today in math 12-14-09

Today in math class we reviewed the scale factor,and similar figures. The scale factor is the number used to multiply the x and y cordinates. For example if the scale factor was two then the x and y cordinates would be multiplied by two times the original cordinates. Similar figures are any shapes that have corresponding angles of equal measurements. For example b is similar to a and the scale factor for a to b is 2.

__
[__] a ____
[ ]
[____ ] b

Stretching & Shrinking Scale Factor

Stretching & Shrinking Wrap Up 2.3 Rr

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Today we Learned

Today in math we learned about how similar shapes are scaled, and we used a program on the computer to show us how you change the side lengths and the position of a similar figure on a grid. Using the scale factor we learned if you multiply a number by both the x and y axis you will get a corresponding figure. The example Ms. Favazza gave us was that if you multiply a rectangle with dementions of 3cm width and 2cm height by 3 you will get a figure that is corresponding that has a 9cm width and a 6cm height, that is exactly 3 times larger than the original image. On the computer program geometric sketchpad where you could change the scale of the image, you could make it both corresponding and not, you could also change it so the image would be parralel or above the original image.

Stretching & Shrinking Zug

Zug Rr

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Moving a shape on a grid

Today in class we were reviewing formulas and the effect on the x and y axis. When you add to the x coordinate the object moves to the right. When you subtract from the x coordinate the coordinate moves to the left. When you add to the y coordinate the shape moves up and when you subtract the shape moves down. An example would be hat 1, 2 and 4 are similar because hat 1 and 2 are moved to a different place. Their formulas only include adding and subtracting so the size or shape never changes. Hat 4 is reduced by two or times by 1 half. Since it was that on both axes, they were both reduced by the both amount leaving them the same shape but a different size. When you multiply the coordinates by a fraction or a decimal the shape or object gets smaller. If you multiply it by a whole number the object will get bigger and is similar. If both coordinates are multiplied by the same number the image is similar. If they are multiplied by different numbers the image is an “imposter” or not similar.

Example: What rule would make a hat with a line segments twice as long as Hats 1 and moved 8 units to the right?

(x+2, 2y+3)=Hats 1 formula

(2x+10, 2y+3) would be one answer because 2x and 2y would be the twice as long part. X+2+8 would be the 8 units to the right but you have to take notice that this is for Hat 1 and so you must add two to x because that was in the Hat 1 formula. So 8+2 is to. Same thing with y.

Stretching & Shrinking problem 2.2 Hats off to the Wumps continued

Stretching & Shrinking 2.2 Summary + Tests For Similarity

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Tuesday December 8, 2009

Today we compared the Wumps. Glug and Lug are impostors because their formulas do not multiply x and y by the same number. This makes them not similar to Mug Wump because Glug and Lug are either long and skinny or short and fat. If the Wump is not an impostor (like Bug, Zug, and Mug) they are similar figures to Mug. Also, the area of the Wumps do not go up at a steady rate. The area changes differently. For example, the area of Mug's mouth equals 4, Zug = 16, and Bug= 36. When our group compared the Wumps, our notes were:

• all of Zug's features are twice as long as Mug's
• Glug is 3 times taller than Mug
• Lug is 3 times as wide as Mug
• Lug is 24 units wide and 7 units high
• Mug is 8 units wide and 7 units high
• Zug is 16 units wide and 14 units high
• Bug is 24 units wide and 21 units high

Stretching & Shrinking problem 2.2 Hats off to the Wumps

Stretching & Shrinking 2.2 rr

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Pixels, and Similarity

Today in class we learned about pixels. In old video games things are more square and unrealistic. The more pixels you have the more expensive cameras are. Things are rounder the more pixels they have. We also learned that when the image is distorted it isn't similar to the basic image.

Stretching & Shrinking problem 2.1 Introducing the Wumps

Stretching & Shrinking 2.1 Rr

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area, perimeter, and corresponding

Today while we were correcting homework we talked about how hight and base meet at a 90 degree angle. When finding an area always do ase times hight. If it's a triangle then you would do the base times the hight times one half. In order to compare the parts of these triangles we use the terms corresponding sides. and corresponding angles. The rectangles angles are all 90 degrees. Corresponding can be sides or angles. It is also the same position on both sides. we learned today that corresponding means to be similar in many ways.

Scaling Up & Down

Our notes from Stretching & Shrinking Problem 1.3.

Stretching & Shrinking Problem 1.3 Rr

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Similarities In Real Life Compared to Pictures

Today in class we learned the similarities between an image and what actually happened.

