Stretching & Shrinking Scale Factor

Stretching & Shrinking Wrap Up 2.3 Bt

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Scale Factors

Today in class we took some notes on scale facors. We found the shapes that were similar and then we found the difference between the similar figures. The rectangles that were similar were L, J, and N. The difference from L to J was 2, the difference of the area was 4. The difference from J to L was 1/2, the difference of the area was 1/4. The difference from L to N was 3, the difference of the area was 9. The difference from N to L was 1/3, the difference of the area was 1/9. the difference from J to N was 1 1/2 or 3/2. The difference from N to J was 2/3.
We also found the difference between triangles. The triangles that were similar were O, R, and S. The difference from O to R was 2, the difference of the area was 4. The difference from R to O was 1/2, the difference of the area was 1/4. The difference from O to S was 3, the difference of the area was 9. The difference from S to O was 1/3 the difference of the area was 1/9. Tghe difference from R to S was 1 1/2 or 3/2. The difference from S to R was 2/3.

Scale Factor

Today in class we learned about scale factors. A scale factor is the number that you multiply x or y by. For example, 3x, 3y, the 3's are the scale factors. The scale factor can be the number of times you multiplied the x or y. Also in class today, we did a geometry sketchpad. It was with a figure of zug and then a copy of zug (image). We also learned how to make the other image move up and down and to the side. If you add to the y axis the shape moves up and if your subtract from the y axis the image moves down. If you add to the x axis the image will move to the right. If you subtract from the x axis it moves to the left. We experimented with the images and found out some cool things.

Finally, we reviewed how if you multiply the x and y axis by the same thing you we make the image bigger or smaller. The image will also be the same. If you multiply two different numbers then the image won't be the same.This is Daily Scribe

That is what we did on Thursday december 10, 2009!!

Stretching & Shrinking Zug

Zug Bt

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Daily Scribe by Eli L.

Today in class, we learned that if you add or subtract to the verticies of a shape, it will move. When you add to the "x" axis, the shape moves right. If you subtract from the X axis, then the shape will move to the left. When you add to the Y axis, the shape moves up. If you subtract form the Y axis, the shape moves down. We also learned that if you multiply by a fraction or decimal, the shape gets smaller. The last thing we learned was that if the X and Y coordinates are multiplied by the same number, the shape stays similar, it just gets bigger. When there are different numbers, the shape will not be similar.
BY ELi L

Stretching & Shrinking problem 2.2 Hats off to the Wumps continued

Stretching & Shrinking 2.2 Summary + Tests For Similarity

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Math Blog Post

Today, we continued to work with the wumps. We grouped up and compared each wump, Mug, Glug, Bug, Zug, and Lug. We compared them mathmaticly, looking at things each wumps hieght, width, and side lengths. After we did that, we found that Glug and lug were imposters of mug because their lengths weren't stretched evenly. Zug and Bug aren't imposters because their lengths are evenly stretched out, meaning they were 2 or 3 times than the original mug.

After we found out the area of the non-imposters mouths. We knew Zug was twice as big as mug and bug was 3 times as big as mug. The areas don't follow that rule though. Mugs moth area was 4 units sq., zugs was 16 units sq., and bugs, was 36 units sq. That rule for finding the area is multiply the hight and width and that number is how many times bigger the wump is than the original, mug wump.

Math Blog Post

Stretching & Shrinking problem 2.2 Hats off to the Wumps

Stretching & Shrinking 2.2 Bt

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Enlarging Images by Percents

If you want to enlarge something by a percent, the perimerter and the side length will be increased by that percent, but the area will be different. For example: if you want to increase a square of 16 sq in. by 25%, you would need to find the side length so you can find the perimeter. You can multiply that by 4 since there are 4 sides of a square. The side length would be 4 sq in. for the original figure so the perimeter would be 16 sq in. To find the perimeter of the figure enlarged be 25%, you enlarge the sides by 25%. The enlarged figure's side would be 5 sq in. so the perimeter would be 5x4=20 sq in. To find the area, you would multiply the base and the height. That would be 5x5=25 in. sq. Don't forget about Mug Wump, Zug Wump, Lug Wump, Bug Wump, and Glug Wump, the video game! Remember that on the coordinates of the game characters, "start over" means literally pick up your pencil.

