Teachshirl's Blog

Factoring Quadratics: In My Own Words

teachshirl — Sat, 28 Nov 2009 03:40:35 +0000

x² + 7x + 10

To factor the quadratic above:

1.) Look at the constant of the quadratic, the last number, and lists its factors 1, 10; 2, 5; determine which set of factors when added give you the sum of the coefficient in the middle (2,5). These factors will be the second term in each binomial.

2.) Look at the first term and factor it x²= x ● x these factors will be the first term in each binomial

3.) Write the binomials (x + 2) (x + 5)

Writing the process does help with understanding factoring. I think that students would benefit from explaining their thinking once they have practiced the process several times with success. It would also be beneficial for the students to explain how they would check their work by working backwards form the binomial to the quadratic.

Reflection on Blogging

teachshirl — Sat, 28 Nov 2009 02:11:38 +0000

I have to say that Blogging is an interesting way to communicate with others. The thing I find difficult about it is that it takes time to go to and read peoples blogs. I had to Bookmark everyone’s from class so I could get to them easily, of course I had my favorite few that I would visit first before moving on. I am not a computer person. I check my e-mail at school daily, in the am and after lunch, I only check my personal e-mail every other day or so. As far as keeping this blog going I do not think I will take the time. I will keep an eye on my class mates to see if anyone enters new material and I may even leave a comment every now and then.

This class was interesting and I had to review some of the concepts covered. I have taught pre-algebra and can see that I may be asked to teach algebra I in the near future, since we have a 5th grader coming to the middle school for pre-algebra daily. It’s like that old saying, “it’s like riding a bike…” I have however shared many of the applets and several lessons with my math team. The function machine and the algebra quiz sites are two that I will definitely use in the classroom, because they will give the students a different perspective to the paper and pencil work.

I do have a math blog on my school web page. I have used it twice so far this year. The first blog the students told me what they like about math and did not like about math. My second blog is still posted because my daughter the marketing major needed my help with her senior project. I got permission to give the parents an internet survey that describes their child’s influence on them during back to school shopping. To complete the extra credit the students have to answer three questions about why the survey could be important; which average would give the best information, the mean, median, or mode; which graphs would they use to show the results and why. I told the students I would help them with a little extra credit since they are having their parents help my daughter. My daughter will then come in to answer these questions and more about math in her soon to be profession, after the winter break. I do have some other questions to post later, but now I’m thinking I have some new material that may give more information about what my students know and don’t quite get. I am also using more writing in math this year, having students explain processes in words. I do not think I will use “journals” at least not separate from their notebooks. I may start having students write to prompts and have them turn in one each marking period that made an impression on them or when they looked back felt they made more progress with; not as a graded work but as a class participation grade.

5-D-2: Applets

teachshirl — Tue, 10 Nov 2009 00:05:31 +0000

I really enjoyed playing with many of the applets on the three sites. I have to say that the Illuminations site,

http://illuminations.nctm.org/ was the one where I found the activities that I will use with my students first. I found an activity called “Angle Sums”, http://illuminations.nctm.org/ActivityDetail.aspx?ID=9 ,which I can use on my Smart Board as well as have the students complete activities on their own. I would give the students specific angle measurements to duplicate and specific triangles to form.

I also found an activity called “Turtle Pond”,http://illuminations.nctm.org/ActivityDetail.aspx?ID=83

This activity works with graphing, estimating, and angles to get the turtle from one location to the pond. There are settings that let you change the location of the pond and add trees. The students can cross the grid by using angles. I would have the students try to get to the pond in the shortest distance, fewest commands, and have them have to a specific number of commands.

5-B-1: The Magic Proportions

teachshirl — Sat, 07 Nov 2009 21:34:58 +0000

Like many people I have started going to the gym. I was told that I will burn about 150 calories for 30 minutes on the elliptical. I want to work out for 45minutes today, about how many calories will I burn?

150/30 = c/45

150 x 45 = 6750; c x 30 = 30 c

6750 = 30 c

6750/30 = 30c/30

225 = c

I will burn about 225 calories.

I decided to stop and buy bagels for the Gold team teachers. The store has a sale on bagels 8 for $4. I only want to buy 5 bagels, how much will I pay for only 5 bagels?

4/8 = p/5

4×5 = 20; p x 8 = 8p

20 = 8p

20/8 = 8p/8

2.50 = p

It will cost $2.50 for 5 bagels.

Evaluating Our Definitions: Equations and Functions

teachshirl — Sat, 07 Nov 2009 15:12:26 +0000

After reading many of my peers definitions, I realize my definitions are too simple. I used definitions that are built upon as the students progress though the course. As a 6th grade teacher I teach pre-algebra and we introduce the concepts so that the students have the base to build on in 7th grade, which means we tend to use a simpler idea. I think however, I could go back to my definitions and include more of the vocabulary, such as “domain” and “range” ; the word “function” as a rule; as well as including “variables” as part of the equations definition.

5-A-3: My Definition of Equations and Functions

teachshirl — Fri, 06 Nov 2009 21:56:53 +0000

Definitions of Equation and Function

Equation: an equation is two mathematical sentences linked by an equal symbol. When each mathematical sentence is solved the results should be equal.

