8-B-2 Reflection on Blogging November 25, 2009

8-B-2 Reflections on Blogging

Blogging was the most burdensome part of this course.  This is the first time I blogged and it never worked for me.  When I typed in my entries, I could only see a small portion of what I was typing until I pressed post.  More than half the time I posted comments for people, they vanished, never to be found again.  Until I get further instructions on blogging, I will not be continuing.

 

I learned that I’m getting old.  I never understood how or why people could not use a computer or email and now I understand.  I am so impressed by the fabulous math lessons teachers are creating by having the student’s blog.  I want to learn how to do this so that I can incorporate similar activities into my math classes.

 

My favorite find from this class is the website of equations from Module 7.  The Algebra Quiz Game is something that I have been looking for for a long time.  Not only can you adjust the ability and time but you can get a print out showing how successful the students were and broken down into categories.

 

I have started using journals since this course began and I would love to some day use blogs too.  I think writing about math is an important concept that I have overlooked before.

8-B-1 Factoring Quadratics November 25, 2009

8-B-1 Factoring Quadratics

ax^2 + bx + c

1. Multiply the first and last coefficient together (ac).
2. Find the factors from step one that add up to the middle term (b).  ***A factor tree may help!***
3. Rewrite the trinomial as a polynomial with 4 terms by replacing the middle term with the two factors found in step 2.
4. Using grouping to factor (Pair up the first two terms and factor.  Pair up the last two terms and factor.).
5. Write your factors as a binomial, write what you were left with once you factored as another binomial.
6. Check by multiplying the binomials (F.O.I.L.).

I actually type out these steps for my students and then have them paraphrase my steps once they get comfortable with factoring.  This shows forces the students to think about what they are doing and not just memorize steps that may not make sense to them.

Reflection of 5-A-4: Defining Equations and Functions November 7, 2009

After reviewing my classmate’s definitions, I would absolutely add more to my definition and explanation of the terms.  I would now have the students journal about functions (the inputs and outputs).  I love the idea of using graphic organizers to compare and contrast the different functions.

5-A-3: My Definition of Equations and Functions November 5, 2009

My Definitions of Equations and Functions

 

Equation- a problem with an equal sign.

Function- a pattern or rule where you use a given number (x-values) and solve (y-values)

www.mathplayground.com has great graphics and activities with functions.

The Magic of Proportions November 5, 2009

The Magic Proportions

Thanksgiving Time, a wonderful time to gather with family and eat good food.  It’s time to dig through the recipe box and find Grandma’s famous apple pie recipe.  The recipe calls for 4 apples peeled and cored, and 2/3 of a cup of butter.  Due to popular demand I need to make three apple pies.  To figure out how many apples and how much butter is needed for all the pies I can create proportions.  A proportion is a comparison of two numbers. 

              4 app      x app                2/3 c butter     x cups

            ——-  =   ——-                 ————    =   ———–

              1 pie        3 pies                 1 pie       3 pies

To solve, I can cross multiply.  4 times 3 is 12, 1 times x is x.  That means I need 12 apples total.  For the butter, 2/3 times 3 is 2, 1 times x is x.  I need two cups of butter.

Now when I go shopping for my ingredients I will be sure to buy enough so that I’m not running back to the grocery store.

5-D-2: Applets November 5, 2009

Exploring the World of Applets

 Line of best fit is one of my least favorite concepts to teach.  I find it difficult to show the students where the line should be created.  It even more difficult for the students to take notes on, copying down points and then I run around the room checking everyone’s line of best fit.  The marathon activity on mathforum.org is a wonderful way for the students to practice with creating lines of best fit, as well as reading the graph and making inferences. 

 

http://mathforum.org/escotpow/puzzles/marathon/applet.html

 

Math Myths October 27, 2009

Math Myths

 

#5- There is always one best way to do a math problem.