Stretching & Shrinking problem 2.1 Introducing the Wumps

Stretching & Shrinking 2.1 Bt

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Daily Scribe

Today in class, we learned about area, perimeter, percents and about corresponding sides and angles. We learned that to find the area of a square, rectangle or parallelogram you multiply the base by the height. Multiplying the length by the width is the same as multiplying the base by the height. We also learned that to find the area of a triangle you multiply the base by the height but then divide by two. We learned that the base and the height always meet at a right angle. For area, you want to take the height of a parallelogram or a triangle instead of taking the length of the sides, for the height. We learned about area is class.

Today we also learned about perimeter. To find the perimeter you add the length of all the sides together. In this case you do not take the height of the sides but you take the length of each side.

We learned today, how to find the length of the sides of an image from the original. There was one copy that was 75% and the other copy was 150%. We had to figure out the length of the sides of the images, using the lengths of the sides of the original. We also had to compare the length of the sides of the images to the length of the sides of the original, the angle measurements of the images to the original and the perimeter of the images to the original. Today we learned about percents.

Finally, we leaned about corresponding angles and sides. We learned that corresponding angles and sides are either angles or sides that are in the same place on each shape.

We learned about area, perimeter, percents and the definition of corresponding on December 4, 2009.

Scaling Up & Down

Here are our notes from Stretching & Shrinking Problem 1.3.

Stretching & Shrinking Problem 1.3 Bt

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Similarities

Today in class, we practiced drawing things that are similar, and we discussed what similar means. To be similar, is to have things in common. When an image is redrawn in a similar way, the first image that is referred to that is used to draw the second drawing is known as the original drawing. The second image that is similar to the original drawing is known as the image drawing. Today in class, we worked on a figure activity, and some things that were similar between the two shapes, is the general shape, the degrees of each angle, and the vertices. What was different about the two shapes, is the lines of each angle get longer or shorter, the size of each shape, the area of each shape, each length of the image is twice the length of the original, and the perimeter of each shape. This is what we did in class on December 3rd, 2009.

Stretching & Shrinking

What is the same in similar shapes? What is different? Here are our notes from today as we begin to explore similarity.

Stretching & Shrinking 1.2 Bt

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Today in math we reviewed for the test on GCF (greatest common factor), LCM ( least common multiple), adding, subtracting, dividing, and multiplying fractions and mixed numbers.

To find the greatest common factor of two numbers you figure out the prime factorization for each number. For example: 40 and 60.

40- 2*2*2*5

60- 2*2*3*5

then you find all of the factors that the two numbers have in common.

2 2 and 5 so the GFC is- 2*2*5 or 20

To find the least common you...

1. write the prime factorization

2. Use the greatest power of each factor

3. Write the LCM as a product

For example: 12 and 8

STEP 1

12- 2*2*3 =

8- 2*2*2- 2

STEP 2

2 to the second power * 3

2 to the third power ARE = TO 2 TO THE THIRD POWER *3

STEP3

two to the third power * 3 =

8* 3= 24

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To add fractions you have to find a common denominator. For example: 1/2 + 3/4=?

To find the common denominator you could multiply both denominators. Or you could divide the

denominators. In this case 2 goes into 4 evenly so the new fractions would be: 2/4 + 3/4=? Now

you add across but keep the denominator the same. so the answer is 5/4 or 1 1/4.

The same thing applies for subtracting fractions.

To multiply fractions all you do is multiply across.

To divide fractions, you keep the first fraction the same and flip the second upside down. For

example: 3/5 divided by 3/4, you keep the first fraction and change the second on to its

reciprocal 4/3 and change the division sign into a multiplication sign.

