Final Blog Entry

Your final blog entry is due by midnight tonight. It should be at least two paragraphs in length and it should contain the following:

1. What question or questions you have been investigating since your last blog entry


2. The data that you have collected about that question


3. Any patterns or conclusions that you have found, or an explanation of why you haven’t been able to find any


4. A suggestion for what the next question in your investigation might be (you don’t actually have to investigate it, so think big – this is the usual way to end scientific papers)

You should also make sure that you have made at least 2 substantive comments on other students’ blogs.

Make good use of your time today and you will have long homework holiday.

More About Tables

Several of you have started to create your own tables using html. Some of you have come upon the problem of big spaces before your tables. I looked up this problem and came across a good solution at Blogger Tips and Tricks. Check it out if you want to make your tables pretty.

WOW!

So, I went in to this project not really knowing what to expect. I was hoping that students would gain a better sense of triangles, better understand what math research is all about, and increase their confidence in their own math abilities.

I have to say that so far, my students have totally amazed me. They went in lots of different directions despite starting from the same few questions. And we are just now getting into the part where they investigate their own questions.

I spend a lot of time pushing students to work more, think harder, and keep going despite difficulties. So I want to take this opportunity to say publicly that I am completely impressed and amazed by what all my students have come up with so far and I am really excited to see what they do next.

3rd Blog Entry

Your third blog entry should include the following:

• What question you have been looking at since your last blog entry


• What you have found


• What questions you are thinking about investigating next - these should be your own original questions about right triangles

You should also be starting to read other students' blogs and make comments on them.

MCAS Considerations

Okay, since MCAS ELA testing is this week for 7th and 10th graders, here are the revised expectations for those grades:

There will only be one blog entry due this week for 7th and 10th graders (9th graders will still be expected to blog twice, due Tuesday and Friday at 5pm). 7th and 9th graders may choose when they want to blog this week - 7th graders should remember that they will only be in class on Monday, and will miss class for the rest of the week. 10th graders will be in class Monday and Friday.

Please let me know if you have any questions or concerns about this.

Diophantus's Method for Generating Pythagorean Triples

Diophantus, an ancient Egyptian mathematician (he lived in the 200's), created the following way of generating pythagorean triples.

Take any two integers and find:

• twice their product


• the difference of their squares


• the sum of their squares

Reference Information: Professor Stewart's Cabinet of Mathematical Curiosities

This may be useful to those of you studying Pythagorean triples.

Second Blog Contents

Your second blog should include the following:

• What you have investigated since your last entry


• What you have done to collect data


• What data you have collected (perhaps in a table)


• What conclusions you have made based on your data


• What your next step will be - this should be the logical next step in answering your original question.

First Blog Entry Content

Be sure to include the following in your first post:

• The question that you are planning to investigate


• How you plan to investigate it


• The data that you have collected so far


• Any conclusions or questions that you have based on your investigation so far

If you have already posted and you haven't included one of these, you can either add to your original post (by going to edit posts) or you can just add another post before Tuesday, 5 pm that includes the additional information.

Online Triangle Resources

Here are a few online tools that you can use to complete investigations:

This British website from Nrich is a trigonometric protractor that allows you to investigate how triangles are related to circles and also allows you to draw and measure triangles.

This applet is actually for looking at similar and congruent triangles (which might be relevant to your question) but is also useful for looking at one triangle at a time.

This collection of tools is more limited in how you can create your triangle, but might be applicable to your questions.

This site from Interactivate is really useful for looking at right triangles with integer lengths less than 10. If you have trouble getting to it (sometimes it asks you to log-in) just go to http://www.shodor.org/interactivate/ and search for "squaring" then choose the activity.

If you find other helpful sites, let me know and I will include them in a later post.

All About Triangles

I'm creating this blog to help tie together the blogs that my students are creating about their triangle investigations. I've been thinking a lot lately about how math in classrooms has very little to do with what mathematicians actually do (which is to create and investigate their own questions). I also know that my students always surprise and amaze me when I give them open ended projects. So, this is a bit of an experiment to see what they can come up with.

Here are the instructions I gave them:

Overview: In this project you will investigate relationships between the sides and angles of right triangles and communicate with your teacher and your classmates about your investigations and discoveries.

Questions: you will begin your investigation by looking at one or more of the following questions:

-We have discovered that there are patterns that appear in the lengths of right triangles with the angles 30-60-90 and with the angles 45-45-90. Are there any other angle combinations that show similar patterns?

-Pythagorean triples are right triangles that have integer side lengths. How many of these are there? Can you predict when they will occur?

-If you know the side lengths of a right triangle, can you predict what the angles will be?

-If you take a right triangle, and change one side length, how does that change the other side lengths? How does that change the angles of the triangle?

Students are also required to create and investigate at least one original question. Their first blog entry is due Tuesday, but a few have already posted, which has whet my appetite to see more of what they come up with.