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.

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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.

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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!

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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.

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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.

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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

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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?

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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Linear Patterns- A pattern that moves in a straight line and is easy to notice.

Formal Definition of a Linear Pattern- A** linear pattern** is said to exist when the points examined form a straight line

My definition and the researched formal definition of linear patterns are very similar in the fact that they both mention a straight line. The word Linear tells us that were evaluating something that is in a straight line. Pattern tells us that were looking for something that is repetitive. The only difference that I noticed is that in the formal definition they mention “points”, which I presume they are talking about on a coordinate grid.

I could explain to my students that in order to determine the linear pattern, we must look for the repeated process throughout a graphed line. We must look at the rise compared to the run of a line that is graphed.

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**Myth 1:Boys are better than girls**

While a student in school, I noticed that in many of my upper tier courses the class was mainly made up of boys. At that time, I was unaware of what was taking place but I believe that it was mainly because that’s what we were told and female students looked at it as a boy’s subject, so they did not pursue it as heavily. I also feel that boys did better in math because it was “quick” work and not a lot of explanation.

Now as a teacher, I am noticing that my female students are really overcoming this myth. I believe now that we put a lot of emphasis on writing in math such as open-ended response questions, female students are starting to excel more than boys. I also feel that the stereotype of math is only for boys is being overhauled due to the fact that math is a stronger focus for getting into college and starting careers.

I always tell my students that any student can be successful in math as long as they are willing to pay attention, practice, and ask questions. I also let them know that math is very important for being successful in their future. In this day of age, women are competing with men in every field, which means that no subject is only one gender.

**Myth 2: There is always only 1 good way to solve a problem**

While a student in school we were always taught that you needed to follow a certain process to find an answer and if you were unable to do so, you would not excel in that area. This had a very negative effect on me as a student, because I sometimes did not find it easy to work on a problem using the method of the teacher. I would struggle to focus on the lesson’s because of this and often lost credit for not showing work.

Currently, I teach my math lessons using the PowerTeaching approach. In this approach, the teacher teaches a lesson showing the standard approach to complete a task. However, encourages students by expressing to them they can use different methods to complete the task. Part one of the lesson is called Active Instruction. Part two of the lesson involves students working in Team Huddles where students work together to complete their task by way of the teachers methods or their own. This allows students to learn a concept using multiple approaches.

By using this approach, I have encouraged students to by all means, use whatever approach they are comfortable with to solve a problem.

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