Voice thread on Transformations
Here is the link to my voice thread about transformations I saw on my field trip
A Place to share our mathematical understandings.
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Here is the link to my voice thread about transformations I saw on my field trip
The distance from the center to any point on the shape stays the same.
Every point makes a circle around the center.
With Rotational Symmetry, the shape or image can be rotated and it still looks the same.
How many matches there are as you go once around is called the Order.
Is there Rotational Symmetry of Order 1 ?
Not really! If a shape only matches itself once as you go around (ie it matches itself after one full rotation) there is really no symmetry at all, because the word “Symmetry” comes from syn- together and metron measure, and there can’t be “together” if there is just one thing.)
Examples:
A Dartboard has Rotational Symmetry of Order 10.
The US Bronze Star Medal has Order 5
Observe:
Rotations can be clockwise or counter clockwise (anti-clockwise).
After a rotation the image and pre-image are congruent.
A square has rotational symmetry of order 4 (4 fold)
A regular hexagon has rotational symmetry of order 6 (6 fold)
An equilateral triangle has rotational symmetry of order 3 (3 fold)
A rectangle has rotational symmetry of order 2 (2 fold)
A parallelogram has rotational symmetry of order 2 (2 fold)
Voice thread on Transformations »« Reflections and Symmetry from MathsNet and Math is Fun
Every point is the same distance from the central line ! … and …The reflection has the same size as the original image.
The central line is called the Mirror Line… and it doesn’t matter what direction the mirror line goes, the reflected image is always the same size, it just faces the other way.
A reflection is a FLIP over a line.
Labels
It is common to label each corner with letters, and to use a little dash (called a Prime) to mark each corner of the reflected image.
i.e. the original is ABC and the reflected image is A’B'C’
X-Axis
If the mirror line is the x-axis, just change each (x,y) into (x,-y)
Y-Axis
If the mirror line is the y-axis, just change each (x,y) into (-x,y)
Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry) is easy to recognise, because one half is the reflection of the other half.
REFLECTIONS FROM MATHSNET
OBSERVE:
For regular polygons (i.e. square, hexagon) the line of symmetry is in the middle of the figure and it bisects the figure into two congruent parts that match up exactly when flipped over the line of symmetry.
The letters “E” and “A” have one line of symmetry. The letter “H” has two lines of symmetry. The letters “F”and “N” have no lines of symmetry.
UNDERSTAND:
If the mirror line is the x-axis, just change each (x,y) into (x,-y)
If the mirror line is the y-axis, just change each (x,y) into (-x,y)
If the mirror line is y=x, just change (x,y) to (y,x)
If the mirror line is y=-x, just change (x,y) to (-y,-x)
Answers from website questions:
#14) Letters A, B, C and D each have one line of reflectional symmetry.
#15) E has one line of reflectional symmetry, F and G have none and H has two.
Rotations and Rotational Symmetry »« Transformations and Translation Notes
Transformations from Math is Fun
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Turn! |
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Flip! |
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Slide! |
| After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths. |
| In Geometry, “Translation” simply means Moving … |
… without rotating, resizing or anything else, just moving. |
Every point of the shape must move:
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| Example: if we want to say that the shape gets moved 30 Units in the “X” direction, and 40 Units in the “Y” direction, we can write:
(x,y) to (x+30, y+40)
This says “all the x and y coordinates will become x+30 and y+40″ |
Translations from MathsNet
OBSERVE:
The main point from the questions was that after a translation the image is ALWAYS congruent to the preimage.
UNDERSTAND:
The main point of these questions is that:
Reflections and Symmetry from MathsNet and Math is Fun »« Chapter 5: Patterns Leading to Addition and Subtraction
Look over Chapter 5 and do a blog entry answering the following question. Title it: Chapter 5 Introduction
In general, what will you be learning in Chapter 5?
Possible response: “In chapter 5 we will be learning about….”
Note: We will not be covering 5-6, 5-8, 5-9 or 5-10
Transformations and Translation Notes »« Commenting on Sketchcasts Assignment
You are to listen to the sketchcast of the student below your name in the class list, if your name is at the bottom of the list you are to listen to the student at the top of the list. If the student below you does not have a sketchcast yet move to the name below it.
As you listen it may be helpful to take notes on what was done well in the explanation, what you found confusing, ideas for improvement or questions that arise as you watch and listen. This way you will only have to listen to it once. Please keep in mind the commenting guidelines below that we discussed in class.
Commenting Guidelines:
As a blogger, you will be commenting on other people’s work regularly.
Good comments:
Chapter 5: Patterns Leading to Addition and Subtraction »« Finding the Percent of a Number Two ways
Title your blog entry: Finding the Percent of a Number Two ways
Copy and paste the following problem into your blog post and follow it with both of your sketchcasts:
The Girls A team made 28% of the 25 shots they took in the game. How many shots did they make? How many points did they score? (this is fictional) 
Your task: Using Sketchcast show your understanding of how to solve the above problem two different ways (using decimals and using fractions). Please make sure your explanations show your understanding of how to solve the problem using decimals and how to solve the problem using fractions and canceling out common factors. Post the sketchcasts underneath the problem that you pasted into your blog post.
Commenting on Sketchcasts Assignment »« Your First Blog Post
Title your post: Quiz 3-1, 3-2, 3-3 Reflection
In your post answer the following questions in complete sentences (either in paragraph form or copy the questions and answer in complete sentences):
1. Your quiz shows a good understanding of what mathematical concepts or skills?(Please be specific.)
2. Your quiz shows that you still need to work on what mathematical concepts or skills? (Please be specific.)
Your reflection should include your thoughts on your understanding of the following concepts/skills:
A. Ordering positive and negative decimals.
B. Locating a decimal on number lines with different intervals.
C. Prime factorization and writing your answer using exponents.
D. Finding equivalent fractions to a given fraction.
E. Adding and subtracting mixed numbers. Finding the common denominator. Simplifying your answer. Please mention your understanding of how to borrow when subtracting fractions and subtracting a whole number from a mixed number and subtracting a mixed number from a whole number.
THANKS!
Finding the Percent of a Number Two ways »« Welcome to our Math Class Blog!
This will be a place where you will be showing your understanding of the mathematics we are studying in class. I am really excited to see what creative ways we can come up with so that you can SHOW your understanding in different ways. One way I have already come up with is using Sketchcast. Please let me know if you have other ideas…maybe you could do a video blog entry… maybe you could make a voice thread. The options are endless and I know this will be a great experience for you and for myself. And so… let’s begin to shape our NEW MATH WORLD!
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