In real life, things are balanced when it comes to size. In an image, everything is out of proportion. When we used computers in class today, we used a document called "rubber band", which was used to show the different sizes of proportion. There was a line with three points. The first point could be moved around and would decide the size of the image, the point in the middle was used to draw around the already existing figure, and the last dot on the right would draw the image as you traced over the figure. The image of something that happened may look like the situation, but really it's all out of proportion.

Stretching & Shrinking Problem 1.2

When enlarging a figure, what changes and what stays the same? See our notes from today's class.

Stretching & Shrinking 1.2 Rr

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Multiplying and Dividing Fractions, GCM, and LCM

Today in math we reviewed multiplying and dividing fractions. To multiply fractions; you reduce them and then multiply the numerators and then the denominators. Then you simplify. If you want to multiply mixed numbers you have to change them to mixed numbers. To divide fractions, you multiply the first fraction by the second fraction's recipricle. Also, we reviewed Gcf and LCM. To find two numbers' GCF you find the prime factorization of each number and the largest number they both have in common is the GCF. To find the LCM you put the factors of each number in a venn diagram (the numbers that they have in common go in the center) and then multiply all of the numbers together.

Multiplying and Dividing Fraction

Multiplying fractions is very easy. First, you reduce your fractions. For example, 2/3*1/2. You can divide the twos by two because the greatest common factor of both numbers is two. This is because one is a numerator and one is a denominator. So the fractions become 1/3*1/1. Then, you multiply the numerators and the denominators. In this case you get (1*1)/(3*1) so the answer is one third or 1/3.
To divide you do the same thing as multiplying but you multiply the first fraction by the reciprocal of the second fraction. For example, 4/5 divided by 3/6 equals 4/5*6/3. You can reduce before and after you find the reciprocal of the second fraction. The answer is 24/15 which can be reduced to 8/5 and that equals 1 and 3/5. Remember, when dividing always find the reciprocal of the second number and never the first.

Posted by Duncan D.

ADDING and SUBTRACTING FRACTIONS

Today in math class, after we went over our homework we learned how to add and subtract fractions. Adding and subtracting fractions is like adding and subtracting numbers except there is a numerator and a denominator. Both the numerator and the denominator are added and subtracted by each other so like the line thing that separates them is like a line separating two different kinds of problems. This is easy until there are letters that I forget what they are called come into play. When you add or subtract a fraction with a letter/symbol thing, you have to times the numerator by what ever the denominator was multiplied by. So three over five and W over 15. Because the two denominaters are 5 and 15, you divide and you get 3 so you do 3 times 3 and get for the other denominator 3W. This is adding and subtracting fractions

-Dan

Adding & Subtracting Fractions

Here's the work we did today with adding and subtracting fractions with negative numbers and variables.

5.3 Rectangles

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Converting Fractions to Decimals

Today in class we learned about converting fractions to decimals. You do this by dividing the numerator by the denominator.For example 4/5 is equal to .80. This is because 4 divided by 5 is 0.8 so that is the decimal. Sometthing a little more complicated is say -4 and 7 tenths is -4.7 because 4 is the whole number so thats where you get the 4 and 7 tenths is just the same as 0.7.

We also learned about about how to convert decimals to fractions; in their simplest form. All you have to do is 0.25=25/100=25/100 divided by 25 = 1/4. when doing this you always want to right the fraction in simplest form.

Also you can do 0.625=625/1000=625/1000 divided by 25 is 25/40 which divided by 5 is 5/8.

Least Common Multiple and Fractions

Here are our notes from today.

Ch. 5 2 Rectangles

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Least Common Multiples

Today we learned about least common multiples. The least common multiple of two numbers is the smallest number (not including 0 or 1) that is a multiple of both. It basically means that if there are two numbers, the least common multiple is the multiple that both numbers have in common. Example- What is the LCM(least common multiple) of 3 and 8?

Multiples of 3- 3, 6, 9, 12, 15, 18, 21, 24...

Multiples of 8- 8, 16, 24, 32...

LCM of 3 and 8- 24

Multiples do NOT mean factors. A non example would be to say that the least common multiple of 6 and 8 is 2. Don't get multiples mixed up with factors. Another way to find multiples is to do a venn diagram. Example- What is the LCM 16 and 36? It is not possible to do one on here, so I'll try my best. Put 16 and 34 in a venn diagram. 16 in one circle, and 34 in the other. Put what they have in common in the middle.

16 - 2*2*2*2 They have 2 in common. 34 - 2*17

Cross one 2 from each one.