To add mixed numbers you do the same thing, find the common denominator and add the

add the fractions and then the whole numbers. Simplify if possible.

Do the same to subtract.

To multiply change the numbers into improper fractions, multiply across and then simplify.

Example-2 3/4 * 1 1/5 = 11/4 * 6/5= 66/2o= 33/10= 3 3/10

To divide change the mixed numbers into improper fractions. Then keep the first the same and

change the second one to its reciprocal. change the division sign to a multiplication sign.

Then simplify.

3 1/4 divided by 1 1/2= 13/4 divided by 3/2= 13/4 * 2/3=26/12= 2 1/4

=D =P =] =O

Today in class, we reviewed multiplying and dividing by fractions. Multiplying and dividing by fractions is easier than adding and subtracting by fractions.

When you multiply by fractions, all you have to do is multiply across. You multiply the numerators together, and the denominators together. For example:

2/5 * 5/8. You multiply the numerators, 2 and 5, together, then the denominators, 5 and 8, together, and you end up with 10/40, which can be simplified to 1/4ths.

Another example is 1/2 * 3/4. you multiply 1 and 3 to get 3 in the numerator, and 2 and 4 to get 8 in the denominator, so you get 3/8ths.

When you divide by fractions, you take the first number and keep it the same, and you multiply it by the reciprocal of the second number, which is the fraction flipped, so 3/4 would be 4/3. For example:

1/2 divided by 5/6, you first make it 1/2 and 6/5, then multiply, so 1/2 * 5/6 is 5/12ths.

Another example is 3/4 divided by 4/5. you switch around 4/5 to 5/4, and then multiply to get 15/12, which is equivalent to 1 and 1/4.

It is the same thing with negatives, except that if you are multiplying or dividing one negative and one positive, it will be negative, and if it is two negatives, it will be positive. For example:

-5/8 *1/2 is -5/16.

-3/4 *-6/7 is 9/14

Adding & Subtracting Fractions

Here is the work we did today with adding and subtracting fractions including negative numbers and variables.

Ch 5-3 Triangles

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Fractions, Decimals & Least Common Multiple

Here are our notes from today:

Ch. 5 2 Triangles

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Daily Scribe!

Today in math class, we reviewed turning fractions into decimals, and we learned that the least common multiple is the same as the lowest common denominator in a fractions. You turn a fraction into a decimal by dividing the numerator by the denominator. When you're turning a mixed number into a decimal, the decimal will be more than one, and the whole number will be before the decimal point. For example, if the mixed number was 2 and 1/10, the decimal would be 2.10 .

To find the decimal of a fraction, you can put the fraction over 100, then it is easier to find the decimal. For example, if you take 1/5 and put it over 100 as 20/100, it sound like 20 hundreths, which is written as .02 in decimal form.

We learned about two kinds of decimals called terminating and repeating decimals. A repeating decimal is a decimal that never ends, and goes on and on and on and on and on repeating the same 1 or 2 numbers. An example of a terminating decimal is 0.3176 because it doesn't repeat the same numbers on and on forever, and it comes to an end after 4 numbers. On the other hand, the decimal 0.33333 repeats the same number over and over again, which means it is a repeating decimal.

HOW TO TURN A REPEATING DECIMAL INTO A FRACTION!

1. Identify how many digits there are that repeat over and over again.

2. Place the repeating digits in a fraction over the same amount of 9's.

3. Simplify as much as possible.

For Example: the repeating decimal 0.66 would be 6/9, which can be reduced to 2/3

☺ BY ASHLEY V ☺

Daily Scribe

Today we learned about the Least Common Multiple (LCM). The least common multiple is the smallest number that two numbers have in common. For example the least common multiple of 10 and 30 is 30 because 10 times 3 is 30 and 30 times 1 is 30.

We also found out how to find the LCM using prime factorization. First you need to write the prime factorization. Next you need to use the GREATEST power of each factor, so if you had one number that was two to the third power and another that was two to the second, two to the third would go into the prime factorization. Then you write the least common multiple as a product.

