Wednesday, April 10, 2019

Geometry: Transformations Lesson

Go through this page to learn more about transformation. It is all around you. Did you are doing transformations everyday without realizing you are doing it? That's correct!

Any of these videos can be watched at quietube. Just drag the image to your toolbar on your browser. This will give you no ads or distractions.

Types of Transformations
Activity
Make interactive papers to go inside your interactive notebook as you learn about transformations.

Make a 4 flap interactive foldable. You can make an extra section on the top or on the side for the title, TRANSFORMATIONS. On the front of each flap, write: Translation, Rotation, Reflection, and Dilation. In the inside of the interactive, define the types of transformation and give examples of each. You will find these definitions on this page or the links listed on this page.

Use lots of color. Write anything found on this page or on the web in your interactive notebook that relates the transformations. If you prefer, you can just write these terms and definitions using lots of color instead making an interactive.

Watch these Videos
Translations Reflections and Rotation: Turtlediary @ YouTube
or
quiettube: Translations Reflections and Rotations
Note: The default setting is too slowly. I find it easier to watch at the speed of 1.25. To do this, go to "Settings" (it is next to "CC"). Select "1.25" under "Speed". This should be a better setting.

0:56 Reflections
4:12 Rotations
6:20 Translations
7:48 Examples of each type of transformation
8:46 Summary

Transformation Geometry (Translations, Rotations, Reflections): YouTube
or
quietube: Transformation Geometry (Translations, Rotations, Reflections)
This has worked out problem examples. It is very well explained using graph paper.

Three Types of Transformations
Harcourt Math Glossary: Transformations

Read this Animated Lesson
Transformation: Mathwarehouse

Play these Interactive Games
Translations and Rotations: Geogebra
RoboPacker: eduplace
Shapes in Motion Shape Game Sheppard Software's -- Choose which transformation the objects are.
Transformation Game for Kids -- Use the shadow of a house in this game.

Translation
Translation: A translation slides or moves an object along a straight line.

Translate = Slide or Move

Slide   Slide   Slide

Move
              Move
       Move

Watch this Animated Example
Harcourt Math Glossary: Translation Example

Read this Animated Lesson
Translations, An interactive activity: Mathwarehouse

Activity
Place a book on a table, desk, or floor.
Move the book in a straight line to another location without picking the book up.
Repeat this process several times or until you understand this type of transformation. 
What type of transformation is this?
Double click on the below rectangle to reveal the answer.
TRANSLATION
Play this Interactive Game
Translations and Rotations: Geogebra

Activity
Grab some graph paper. Make your own shapes. You can use the instructions at: Transformation Geometry (Translations, Rotations, Reflections): YouTube or quietube: Transformation Geometry (Translations, Rotations, Reflections) to complete your own translation transformation.

Rotation
Rotation: A rotation turns a shape by turning it around a fixed point.

Rotate = Turn

Turn, Turn, Turn

Watch this Animated Example
Harcourt Math Glossary: Rotation

Read this Lesson
How to Rotate a Point: Mathwarehouse

Activity
Place a book on a table, desk, or floor.
Move the book to the left or right.
Repeat this process several times or until you understand this type of transformation.
What type of transformation is this?
Double click on the below rectangle to reveal the answer.
ROTATION
Play these Interactive Games
Translations and Rotations: Geogebra
Rotation about a point ON the triangle Geogebra

Activity
Grab some graph paper. Make your own shapes. You can use the instructions at: Transformation Geometry (Translations, Rotations, Reflections): YouTube to complete your own translation transformation.

Reflection
Reflection: A reflection flips a shape over a line.

Reflect = Flip
This is like reflecting in a mirror. You flip the image. If you have a number 7 on your shirt, it will flip.
Flip, Flip, Flip

Watch this Animated Example
Harcourt Math Glossary: Reflection

Read this Animated Lesson
Transformations: How to reflect a point: Mathwarehouse

Activity
Place a book on a table, desk, or floor.
Flip the book to direct opposite side of where it was originally.
Repeat this process several times or until you understand this type of transformation.
Double click on the below rectangle to reveal the answer.
REFLECTION
Play these Interactive Games
Reflections: Geogebra
Reflection of the plane about a line

Activity
Grab some graph paper. Make your own shapes. You can use the instructions at: Transformation Geometry (Translations, Rotations, Reflections): YouTube to complete your own translation transformation.

When you translate, rotate, or reflect an object, they are all CONGRUENT.

