Tracygillespie's Blog

tracygillespie — Sat, 28 Nov 2009 18:23:51 +0000

Factoring Quadratics – in my own words

5x²+ 7x + 2

1. Circle the coefficient in the 1^st term and the # in the 3^rd term.

Multiply them together. 5 × 2 = 10

2. Find the factors of 10. (1,10 & 2,5)

3. Circle the 2^nd 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

tracygillespie — Sat, 28 Nov 2009 17:34:39 +0000

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.
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.

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.
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

tracygillespie — Tue, 10 Nov 2009 02:00:40 +0000

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.

http://matti.usu.edu/nlvm/nav/

Evaluating our Definitions: Equations and Functions

tracygillespie — Sat, 07 Nov 2009 15:35:51 +0000

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

tracygillespie — Sat, 07 Nov 2009 14:29:56 +0000

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

tracygillespie — Sat, 07 Nov 2009 13:54:57 +0000

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!

*****************************************************************

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

tracygillespie — Mon, 02 Nov 2009 02:22:17 +0000

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.

Translating Pattern Narrative into Formal Language

tracygillespie — Thu, 29 Oct 2009 18:14:54 +0000

Pascal’s triangle can be described as an quilateral triangle. It is bordered by 1′s going down the right and left sides of the triangle. The second row of diagonals are counting numbers 1,2,3,…. The interior triangles are created by the sum of the two numbers above. Each row starts and ends with the number 1. If you folded the triangle symmetrically, every odd row would match. Looking at the apex and down, the numbers are increasing.

“Working with the definition of linear patterns”

tracygillespie — Thu, 29 Oct 2009 17:18:45 +0000

“Working with the definition of linear patterns”

Formal Definition: Non-traditional patterns – patterns that do not follow a repetitive format

Kid’s Language: Non-traditional patterns – a group of numbers or objects that do not follow a specific order

Formal Definition: Linear patterns – repeating indefinitely in either direction along a line/ exists when points form a straight line

My Definition: Linear patterns – a set of objects repeating in a line

The difference between the formal definition and my own is the word usage. Students can relate to a concept by examples. In order to have students learn definitions, you need to have them be a part of creating the definition. Before students are given formal definitions show them examples of number patterns and object patterns. Ask them what they see. Have students work in small groups to create patterns of their own. Then ask the students to come up with a class definition. After, give them the formal definition. Students can then perfect their class definition. They will remember what they created.

“My Reflection on Math Myths”

tracygillespie — Thu, 29 Oct 2009 02:50:31 +0000

After reading “Math Myths”, there were two myths that I encountered when I was a student. Myth #1 for me was “Math requires a good memory, and memorizing formulas and rules is the best way to learn it.” Throughout my math education, I only remember memorizing. If there was a rule, the way to succeed was to memorize. Understanding what I was doing rarely happened. Since I have been in education, I have learned the importance of understanding what you are doing in math. I do believe that there is also an importance to memorizing after you understand. There are some rules that will never leave me, for example adding, subtracting, multiplying and dividing integers. Students should be taught to understand what they are learning, the meaning. When the understand, memorizing rules and formulas will not be difficult.

Myth #2 that I encountered as a student was “There is a “math mind” some people have it and some people don’t”. I remember being told this by family members. Not that I didn’t have the math mind but that it was in the family and that I should have one. The problem with this was when I wasn’t successful in math, I felt worse. I eventually realized some concepts I got quickly while others just took some time. There are always students who say, ” I just can’t do math!” It is important to take time with these students to find success in math. Giving them a little confidence could dispel the “math mind” myth.

Having the students make connections, engaging them and having the patience to find a way to make them understand will create “math minds”.