Archive for October, 2009

5-D-2: Applets

Posted in 1 on October 16, 2009 by coltswet

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


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.

Putting Pascal’s Triangle into Formal Terms

Posted in 1 on October 7, 2009 by coltswet

Pascal’s triangle I notice is a large triangle containing many smaller triangles in its interior. The two outer edges of the triangle are made up of the number 1.  As we move down a level from the peak we create new triangles.  Now you must follow a vertical line from the peak of this outer triangle to the bottom of the triangle to understand my next explanation.  Each time we move down this vertical line from the peak we get a larger number. This number is determined by adding the sum of the previous interior triangles steps. For example, The first number after following our vertical line down the center of our original outer triangle is 2. We get this total by adding 1+1, which is the first two steps that bring us down to this level of our vertical line. The next number on this vertical line is 6. We get this sum by adding the previous 3 steps sum which is 1+2+3. So each time we take a step down this original vertical line we add another step in our sum.  Once you determine the pattern, you can repeat this process to expand outward in the triangle.

Working with the definition of linear patterns.

Posted in 1 on October 5, 2009 by coltswet

Nontraditional patterns are simply patterns that do not follow a repetitive format.

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.