Congruent
Congruent: Congruent is when a shape has the same size and shape.

Same size, same shape
Same size, same shape
Same size, same shape

Activity: Cut out a small piece of paper and fold it in half. On the front write Congruent. Inside behind the title, define what it is, and on the next part, give examples.

Watch this Animated Example
Harcourt Math Glossary: Congruent

After you do these three types of transformations, the shape is still the same shape and size.
Now, you can perform the next type of transformation which is called dilation.

Dilation
Dilation: A dilation is to make something larger or smaller.

Larger or smaller
Larger or smaller
Larger or smaller

A dilation is a similarity transformation (or a similarity).

You use dilation to show that objects are SIMILAR even though they are different sizes.

Steps to Dilation:
1. Multiply both coordinates by scale factor
2. Simplify
3. Graph (if required)

Read this Animated Lesson
Dilations in Math: How to perform dilations: Mathwarehouse

Play one or more of these Interactive Games
Properties of Dilation: Geogebra
Exploring Dilations: Ex. 19: Geogebra -- This is using Curious George's picture.
Dilation: Geogebra
Dilation #2: Geogebra

Activity
To understand dilation, grab some graph paper.
Draw a shape. It can be a triangle, square, rectangle, etc.
Follow the above steps, "Steps to Dilation", to make an object larger.
Repeat with different shapes.

Let's review some terms and definitions about transformation.
Translation: A translation moves or slides an object along a straight line.
Rotation: A rotation turns a shape.
Reflection: A reflection flips a shape over a line.
Congruent: Congruent is when a shape has the same size and shape.
Dilation: A dilation is to make something larger or smaller.

Now you know more about transformations. Enjoy transformations in your daily life. :0)

Note: More transformation resources located at: Geometry: Transformations.

Saturday, March 16, 2019

Recycle

SAVE THE PLANET -- PLEASE RECYCLE

You can recycle a lot of items. You can recycle most plastic bags, wraps, and films at your local grocery store. Go to this site to read more about recycling.

https://how2recycle.info/sdo

Friday, March 15, 2019

Prime Factorization

PRIME FACTORIZATION
This page is just a rough draft.

Prime and Composite Numbers
Prime Number: A whole number greater than 1 whose only factors are 1 and itself.
Composite Number: A whole number greater than 1 and has more than two whole number factors.

Factors

Activity
Write down a multiplication problem.
Label the factors. Label the product.

Example:
3 x 2 = 6
/     \     \
factors   product

Factors: A number that is multiplied by another number to find a product.
Product: The answer to a multiplication problem.

1.3 6th Grade Big Ideas Math

PRIME FACTORIZATION

Factors
Find all the factors of …
List the factor pairs.

Examples:
6
Factor pairs of 6: 3,2

18
1 X 18
2 X 9
3 X 6

Factors of 18:
1, 2, 3, 6, 9, 18

Factor pairs of 30:
8 factor pairs …

Activity:
Show Examples in Your Interactive Notebook

Factor pairs of:
___
___
___

Prime Factorization
Terms:
Prime Factors: These are prime numbers that divides into a number exactly.
Prime Factorization: Is a number that is written as the product of all its prime factors.
The prime factorization of a composite number is the number written as a product of its prime factors.

Examples:
So, if we want to find all the factors of _____, we just want to list all the ways we can get _____ using whole numbers and multiplying.

Let’s look at the number 18 again. Let’s find the prime factorization of this number. We can use a factor tree.
We write the prime factorization by factoring until only prime factors are in the product.
We start with two factors of 18. This can be any two factors of 18. Let’s start with _____ 2 X 9. What are two other factors that could be used? (3 X 6)

Factor Tree

    18
   /   \
  2    9
      /  \
     3    3

Step 1: Write down the number you are trying to find the prime factorization.
Step 2: 2 X 9
Step 3: 2 is a prime. 9 is a composite number.
Step 4: We can factor 9 as 3 X 3.
Step 5: Now all the numbers are primes, 2 x 3 x 3
Step 6: Writing the prime factorization using exponents, we have 2 X 3^2.
The prime factorization of 18 is 2 X 3^2.        
Check: 2 X 3^2      2 x 9 = 18
18 = 2 X 3^2

Activity:
Pick a number. Find the prime factorization for that number using a factor tree.

Example:
         72
        /   \
       8    9
     /  \  /  \
    2   4 3   3
       /  \
      2   2

The prime factorization of 72 is 2^3 x 3^2.

Prime Numbers and Composite Number
Activity: Foldable