Ex: 3 x 6 = 20 – 2

18 = 18

Ex: x ● 5 = 30

x = 30÷5

x = 6

6 ● 5 = 30

30 = 30

Function: is a matching of items from one data set with an item from a second data set. The first item is the input factor the second item is the output factor, there can only be one output factor for an input factor.

Input (x)	1	2	3	4
Output (y)	2	4	6	8

Non-Linear Pattern Web Quest

teachshirl — Mon, 02 Nov 2009 07:31:04 +0000

The two key word searches I used were “Fractals” and “Nature” and “Patterns” and “Fibonacci” and “Phyllotaxis” and “Prime Numbers”
1. Were there ideas or concepts you were not familiar with? What were they? I have heard of but am not familiar with the “golden ratio”; I remember it being mentioned in high school. I know of the “golden rectangle” from the ancient civilizations we study in social studies and I always try to make the connections to math when they lend themselves. In one web site I also found out about the “golden angle”
Fibonacci Numbers – Golden Angle

The number of visible spirals (parastichies) in spiral arrangements are most often Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21 …) and the angle between successive leaves is close to the Golden Angle – about 137.5 degrees. This frequent type of pattern is called Fibonacci phyllotaxis. Fibonacci numbers and the Golden Angle have a precise mathematical relationship. http://www.math.smith.edu/phyllo/About/index.html
1. What images did you find particularly striking? I found some beautiful photos of viruses, molds and fungus at http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html
2. Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they? My son is studying at the University of the Arts so we several “art projects” that fit into this category. My wall paper in my kitchen is random pressings of leaves, which as the paper repeats show a pattern between them.
3. How can you adapt this webquest activity for your classroom? I found quite a few that really looked kid friendly. With our enrichment and advanced students we have the complete projects one on famous mathematicians and another on interesting math concepts. these projects are perfect for a web quest, as long as I make sure the keywords lead to sites that are appropriate. I also found a site that had amazing drawing, photos of fractals.These fractals were made by students ranging from 5th to 11th grades. I think I will make the a site available on my school web page for students to visit.
4. http://fractalfoundation.org/images/

Pascal’s Triangle

teachshirl — Sun, 01 Nov 2009 09:09:04 +0000

The pattern that I saw first were the 1′s down both sides of the triangle. Then I saw the consecutive numbers in the second row down both sides. From this point I noticed that the numbers above the beginning of the next diagonal was the sum those two numbers. As I continued with this pattern I found this was consisant thoughout the triangle.

1 + 1

1 + 2 + 1

1 + 3 + 3 + 1

1 + 4 + 6 + 4 + 1

Algebraically the pattern looks like this. 1a when a =1. We know from the Identity Property for Multiplication that the product of a real number multiplied by 1 is that number.

1a + 1a

1a + 2a² + 1a

1a + 3a³ + 3a³ + 1a

1a + 4a³ + 6a³ + 4a³+ 1a

And so on…

Note: Unfortunately I am unable to arrange my Triangle so that it remains a triangle, which would shows the pattern more clearly.

Working with the Definition of Linear Patterns

teachshirl — Sun, 01 Nov 2009 08:18:17 +0000

Definition: Non-traditional patterns are simply patterns that do not follow a repetitive format. (Taken from the module)

Kid friendly definition: Linear patterns are patterns when graphed create a line.

Formal Definition: If the plotted points make a pattern, then the coordinates of each point may have the same relationship between the x and y values. In such a case, the x and y values are connected by a certain rule.

A linear pattern is said to exist when the points examined form a straight line. (http://www.mathsteacher.com.au/year8/ch15_graphs/02_linear/patterns.htm)

Looking at the two definitions my “kid friendly” definition is less intimidating because the math, other then graphing, is not mentioned. In the formal definition the students see the use of variables that have relationships and follow a rule, and they get nervous about having to find numbers and memorizing rules and decide they can not do it before they try.

To make the students understand these definitions I would first let them graph coordinates and find the pattern creating the line. Then we would write an equation to fit the pattern. Once that is complete I would introduce the formal definition and show them that they followed it without knowing it.

My Reflection on Math Myths

teachshirl — Sat, 31 Oct 2009 21:16:07 +0000

As a student I thought the myth about Boys being better at math than Girls was true. I mean I completed up through algebra /trig and there were only 5 or 6 girls in the class. I actually stopped at that point because none of my friends were going any further. I met all of my math requirements, so why keep going especially if I was going it alone. Another myth that was hard for me was the “it’s wrong to count on your fingers”. It was not so much the counting but the using my fingers for the 9s times tables. For what ever reason I had a mental block when it came to them. It may be I had several ways to solve without memorizing.

As a teacher I see that Boys and Girls are both equally capable in math. In fact I find girls can be so much better at explaining processes and showing their work then boys. I think one reason girls loose ground, especially in middle school, is because this stage in their lives is all about who likes you and who doesn’t. If a girl can find a group of girls that are studious then they will stick with it, otherwise fitting in is more important.

“Counting on your fingers” is acceptable to me if it helps the students in their computation. I tend to think it is a habit, they have been doing for so long they can’t stop. It may also be a comfort thing, they know they can get a correct answer so they’re going to keep doing it. As much as I wish they did not have to do this I do not say anything to them to discourage it. I have been there. I actually show my students my tricks for the 9 facts just in case they can use them.

I have to say I like the questionnaire attached to this chapter. I am going to share this with my math team and see if we want to use it in the classroom. I think if we can see what our students “believe” will help use teach them better.