Tracygillespie's Blog
Just another WordPress.com weblogArchive for November, 2009
Factoring Quadratics – in my own words
5x2 + 7x + 2
1. Circle the coefficient in the 1st term and the # in the 3rd term.
Multiply them together. 5 × 2 = 10
2. Find the factors of 10. (1,10 & 2,5)
3. Circle the 2nd term. Which multiples in step 2 equal 7? (2,5)
4. Rewrite breaking the second term apart with the answer from step 3.
5x2 + 2x + 5x + 2
5. Distribute the above into 2 parenthesis.
(5x2 + 2x) + (5x + 2)
6. Now factor out into binomials.
5x(x+1) + 2(x+1)
7.Both binomials are the same keep (x+1) And take (5x + 2) for the second term.
(x+1) (5x+2)
Reflections on Blogging
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Describe your blogging experience in this course. Do you think you will continue using your blog? Why or why not? Blogging was very new to me. I have read other people’s blogs and thought that I would never be able to create one for myself. I liked reading my classmates posts and others out there on the internet. However, I liked using the forums for communicating ideas with our classmates. I do not think I will continue to use blogs unless benefit my students. I think it poses as another thing to do and keep up with.
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What did you learn about yourself and your abilities or interests in Math or Algebra? I learned that I once I got started I remembered more about Algebra than I thought. Doing some of the activities reminded me of how much I enjoyed solving problems. I also realized for a class like this I may have benefited more by being in a classroom.
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Did you learn or discover anything you found particularly interesting through your course active or your own internet research? Describe one interesting discovery and why you found it fascinating. I learned a lot about the resources on the internet. There are so many activities out there to reinforce algebra concepts. The most interesting discovery that I learned about was the National Library of Virtual Manipulatives. I already have had kids go on it to reinforce some concepts that they have been struggling with after the results of a recent quiz. The students really enjoyed using it and wanted to go on the website and check out the different activities. Next week we are introducing one step equations and I intend on using the algebra quiz game with the students.
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Do you think you will use journals with your students? Do you think you will use blogs? Why or why not? I do think that I will use journals with my students. I was thinking of incorporating the journal with their warm up problem twice a week. This will require them to explain the strategy that they used to get their answer. I do not think that I will use the blog with my students because a very low number of students would be utilizing the blog. Some of the students have a hard enough time going on the programs that they need to go on like First in Math and Study Island.
Exploring the World of Applets
I really like the NLVM website. There are many user friendly actvities and most of them kept me engaged. The activity that I would use with students is the Algebra Balance Scales – solving simple linear equations using a balance beam. First, you need to move the tiles to rewrite the equation. Then, you solve the equation. I would use this as a follow up activity for solving equations. You can also use it as a warm-up projected on the white board.
Evaluating our Definitions: Equations and Functions
After reviewing my classmates defintions, I noticed a lot of similarities. You can tell that the other posts were done by math teachers. The words used were more formal using specific mathematical terms. I would have added a visual to help student’s see the image. I did try to but I could not download the image for some reason – it was a balance under the equation term.
I would ask students for their definition first, as an introduction and then, we as a class would work on improving the definition. I would have the students partner up and come up with examples for equations and functions.
5-A-3: My definitions of Equations and Functions
5-A-3: My Definition of Equations and Functions
Equation – balance on both sides of the equal sign
3+2 = 4+1
10 pennies = 2 nickels
Function – relationship between two numbers when one number (output) depends on the other number (input)
As a fundraiser, the local pizza shop will donate $2.00 for every pizza sold between 6 p.m. and 8 p.m.
| Input:Pizzas | Output:AmountDonation |
| 0 | 0 |
| 2 | 4 |
| 3 | 6 |
| 5 | 10 |
| 10 | 20 |
5-B-1: The Magic of Proportions
5-B-1: The Magic of Proportions
Cleaning the bathroom is my very least favorite chore. I leave it for Saturday morning but all I want to do is get to family time. We have 3 bathrooms in our house. If it takes me 30 minutes to clean 1 bathroom, how long will it take to clean 3?
Let’s set up the proportion like so…..
1/30 = 3/?
First I ask myself, how many times does 1 go into 3? Answer: 3 times.
Then I take 3 and multiply it by 30. Answer: 90.
1/3 = 3/90
If it takes 30 minutes to clean one bathroom, it will take 90 minutes to clean 3 bathrooms. So after 1 hour and 30 minutes I am free to play!
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My sons’ soccer tournament is today. His coach said it is 125 miles away. I drive very slow, 50 miles per hour. We need to be there by 10:00 a.m., what time do we have to leave?
Let’s set up the proportion like so….
1 hour/50 miles = ?/125 miles
First I ask myself, how many times does 50 go into 125? Answer: 2.5 times. Then I take 2.5 and multiply it by 1. Answer: 2.5
1 hour/50 miles = 2.5 hours/125 miles
It will take 2 ½ hours to get to the soccer game. Since we need to be there by 10:00, we will need to leave at 7:30.
Non-Linear Pattern Web Quest
Being a special education teacher, I knew that this web search would be very educational. The key words were familiar to me but I can definitely use a lot of refreshing.
My web search began with “Fibonacci”and “Phyllotaxis” and “Prime Numbers” . www.daviddarling.info/encyclopedia/F/Fibonacci_sequence.html was very informative. It was very engaging and easy to understand.
Searching “Fractals” and “Nature” and “Patterns”, www.miqel.com/fractals/_math_patterns/visual-math-fractals.html had great pictures of fractals in nature.
www.contracosta.edu/math/Pentagrm.htm was the website that I found interesting because this concept was one that I knew very little about.
Were there ideas or concepts you were not familiar with? What were they? The term “phyllotaxis” and it’s connection to nature – the arrangement of plant leaves was a new concept. I also learned how connected math and nature are.
What images did you find particularly striking? The fractal picture of the broccoli/cauliflower and the Lichtenberg figure was striking.
Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they? In my house I have a vase of artificial sunflowers, my bar stools have a swirl pattern and I have many shells that have a spiral center.
How can you adapt this webquest activity for your classroom? I would break the class up into groups and give them websites to search. I would then have each group compare the information that they all collected. Each group would be responsible for sharing a concept.
