Desman

The Desman project was a fun project. I enjoyed figuring out the different equations and applying them to my own Desman. Seeing the equations plugged in and watching them create something on my graph was awesome. Something that was challenging was the initial figuring-out of the equations. I used Mr. McCune's example graph in order to find the numbers that would work with my graph when I got stuck. This project was fun overall.

Lessons 8.1 - 8.3

8.1

A polygon is convex if no line that contains a side of the polygon passes through the interior of the polygon.

A polygon is concave it at least one side that contains a side of the polygon passes through the interior of the polygon

A polygon that is not convex is called concave

A polygon is equilateral is all of its sides are congruent. 

A polygon is equiangular if all of its sides are congruent. 

A polygon is regular if it is both equilateral and equiangular.

Nothing in this chapter really challenged me much. Everything was fairly easy for me.

8.2:

Polygon Interior Angle Theorem:

The sum of the measures of the interior angles of a convex polygon with N sides is (N-2) x 180 

Polygon Exterior Angle Theorem: 

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex is 360 degrees

Everything in this chapter was easy. The most confusing thing was probably the exterior angles and where in the polygon they were located.

I can remember the exterior angles by extending the sides of the polygon and making sure that each angle is facing the same direction.

8.3:

The amount of surface covered by a figure is called its area

Area of a square:

Area = Side (squared) 

Area of a rectangle:

Area = (base)x(height) 

Area of a complex polygon:

To find the area of a complex polygon, divide the polygon into smaller polygons whose areas you can find 

Nothing in this chapter was challenging for me.

Overall:

Overall, I learned the different kinds of polygons, how to find their areas, and was able to find the measure of a specific angle in a polygon, whether it was interior or exterior.

The most challenging thing overall was trying to find the exterior angles of a polygon. I wasn't sure where exactly the exterior angles were located and to which way they were facing. Once I extended the sides of the polygon, I eventually found which way the angles were supposed to face and then find out what each angle measured.

Mark 2:1-11

   In the book of Mark, Jesus comes to Capernaum to preach. The streets flooded with people so not everyone could fit in the building he preached in. Four men brought a paralyzed man to see Jesus, but they could not reach him due to the large numbers of people. The men lowered the cripple through the roof of the building Jesus was in. Jesus god the man that he had been forgiven for his sins, and commanded the man to walk out of the room, and so, he walked. 

   Something that stood out to me the most was the fact that before allowing the paralyzed man to walk, he forgave him of his sins. What the people didn't understand was the fact that sins were more crippling than a disability. Jesus freed the man from being paralyzed, but he also freed him from his sins which is more important. 

7.4 - 7.6

7.4: SSS and SAS Similarity

SSS Similarity Postulate:

   If the corresponding sides of two triangles are proportionate, then the two triangles are similar.

SAS Similarity Postulate:

   If an angle of one triangle and the length of the sides that include these angles are proportionate, then the triangles are similar.

Nothing was difficult in this section

7.5: Proportions and Similar Triangles

Proportionality:

   If GP:PH = JQ:QK then GH and JK are divided proportionally 

Triangle Proportionality Theorem:

   If a line parallel to one side of a triangle intersects 

the other sides, then it divides the two sides proportionally.

Converse of the Triangle Proportionality Theorem:

   If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Midsegment Theorem:

   The segment connecting the midpoints of two sides of a triangle is

parallel to the third side and it is half as long.

Nothing in this section challenged me

7.6: Dilations

Dilation: 

   A dilation is a transformation with center C and scale factor K that maps each point P to an image point P(prime) so that P(prime) lies on CP and CP(prime) = K x CP.

   A dilation maps a figure onto a similar figure called the image.

   In a dilation, every image is similar to the original figure.

Types of Dilations:

   If the image is smaller then the original, the dilation is a reduction.

   If the image is larger than the original, the dilation is an enlargement.

Scale Factor:

   The scale factor of a dilation is the ratio of CP(prime) to CP.

   

The most challenging thing in this section was the scale factor. I learned that, once I found that CP(prime) is always over CP, the scale factor wasn't hard to figure out.

Overall:

   Overall, I thought the most challenging thing was the scale factor and how to find it. I eventually figured out that CP(prime) is over CP and from there, I could find the ratio of the scale factor. 

Chapters 7.1 - 7.3

7.1: Ratios and Proportions

A ratio is a comparison of a number a and a nonzero number b using division.

    Ratios can be written in four different ways.

    Ratios are usually written in simplest form.

An equation that states two ratios are equal is called a proportion 

    In the proportion A:B = C:D, the numbers B and C are called the means, and A and D are the extremes 

In a proportion, the product of the extremes is equal to the product of the means

In this lesson, the means and extremes were the things to trip me up the most. I learned to just remember that, when set up in factor form, the means were always the bottom number of the first listed ratio and its diagonal, and the extreme was the top number of the first ratio and its diagonal.

7.2: Similar Polygons

Similarity:

Two figures that have the same shape, but not necessarily the same size are called similar

Similar Polygons:

If corresponding angles are congruent and corresponding side lengths are proportional, then the two polygons are similar polygons.

