Reflections on Blogging

Posted in 1 on November 4, 2009 by coltswet

I was very hesitant with blogging initially, but I developed many ways that I could use it to help students when they leave school.  I definitely think blogging is a great asset for teachers. As far as this year goes, I doubt I will use it with my students because I have a set routine for my current students.  There is no doubt in my mind that I will have this ready to go next year, when I can introduce my blog to students in the beginning of the year with my syllabus and on Back to School Night with parents.

Throughout the course I was able to learn a lot about myself and my views on math concepts.  By reflecting on my math background through the prompts given, I am now more attentive to student needs.

The one thing that I found very interesting in this course was using virtual manipulatives to help teach concepts.  I used several of them in my classroom throughout the past several weeks. For example, algebra tiles for integer operations and the Algebra Balance Scale.  My students were very receptive to both tools.

I already use journals with my students, however, I ve learned to use them more efficiently.  I will use blogging in the future with my classes to help keep students updated with homework, vocabulary, and class examples.  I think its a great way to reach students outside of the classroom.

Factoring Quadratics – in My Own Words

Posted in 1 on November 4, 2009 by coltswet

Quadratic Equation Example-  Ax² +Bx+C

In a quadratic equation, we have 3 terms. A, B, and C.  Our first term is x squared, our second term is a coefficient, and our third term is a constant term.  In order to factor a quadratic equation we must first determine the factors of the third term C.  Then we must determine out of those factors, which two can we add together to match our coefficient term.  Since our first term is squared we will start both binomials with x. (x+___)(x+__). Lets say that “B” is 5 and “C” is 6.  Since our two factors of six that we can add together are 2 and 3, we will complete our binomial with each term. Our final quadratic equation can be factored as this: (x+2)(x+3).  Using the foil method we would get x² +2x+3x+6. Now we combine the like terms we get x²+5x+6.

 

By paraphrasing the words from the “key information”, I was able to get a deeper understanding of how to factor a quadratic equation.  This was an interesting way to make the task more concrete.  I will use this method with my students in the final activity of my lesson in which we summarize the days concept by answering the essential question.

5-D-2: Applets

Posted in 1 on October 16, 2009 by coltswet

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

At this website you can find a game called “Algebra Balancing Scales”.  This game is a great interactive equation solver.  In this game you are given a one step or two step equation that you must first represent by dragging icons to the appropriate side of the balancing beam.  The nice thing about this game is that you are not allowed to move on to solve the problem until the scale is balanced.  If you do make a mistake, the computer will tell you what is wrong and allow you to tinker around until you get it correct.  The visuals are excellent and very easy to understand.  Once you set the scale up correctly, you are then able to solve the problem using inverse operations by dragging typing in commands.  As you type in commands the computer guides you along by showing how things cancel out from each side of the equation by keeping the scale balanced.

This activity is definitely one that I will use in my guided practice when discussing two step equations next week.  On my smartboard, the students will be able to help solve the equations and see it as a visual to help them understand the practice of solving equations. Great website!

5-B-1: The Magic of Proportions

Posted in 1 on October 16, 2009 by coltswet

It takes one large pizza of 8 slices to feed three adults.  This weekend, we are having 12 adults over to watch football. How many large pizzas’ should we buy to feed everyone?

I would write the ratio for 3 adults as such

8 slices =                 x amount of slices

3 adults                                    12 adults

In order to find out how many slices of pizza we need, we can cross multiply 8 slices by 12 adults to get 96.  We could then cross multiply 3 adults with “x” slices to get 3x.  Next, set up the equation 3x=96 to find that we would need 32 slices of pizza.  We could take it one step further to find out how many pizzas that would be by setting up a unit rate of 1 pizza feeds 3 adults so “x” pizzas feed 12 adults.  Which if we followed the steps earlier we would know we need 4 pizzas.

Problem 2

It takes 2 bags of peanuts to make twelve cookies.  How many bags would we need to buy to make 48 cookies? Set up the proportion as follows.

2 bags =    x bags

12 cookies           48 cookies

To solve:  Cross multiply 2 bags times 48 cookies and cross multiply 12 cookies by “x” bags. To get the equation 12x=96.  “X” would then equal 8, so by substituting this in for x we find we would need 8 bags.

Evaluating Your Own Definitions – Equations/Functions

Posted in 1 on October 16, 2009 by coltswet

After looking at several other blog posts, I would not really change my definition for either of my vocabulary words.  My reasoning for this is that in the blogs that I viewed everyone shared the same information that explained that an equation is about balancing two separate sides where an equal sign splits the number sentence into two parts.

The definition that I gave for function was also accurate with others.  We all included the words input and output.  I also noticed however that some classmates did not identify which variable represented the input and output.
I would have students create an equation for other students to solve. Here they would know their input and output before others. They would notice that it is much easier to find only one number value when given only one variable. Then I would have them change their totals to see how their value for the variable changes. Hopefully, they would notice that as one side of the equation changes, the other side must adapt to keep it balanced.

5-A-3: My definition of Equations and Functions.

Posted in 1 on October 16, 2009 by coltswet

Equation- a number sentence that compares one expression to another.

3 + x = 12

3x=15

20 – x = 10

We can look at these equations in a way that we are trying to find out what we can replace “x” with to make it balanced on both sides.  We can view an equation as a “seesaw”.  In order to make the “seesaw” balanced an even we must replace the variable with a number so that both sides have the same amount of wait.

Function-  something that is done to one number (x) to create a new value (y).

x (input)     1           2          3             4
___________________________                   Function Y= X +3

y (output) 4            5          6            7

Non-Linear Pattern Web Quest

Posted in 1 on October 8, 2009 by coltswet

Were there ideas or concepts you were not familiar with? What were they?

Up until this class I have never really researched or looked in-depth about the golden ratio.  I was also not very familiar with the pentagram until doing research and found how important of a role this figure played in a religous aspect. In short, I was not familiar with either concept, which led me to investigate this topic.

What images did you find striking?

File:Bolzani XP Pentacle.JPG

Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?

Some of the nonlinear patterns that I have noticed around my home are the seashells that we found at the beach and placed in my daughter’s sandbox.  I also noticed the fake stone that they used on the front of my house as having non-linear patterns as well.

How can you adapt this webquest activity for your classroom?

In my class, I would have to provide visuals of the golden ratio and basically keep it simplified to analyzing a pentagram.  I believe this concept is way too far advanced for middle school students and basically would only stick to using visuals to help students understand non linear patterns.

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