcro. Other students created their own digital demonstrations of one of the proofs. Some simply created diagrams. Again, I will leave it up to them to choose a method they can work with.

I can’t wait for the fun to begin.
Have a great week.

Playing with Platonic Solids

Math No Comments »

This week I am starting to explore platonic solids with my grade 8 students. The key question that I want them to answer is “Why are there only five platonic solids?” (For a brief explanation, see the MathsIsFun website.  For a more detailed explanation, read this entry from The University of Utah.)

I want this to be a true exploration activity, and as such, I will give my students limited information. I will not volunteer this information, but I will give it only after they determine the right questions to ask.

First, the students will be given nets of the platonic solids so that they can build them and use them in their exploration. I will be giving them the copy from the learner.org interactives.

They will also get scissors and a handout with the regular polygons. They may cut out the polygons and use them as manipulatives. There are eight copies of each polygon, from three-sided to eight-sided figures.

Regular Polygons Handout

I have also created a Notebook file for the Smartboard. This will be open for the students to come and explore with, as well. It is not fancy. On one side of the page are the platonic solids for the students to see. On the other side of the page are the regular polygons, set up as infinite clones. In the middle of the page is a play area. Students can thus pull out copies of the polygons, turn them around, and see how they fit together. (The polygons were created from the tools in the program, and the platonic solid images were taken from Wikipedia. If you click on each image on the second page of the file, you will be taken to the home site for that image. )

Platonic Solids Notebook File (Unfortunately, this is what the Notebook file looks like as a PDF. WordPress will not allow me to upload the Notebook file. Help anyone?)

Should students get frustrated, I will begin to lead them through the following thought process:

  • Consider the regular polygons. Starting with the triangle, what is the measure of each interior angle? Continue for the rest of the polygons.
  • What do you notice about the sum of the interior angles of the polygons, as you go from three-sided figures up to eight-sided figures?
  • Which of these polygons are able to tessellate? Why are they able to tessellate?
  • Which of these would be able to be constructed into a polyhedron? Why wouldn’t all of the regular polygons be able to be constructed into a polyhedron?

They can then go play on the Learner.org website.

The final task will be for them to submit an explanation as to why there are only five platonic solids. I will accept written work or digital work – students can choose which method suits them best.

Have a great week.

The Escalator

General Science, Math No Comments »

I came across a neat resource from the University of Toronto. As an educator who lives in Toronto and a University of Toronto alumnus, I am surprised that I had never heard of it before. The resource is called The Escalator. It is an outreach site from the University of Toronto, with an emphasis on math and science.

Under the Math tab at the top there are two options: Mathematics and Fields. Click on the Mathematics link and you are taken to the University’s Department of Mathematics page. Here you can find links to math competitions, teacher resources, and other tidbits.

There are two links under the Physics tab. The Physics link takes you to information for the Physics Outreach program and the Physics Olympiad Preparation program for high school students, complete with practice problem sets. The Candac link takes you to the Canadian Network for the Detection of Atmospheric Change, which has a variety of links and information, as well as a teacher resource page. The Chemistry tab also takes you to an access page for the Canadian Chemistry Olympiad for high school students, again complete with practice problem sets. The Engineering tab takes you to a list of robotics competitions and a variety of summer programs for students in grade 5 and up.

Click on Universe under the Astronomy tab, and you are directed to University of Toronto’s public portal. Here you can video chat with astronomers and send them questions, or book a planetarium visit or speaker. There is also a link here to the Transit of Venus. On June 5, 2012 Venus will pass across the sun. This has not happened since 2004 and will not happen again until 2117.  (Alternately, you can read about the Transit of Venus here.)

The resources tab has a few areas to explore, including a link to the teachers’ resource page of the Canadian Mathematical Society, which has its own database of resources to search through. The curriculum link is still being developed, so check back to see its full potential. Currently you can find the link to the Science Rendezvous for Educators site. The Science Rendezvous is what first led me to The Escalator website. It is a one-day science festival, hosted on university campuses, research institutions and community sites across Canada on Saturday, May 12, 2012. The database on the educator page is not yet built, but again, I am curious to see what will be included there.

Have a great week.

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