            Students get so nervous if someone shows them a different way to solve a problem.  Every year I have students tell me that a parent or sibling showed them a different way to solve something.  Some are panicked about it and other students think that I must have showed them the incorrect way.  I tell students all the time that there are multiple ways to get to a solution and as long as the student can verbalize and show how they got to the solution, it is fine.  Showing students too many different ways to get to a solution can be confusing so I try to do things consistently, however when students are struggling with a concept I will usually show them alternate methods to solve it, on a one-on-one setting.  By encouraging and praising the students for being able to show their work and verbalize their thought process, students are finding it is possible to get a correct solution by solving it differently.

 

#7- It’s wrong to count on your fingers.

            Some students still struggle with basic addition and subtraction even in 8^th grade.  I must admit it does aggravate me to see students counting on their fingers at this age level.  I actually find it sad that students are that weak with their basic computation skill.  Since I have been teaching, I have come to terms with the finger counting and now I feel if simply using their fingers will help get them to the solution, why not use your fingers.  I also use number lines to help the students add and subtract numbers larger than their ten fingers.  Showing students how to find the correct answer is my new approach to teaching.  If there are abaci, number lines, and drawings to aid in the finding of the solutions, I will take the time to show the students how to use these aids.  I’m still not on board with calculators yet.  Most of my students seem to forget everything as soon as they are given the opportunity to use them.

 

 

Translating Pattern Narrative October 27, 2009

Pattern Narrative in Formal Language
Pascal’s Triangle is symmetrical.  Each side and row of the triangle are symmetrical (both sides are the same).  The first row of the triangle is a 1, and every other number in the triangle is the sum of the two numbers diagonal to it in the row about it.

Non-linear Pattern Web Quest October 27, 2009

Nonlinear Patterns and Fermat’s Theorem
Were there ideas or concepts you were not familiar with?  What were they?
I am not familiar with Fermat’s Theorem, actually I’ve never heard of it.  Fermat’s Theorem takes the concept of the Pythagorean Theorem, one of my favorite concepts to teach, and expands it.  He asks the questions of what would happen if we raised the a, b, and c, to a power higher than two.  Fermat hypothesizes that it is mathematically impossible to find three non-zero numbers for a^n + b^n = c^n when n is greater than two. 

What images did you find particularly striking?
I find this amazing that with all the number combination in math, this theorem is so hard to prove. 

How can you adapt this web quest activity for your classroom?
I would like to use this as an extra credit activity with my honors students.  I find that the honor students do not like to think.  They just want to regurgitate what is being taught without having to think or analyze.

Fibonacci and Phyllotaxis and Prime Numbers
Were there ideas or concepts you were not familiar with?  What were they?
I am familiar with the Fibonacci sequence; I remember studying it in a methods course in college.  I am unfamiliar with the term phyllotaxis; however I have learned that it is a term for plant leaves.  The arrangements of plant leaves unfold follow the Fibonacci sequence.  It allows the leaves to be spaced so that the necessary amount of light can reach them.

What images did you find particularly striking?
The Fibonacci sequence is a very visual topic.  The sequence shows up so often in nature, flower pedals, pine cones, and tree rings are just a few places that can visually depict the Fibonacci sequence. 

How can you adapt this web quest activity for your classroom?
When discussing the Fibonacci sequence, I could have the students find objects in nature and bring them in to class.  From the contents that they bring, the students could write about the Fibonacci sequence.

Nonlinear Patterns within your home or work:
The tiles on my kitchen floor are a nonlinear pattern.  I have 3 different size tiles in my kitchen that do not show a linear pattern.  Two tiles are square (one is 1 foot by 1 foot; the other is 4inches by 4inches).  The other tile, a rectangle (2 inches by 8 inches) and this tile is laid in two different directions, some are vertical, others are horizontal.

Defining Linear Patterns October 27, 2009

Non-traditional Pattern

Kid-Friendly Definition of Linear Pattern- a pattern that will make a line when graphed.

Formal Definition of Linear Pattern- “A linear pattern is said to exist when the points examined form a straight line.” http://www.mathteachers.com.au

There is not much of a difference in my definition and the formal.  I try to have my students break down the root of the words to see if it gives them clues, rather than memorizing definitions.  The first four letters of the word LINEar are line, therefore, it will make a line when plotted.