This simulation would have great educational value for my high school Geometry students. The worksheet that goes with the simulation really teaches them what sin, cos, and tan are, and how they relate to similar triangles and each other. This would be a great alternative to the direct instruction that I usually use to teach trigonometric ratios.
I really like that the worksheet is challenging for students, but not too challenging. It is a great example of scaffolding. This simulation would fit in perfectly with the right triangle project I have created for this class.
2. http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=200 This is another really great simulation about right triangles, only this time it covers the Pythagorean Theorem. The student worksheet is very comprehensive, with pre-knowledge questions, information about vocabulary, self-discovery of the theorem, and practice problems. There are even assessment questions. It truly is an entire lesson plan already planned out!
Once again, the simulation itself was very straightforward and easy to use. It is intuitive, and the relationship between the side lengths and their squares is really helpful for students to discover the Pythagorean Theorem for themselves. The actual squares show students what the formula is representing, which makes the abstract concept seem more concrete and may help learners better understand. This simulation would fit perfectly into the right triangle unit I have created for this class. The only thing I did not like about these first two simulations is that they require a purchase to be used for longer than 5 minutes. However, a free 30-day trial is available.
3. http://nlvm.usu.edu/en/nav/frames_asid_164_g_4_t_3.html?open=instructions&from=category_g_4_t_3.html First of all, this simulation requires Java, which is becoming unsupported in some browsers, including Google Chrome. I had to download the plugin and use Safari to even see the activity. Once I got the activity up and running, I was pretty disappointed. There was a very brief explanation, and it did not have any of the pre-knowledge, scaffolding, or assessment that the worksheets from the other assessments did.
The activity was difficult, and I did not understand it at all right away. If I can’t understand it, I can’t really expect my students to.
Eventually, I did get the hang of it. However, I felt like I had finished a puzzle instead of gained information about the Pythagorean Theorem. There was a small attempt to have students understand why the Pythagorean Theorem is true, but it pales in comparison to what my students could learn from the other simulation. I could easily incorporate this into my unit, but I don’t think I ever would, at least not without planning a large explanation to give beforehand. If the teacher gave a good introduction, this simulation might work. After all, it’s free and the other ones are not, so that might be a reason this one could be used.
4. http://phet.colorado.edu/en/simulation/estimation This simulation is about estimation. Estimation is always important in math, especially as students get older. In more complex math classes, numbers are rarely “nice” or “pretty,” so it’s good for students to understand how to work with decimals or irrational numbers. Also, being able to tell if an answer makes sense is an essential tool in math. Whenever students solve a problem, they should examine their answer to see if it makes sense in the context of the problem. This simulation can help with that.
It was intuitive an easy to use. I figured out pretty easily what I was supposed to do. One thing I did not like was that the game doesn’t upgrade you to the next level. You have to end your game and do it yourself, and I think students would get very bored with one level, but they don’t want to “give up” and end the game.
The game starts out with estimating lines.
Then upgrades to area.
And finally, volume.
The line activity would be very helpful for students learning the Pythagorean Theorem. They could use these estimation skills when they solve triangles to determine whether their answer makes sense in the context of the problem. Overall, the simulation is a little too simplistic for my taste. Even so, I think it could be helpful in the right situation.
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20 Resources: 1. http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=221 This is another simulation on the Pythagorean Theorem. It would be another option I could use to teach this important theorem that doesn’t use direct instruction as the main tool. MN Math Standard: 8.3.1.1- Use the Pythagorean Theorem to solve problems involving right triangles.
2. https://www.youtube.com/watch?v=kBw_i6tlQfU This video gives an in-depth yet simple explanation of the Pythagorean Theorem. This would help students understand the theorem in more complex ways instead of leaving it in abstract terms. MN Math Standard: 8.3.1.1- Use the Pythagorean Theorem to solve problems involving right triangles.
3. https://www.youtube.com/watch?v=5tp74g4N8EY This video is a really good overview of the sin, cos, and tan ratios. This would be a good resource for students if they forgot about this topic and needed a refresher. It would fit well with my trigonometry lesson. MN Math Standard: 9.3.4.1- Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.
4. http://www.mathwarehouse.com/trigonometry/sohcahtoa-real-world-applications.php This is a great resource that teaches students about sin, cos, and tan. It has examples of how these ratios can be used to solve real-world problems, and also has practice problems for students to use to test their understanding. I could use this website to help students discover the trigonometric ratios for themselves, instead of me simply telling them what the ratios are. MN Math Standard: 9.3.4.1- Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.
5. https://www.youtube.com/watch?v=D4DMvjTRXeI This video is a great resource on special right triangles. Students could use it to refresh their memories on the properties of these important triangles. This video would give students an opportunity to learn an important topic, while listening to someone else’s voice besides mine, which they already hear every day. MN Math Standard: 9.3.3.5- Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results.
6. https://www.youtube.com/watch?v=eP3J7PClQqQ This video is a song about special right triangles. I would use it with my students to help them remember the ratios of these unique triangles. MN Math Standard: 9.3.3.5- Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results.
7. https://www.youtube.com/watch?v=4iC-gjKvc7A This video is a song about the sin, cos, and tan ratios. I would use it to help my students remember these ratios and use them to solve problems. MN Math Standard: 9.3.4.1- Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.
8. https://www.youtube.com/watch?v=l8-bnZh8Zuc This video is a song about the Pythagorean Theorem. I would use it with students to help them memorize the theorem so they could use it to solve problems. MN Math Standard: 8.3.1.1- Use the Pythagorean Theorem to solve problems involving right triangles.