Scale Factor:

If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor

Determining Similarity:

   1 Check that corresponding angles are congruent

   2 Check whether the corresponding side lengths are proportional

Perimeters of Similar Polygons Theorem:

If two polygons are similar then the ratio of their perimeters is equal to their corresponding side length

This lesson was easy for me, and I didn't really have any problems.

7.3 Angle-Angle Similarity

Angle-Angle Similarity Postulate:

If 2 angles of one triangle are congruent to 2 angles of another triangle, then the two triangles are similar

In the lesson, the angle-angle similarity was easy and I didn't really have any issues with it.

Overall, the lessons were fairly easy and the most challenging things were the means and extremes. As the lessons went on, I learned how to differentiate between the tow of them and I don't have any concerns for these lessons going forward.

Personal Postulates and Theorems

I Love my Family

Statement                            Reason

I love my family                           God loves me

God loves me                           He is a God of love

He is a God of love                           Because He is                        

    Theorem

God is my Father

Statement                           Reason

 God is my Father                           He created me

 He created me                           The Bible says so

 The Bible says so                           Its God's word

Its God's word                           It just is

     Theorem   

I Like the Color Purple

    Statement                            Reason  

I like the color purple                           I just do

       Postulate     

   The first one of the theorems in my life is something I had never really had an answer to. I never actually thought about why I loved my family, despite the fact that they loved me. I found out that the reason I love my family is because God loves me. The second one of my theorems, is the fact that God is my Father. I actually knew why He was my Father, that being He created me and the Bible, His word, said so. The postulate I came up with is simple. I like the color purple because I just do. It looks terrible when I wear it as clothing, I never use it in any of my art pieces for school, and there are so many different colors for me to like. I like the color purple, and I can't prove why, so its a postulate. 

   In learning about personal postulates and theorems, I also realize that there are reasons for almost everything, big or small. Going forward, I will pay attention to my own postulates and theorems, appreciating how they affect me and my beliefs. I will also recognize other people's personal beliefs and respect them, knowing there is either a reason to them, or because they just are. 

       

                                           

       

Hour of Code

During class we were assigned to lear how to use codes to control what happened on our computer screens We were given the option to use either a "Frozen" themed template or and "Angry Birds" template. I chose Frozen, and got to make Elsa and Ana move the way I wanted to with the help of the Hour of Code steps. I really enjoyed this because I got to see how some of the electronic things I use everyday were programed to do their jobs. Something that was challenging was trying to figure out how many degrees the figure was supposed to turn to make the desired shape. I learned how to make simple commands on a computer and make something interact using those same commands. Something that was surprising was the fact that I eventually made around 36 different codes when playing a simple game! One code I used to make a cool shape that looks like a snowflake is listed below, followed by the finished product!

for (var count2 = 0; count2 < 10; count2++) {
  for (var count = 0; count < 4; count++) {
    moveForward(100);
    turnRight(90);
  }
  turnRight(36);
}

This assignment was very fun and a great learning opportunity!

GeomeTREE (octahedron)

A polyhedron is a solid shape with 6 plane sides. The way a polyhedron and a polygon are related, is that a polygon is made up of 3 or more sides, all connected at the endpoints with congruent vertices. A polyhedron is made of 6 or more polygons. For our geomeTREE, I made an octahedron. The shape consists of 8 triangles in 2 groups of 4 triangles each. These four triangles were formed into a pyramid shape and placed base to base with the other group of 4, also formed into a pyramid. The color palate in this shape included dark blue, light yellow, rose red, and dark green. The vertices of the ornament were where each triangle made a point with the others, bound by tape. all of the sides were intersected where the different triangles met. None of the planes were parallel; however, I found the triangles to form pyramids.

Reflection:
I worked on my own for this assignment and spent a class period and a half cutting the triangles out and trying to figure out how everything would fit, and then an additional 30 minutes of finally making the little polygons into the octahedron! I learned what a polyhedron was, and that the octahedron was not made out of octagons, but rather 8 triangles. I was challenged by the actual forming of the octahedron and how the triangles could make a 3 dimensional shape. I really enjoyed the in class time, cutting the triangles out of colorful paper, listening to the Frozen soundtrack, and talking with friends while working. If I had anything to change, it would be to make the shapes due before out test and before the weekend, though my class was the only group that faced this problem. 

 

This is my finished octahedron with my beautiful friend Ruthie in the background!

Polygons

A polygon is a plane figure that is formed by three or more segments called sides. Each side intersects exactly two other sides at each of its endpoints. Each endpoint is a vertex of the polygon.

My phone is a quadrilateral

This bag is a quadrilateral with small dodecagons (shapes with 12 sides)

This is a foam sponge, also a triangle

The scarf has, like, a ton of snowflakes with even more sides

The "F" on the book is a nonagon 

My "M" room letters are dodecagons

Favorites, Improvements, and Pride

The 3 things I have learned so far are that the long side of a right triangle is called the hypotenuse, I learned complementary and supplementary angles, and how to use a compass to make an equilateral triangle.