This is what we learned in class today.

Least Common Multiple

Here are our notes from today on Least Common Multiple.

Ch. 5.1 Bt

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Today in class we learned about how to find he GCF of a variable expression and how to simplify and make equivalent Algebraic Fractions:

GCF in a Variable Expression:

First, you must find the prime factorization of the coefficient. Then write the variable in expanded form. Next , all you have to do is find common factors. It's that simple!

Examples:

8xy² and 6x³y

2*2*2*x*y*y 2*3*x*x*x*y

So, the GCF of 8x² and 6x³y is 2xy

Note: When finding the GCF of a variable expression always list the numbers in numerical order then the letters in alphabetical order.

You can also use a Venn Diagram to find the GCF:

8xy^{2 6x3 y}

2*2*2*x*y*y 2*3*x*x*x*y

Their similarities(which are underlined) would go in the middle.

Algebraic Factions:

To write Algebraic Fractions in simplest form, first write the prime factorization of the expression.

Then, divide the numerator and denominator by the common factors.

Example:

4ab^{2 2*2*a*b*b = b2}

16ac 2*2*2*2*a*c = 4c

GCF of variable expressions & simplifying fractions

4.3b & 4 Bt

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Yesterday in class we learned about primes and composites, greatest common factor (GCF), and prime factorization.

Primes and Composites

-Primes can only be divided by 1 and itself.
-Composites can be divided by more than 2 numbers
-1 is not a prime or a composite because it can ONLY be divided by 1
-Some examples of prime numbers are 2,5,7,11
-Some examples of composites are 4,6,9,12

Prime Factorization

-Prime factorization is a composite number written as the product of its prime factors
-Divide by prime numbers starting with 2

Example: Find the prime factorization of 18. To start you would divide 18 by 2 and get 9. The next step is to break 9 down even more. Since 9 is not divisible by 2 you go to the next prime number which would be 3. Then 9 divided by 3 equals 3. Last step is to put the two numbers we divided by and the end result next to each other. So the prime factorization of 18 would be 2*3*3.

How to Find GCF


To find greatest common factor you first have to find the prime factorization of the first number. Then you need to find the prime factorization for the second number. Then you make a compare the two numbers' prime factorizations. (To make this easier, you could make a venn diagram). the factors that are the same are the ones you are looking for. The highest common factor is your GCF.

Example: Find the greatest common factor of 16 and 28. to start you would find the prime factorization of the two numbers. The prime factorization of 16 is 2*2*2*2. The prime factorization of 28 is 2*2*7. you next compare the two prime factorizations. Seven is the greatest out of the two of them but since 7 is not in the prime factorization of 16, then it can't be the GCF. The only other common factor is 2 so that is the GCF. The greatest common factor of 16 and 28 is 2.

Primes, Composites, Prime Factorization

Today's notes on prime and composite numbers; how to find the prime factorization of numbers and the Greatest Common Factor.

Primes & Composites, GCF

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Divisibility Rules, Factors, Exponents

Lesson on Chapter 4.1 & 4.2

4 1, 4 2

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Multiplying & Dividing Integers

Notes from today's lesson on multiplication and division of integers.

Multiplication and Division of Integers

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Subtracting Integers

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

Subtraction of Integers

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Adding Integers

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

1 5 Bt

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Pre-Algebra 1-4 Integers & Absolute Value

Here are notes from today on opposite, integers and absolute value.

1 4 Bt

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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 class.

Variables & Patterns Problem 2.1

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How to make a coordinate graph.

Notes Monday, September 15

Variables & Patterns 1.2

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How to make a coordinate graph.

Notes from Monday, Sept. 14

V&P 1.2 Bt

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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?"
1. Click on comment.
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Welcome!

Hello! You found our class blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; for parents to find out "What did you do in school today?"; to share your knowledge with other students. Most importantly it's a place to reflect on what we're learning in math this year.

One key to being successful involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, contribute to the conversation and lets get down to some serious blogging!