That leaves 2*2*2*17-----2 cubed *17

8*17

LCM- 136

-Katy DiMuzio :)

Least Common Multiple

Our notes from today on finding least common multiple with prime factorization.

Ch. 5.1 - Least Common Multiple

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GCF of variable expressions, simplifyng algebraic fractions.

Today in class we learned about finding the GCF of variable expressions, and how to simplify algebraic fractions. Even though it looks hard finding the GCF of a variable expression its pretty easy. First you have to find the prime factorization of the number. Like if the number in the expression was 6 the prime factorization would be 2*3. After that you would write the variables out in expanded form. So if the whole expression is 6ab then when you write it out you would have 2*3*a*b. Then you find the common factors.

Example:#1
Find the GCF of 6ab and 8xy
6ab = 2*3*a*b 8xy = 2*2*2*x*y
They both have 2 in common so the GCF would be 2.

Then we reviewed equivalent fractions and also how to simplify fractions. Also we learned how to simplify algebraic fractions. First you have to write the prime factorization of the expression. Then divide the numerator and denominator by the common factors.

Example:#1
4xy^3/ 8ax^2=2*2*x*y*y*y/2*2*2*a*x*x= y^3/2ax

Example:#2
2mn/4m= 2*m*n/2*2*m=n/2

GCF of variable expressions, simplifying algebraic fractions

4.3b & 4 Rr

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hello class im excited to begin this learning journey with the rest of my classmates. This should be a differant new thing and a wonderfull thing at that, lets go red rectangles.

Primes, Composites, Prime Factorization

Yesterday in class we learned about prime numbers, composite numbers and the GCF of a number. A prime number is a positive integer that is not divisible without remainder by any integer except itself and 1, for example 7 is a prime number because its only factors are 1 and itself. A composite number is a number that is a multiple of at least two numbers other than itself and 1, an example of a composite number is 20 because its factors are 4, 5, 1, 20, 2 and 10 but 7 would not be a composite number, neither would 3, 5, 13, 23 and many more. The GCF or greatest common factor of a number is the largest number that is a common divisor of a given set of numbers. An example of this that the GCF of 10 and 20 is 10 because 10 is a factor of both numbers and its the biggest factor for both numbers. Yesterday we also learned how to find the prime factorization of a number by doing the upside division rule. We also learned that you can find the GCF of 2 numbers by using a venn diagram.

by Quillen B

Primes, Composites, Prime Factorization

Class notes on prime and composite numbers; how to use prime factorization to find the greatest common factor.

Primes & Composites, GCF

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Today in math, we learned about exponents. Exponents can be used to show repeated multiplication. For example: 2 to the 5th power=2*2*2*2*2=32 NOT 2 to the 5th power is equal to 10. We learned that a power has two parts: the base and an exponent. The base is the main number, and the exponent is the raised number.
Examples:
4*4*4*4= 4 to the fourth power
3*x*y*y=3xy to the second power
We also went over the divisibility rules for numbers 1,2,3,4,5,9, and 10.
Examples:
1: every number is divisible by 1
2: ends in 0,2,4,6,8,10
3: sum of digits are divisible by 3
486~~~4+8+6=18 is divisible by 3
4: last 2 digits are divisible by 4
594~~~9+4=13 is not divisible by 4
5: ends in 5 or 0
9: sum of digits are divisible by 9
548~~~5+4+8=17 is not divisible by 9
10: ends in 0

Divisibility Rules, Factors, Exponents

Lesson on Chapter 4.1 & 4.2

Chapter 4.1 and 4.2

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Multiplying & Dividing Integers

Notes from today on multiplying and dividing integers.

Multiplication

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Subtracting Integers

Here are the notes from today's lesson on the subtraction of integers.

Subtraction of Integers

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Adding Integers

Notes from today's lesson on the addition of integers.

1 5 Rr

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Pre Algebra 1 -4 Integers & Absolute Value

Notes from today on integers, opposites & Absolute Value.

1 4 Rr

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Variables & Patterns Problem 3.1

Writing Equations

Variables & Patterns Problem 3.1

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Variables & Patterns Problem 2.1

Here are the notes from today's lesson.

Variables & Patterns Problem 2.1

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Introduction to Variables & Patterns

Here are the notes from class on Tuesday, Sept. 8, 2009.

V&P Intro To Unit, Jj

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Ms. Favazza'a Wordle

This is a Wordle I created that shares a little of who I am as a person. You will create one with your Glyph assignment next week.

Please make a comment about my Wordle and answer the question: "What do you want people to know about you when you meet them for the first time?"
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Welcome!

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