My favorite thing from math so far is making lines and triangles using compasses, which were cut out from a cereal box.

To make this class better, I would like to listen to music when we are doing our independent note taking. Music helps me focus, and I'm used to listening to music when I do my homework, study for tests, quizzes, etc.

One thing i'm proud of is the fact that, for the first time ever, I not only have an A in math, but this class is my highest grade overall. Math isn't hard for me anymore and its a whole lot more fun!

Difference Between Parallel and Non-Parallel Lines Cut by a Transversal

  A pair of parallel lines cut by a transversal would follow and apply to the theorems. Non-Parallel lines would not have congruent angles in the same places the theorem suggests, and would not show the same results parallel segments would.

Above is an example of parallel lines cut by a transversal, following the theorems and staying consistent.

To the right is a non-parallel line pair cut by a transversal. The angles, which should be congruent or supplementary to each other, are not due to false angle measurements. Angle 1 is clearly not the same measure as angle 5, which would follow the corresponding angle postulate.

Coplanar Non-parallel lines VS Skew lines

Non-parallel lines, which are on the same plane, are different from skew lines because the fact that skew lines use 3 dimensions in order to be called 'skew'. Non-parallel lines will eventually cross each other. Skew lines, due to their dimensions, will never cross or touch.

Parallel, Perpendicular, and Skew

In class, I learned what a skew line was, and also that a perpendicular line would only be considered perpendicular if it crossed with another line and made a right angle. Before this lesson, I thought that a perpendicular line could cross in any way, make an acute, obtuse, or right angle, and still be considered perpendicular.

Linear Pairs vs Vertical Angles

  Linear Pairs are two adjacent angles whose noncommon sides are on the same line. Vertical Angles are not adjacent, and their sides are formed by 2 intersecting lines. When finding a linear point, there is a line dividing 2 separate angles, and they share the same line on one side. Vertical Angles are across from each other, and share a common vertex.

   

Linear pairs are #'s 2 and 3 or  

4 and 1

Vertical Pairs are #'s 4 and 2 or

1 and 3

Law of Syllogism

  The law of syllogism basically states that if statement P= statement Q, and statement Q= statement R, then statement P= statement R. A syllogism is set up in an "if" and "then" format. For example:
                    "If the sky is dark, then it might storm"
The "if" portion of the statement is the hypothesis, and the "then" portion contains the conclusion.
                    "If the sky is dark" is the hypothesis.
                    "then it might storm" is the conclusion.
An example of a syllogism is:
                    "If it is time for lunch, then I will go to the cafeteria."
                    "If I go to the cafeteria, then I will eat."
                    "If it is time for lunch, then I will eat."

How Many Handshakes?

  For class, we were to find how many handshakes our group of 4 could do between ourselves. In order to find the number of handshakes total, we made small dot diagrams, similar to the one above, and we connected each dot in every way possible. Our solution, was that 4 people could do a maximum of 6 handshakes. In order to find the exact number of handshakes any group of any size could have, we had to find the function rule. For every rectangular function, the rule is n(n+1)÷2. So, we plugged in the number of people for "n" and got out the appropriate number of handshakes.

Desmos House

This is my Desmos house. The acute angles I noticed first were both ends of the roof. The obtuse angle, was the small space between the roof and the chimney closest to the top. The right angles include the windows, and the doorframe. the biggest challenge when it came to creating my Desmos house, was trying to figure out how to make a diagonal line for my roof. I eventually learned how to make one, thanks to Hunter.

Why Math?

  Math is used for personal, practical, and spiritual use. Personal uses include paying rent, giving tips, measuring certain household items, and baking. Practical things involving math include measuring building supplies, and measuring medication for patients. Math is used in biblical times, when Noah was building the ark, and had to use certain measuring requirements that God gave him. One doorway that impacts my daily life the most, is the personal aspects to math. I give the delivery man the right amount in tip money, and I measure things when I bake things from scratch. The verse Exodus 35:30- 36:2 stands out to me the most because it tells us to create using our God given talents. Practical spiritual windows are referred to in this verse. The practical aspect in this verse, is the creating of things, and spirituality comes in because of the biblical reference.

Hello World!

  Hello, my name is Madison. Right now the tree most important things to me are family, friends, and volleyball. This year, I'm looking forward to finding certain shape volumes and areas. I'm anxious about doing things with fractions, seeing that they have never been my strongest area in math. One thing that you might know about me, is that I enjoy alternative music and 80's music. I really like the bands Coldplay, Paramore, and Fall Out Boy.

Page 70 Questions

Page 70 #1:

  The difference between complementary and supplementary angles, is the fact that when 2 angles are complementary, their measurements will always add up to 90 degrees. When 2 angles are supplementary, their measurements will always add up to 180 degrees.
  I will remember the difference between the two, because this lesson clicked for me. I don't need any special way to depict the two, complementary means 90 to me, and supplementary means 180 to me.
  I learned that 2 angles that share the same complementary angle, are congruent. <4 + <5= 90 and
<5 + <6= 90. So <4 is congruent to <6.