https://drive.google.com/open?id=0B8mBmPY5lcozNmNwR0lZQzVKYlk

participation in blogging community

Using document camera in the class room

Using document camera in the class room

1. Look at Small Objects

Small text can quickly be brought to light using the zoom features on most document cameras. Instead of passing around items, they can be viewed by an entire class all at once.

Some manufacturers sell attachments that can be used on the end of a microscope! How cool is that?

2. Bypass Making Copies

The on-going fight with the school copier is over! Why spend the time and money to make 100 different copies that will be found on the floor or in the trash can the next day? Placing a book or passage under the camera will allow for students to discuss the text without the need of excess paper. You’re welcome, trees!

3. Make Images of Student Work 

Sharing student work can be tricky; a document camera allows you to take a photo of the item. This photo can be used for later classes or uploaded to the classroom website for parents and other teachers to access.

Now you will not have to keep up with the original item and can rely on a digital copy.

4. Maps

Roads and locations can be hard to see when showing 20+ kids one map at a time. Use the camera and the camera’s zoom feature.

5. Record Video

Many people don’t realize that the document cameras can also be great media tools. I use the camera to record myself working out a math problem; I then upload the video to my classroom website and YouTube account.

6. Magnify Rulers

Looking at fractions on a ruler? A fraction of an inch is hard to show without the help of zoom.

7. Digital Field Trips

You can point the camera towards the students or the teacher when connecting with other people around the world.

8. Time Lapse

Are you studying something that changes only a little bit at a time like the metamorphosis of a butterfly? This is a great way to show small changes over time.

9. Demonstrate an App on a Tablet or Phone

Some document cameras do not work well with the glare from tablet and phones, but if you find one that works well, you can use it to show an app or website. Some of my favorite tools are apps that students use on my classroom iPad. It is much easier to show the app one time to the entire class as opposed to individual demonstrations.

10. Peer Editing

Did a student do an excellent job on an assignment and you want to share their thinking with the rest of the class? Pop it under the camera and the entire group can see!

Students truly enjoy using technology. Using a document camera not only provides the classroom with another method for learning, but can open the eyes of students to things they may have never been able to see before.

How to teach using an interactive white bard

What is a SMART Board?

A SMART Board is a large, digital, touch-enabled whiteboard which outputs a video source such as the display from a PC, laptop or document camera. You can write on the board in digital ink with a special pen and you can interact with PC applications or document camera images on the board.

How to start the SMART Board using...

...a remote control

1. Log on to the PC Press the red power button on the remote control to turn on the projector Wait for 30-60 seconds for the projector image to display on the screen The SMART Board is ready to use when the indicator light on the bottom right of the board is a steady green. When pressing the power button on the remote, you may see a message "Press off?" This means that the projector is in sleep mode. To come out of sleep mode, press the Enter button, or one of the direction buttons, on the remote. ...SMART document camera Press the power button on the doc cam Select the source to project onto the SMART Board by using the control panel buttons on the base of the document camera, i.e. Select Computer if you want to project the Presentation PC Select Camera if you want to project the document camera imag. ...Lumens document camera Select the source to project onto the SMART Board by using the power button on the document camera Switch OFF the Document Camera to project the Presentation PC Switch ON the Document Camera to project the document using the document camera. Using the AMX keypad Log on to the PC Press Projector On on the keypad Wait for the Projector On button light to stop flashing and the projector to output an image Press the Main PC button The SMART Board is ready to use when the indicator light on the bottom right of the board is a steady green Using the SMART Board Image output The image displayed on your PC monitor will be projected on the SMART Board, together with the SMART Board software toolbar on the left hand side. Annotating the board The pen tray contains different colour coded digital pens and an eraser. After you pick up any item, you will see the blue light, which means that the item is in operation. You can use the pens to draw, write or highlight on the SMART Board screen. To erase your markings on the screen, use the eraser. The pen tray automatically detects which item you have selected, which allows you to write on the board or erase with your finger, so long as you pick up the item. If you want to use the pen as a mouse, press the right click button on the pen tray Using the SMART Notebook Software with the SMART Board You can use the SMART Notebook software to create presentations using a combination of the computer, document camera, and the SMART Board screen. You can then save the presentation as a SMART Notebook file. Ensure the PC is displayed on the SMART Board Start the SMART Notebook software, either by clicking the Notebook icon on the SMART Board software toolbar clicking Start > All Programs > Smart Technologies > SMART Notebook 11 Select File > New to create a new blank file if one doesn't open automatically. Add/remove objects or notations using the PC or the SMART Board screen Select the Add Page icon in the toolbar to create an additional blank page while preserving the existing page Select the Document Camera icon on the toolbar in order to incorporate the document camera display in the SMART Notebook file Saving your SMART Board presentation Select File then Save to save your SMART Board presentation You can open the file later in any Windows or Mac computer running SMART Notebook software. The files can be exported to a variety of formats, including PowerPoint and PDF. More information https://www.youtube.com/watch?v=jIHg3F3C56I: excellent video that shows how you can use the software, plus practical ideas for using the Smart Board in teaching SMART Board instruction manuals: SMART Notebook software for Windows SMART Notebook software for Mac How to use the SMART Document Camera with the SMART Board See the section on SMART Document Camera in the how to use a Document Camera in a Teaching Space guide. Displaying a laptop on the SMART Board You can use your laptop instead of the presentation PC to project onto the SMART Board. You will need to have the SMART Notebook software installed on your laptop. You can download this software from the Deakin Software Library Plug in the 3 cables that are on the desk to your laptop The cables are (left to right): VGA display, network and audio USB. If you use an Apple laptop you will need to bring your own adapter If the laptop image does not display automatically, press the Function and F7 (F5 on some laptops) keys on your laptop in order to send the laptop image to the SMART Board If there is an AMX control panel on the desk, you will need to press the laptop button on the panel If the document camera image continues to be displayed, either For a SMART document camera: Press the Computer View button on the base of the document camera For a Lumens document camera: Power off the document camera If the image still does not appear on the SMART Board, try: Right click on the desktop and select screen resolution Change the resolution to 1024 x 768 If using an Apple device, go through a similar process using System Preferences > Display

different methods of teaching

seminar method

cardinality of sets. ppt

ppt

lecture method

lecture method

Derivation of (a-b)^3

Derivation of a^3-b^3

GEOMETRICAL PROOF OF a^3-b^3

Geometrical proof of (a-b)^3

Geometrical proof of (a+b)^3

Maths Related videos

Algebraic Identities

1.Geometrical proof of a^3-b^3

https://www.youtube.com/watch?v=9RHJt0GXLcY

2.Geometrical proof of (a+b)^3

https://www.youtube.com/watch?v=pK5NBIkLXa4

3.Geometrical proof of (a-b)^3

https://www.youtube.com/watch?v=3HPyrM4kYhk

4.a^3-b^3 derivation

https://www.youtube.com/watch?v=uHpWTnVbUyk

5.(a-b)^3 derivation

https://www.youtube.com/watch?v=miKoWY8q438

MATHS WEBSITES AND ARTICLES

1.HTTPS://WWW.EASYCALCULATION.COM/FUNNY/TRICKS/TRICK1.PHP

MATH MAGIC/TRICKS

Trick 1: Number below 10

Step1:

Think of a number below 10.

Step2:

Double the number you have thought.

Step3:

Add 6 with the getting result.

Step4:

Half the answer, that is divide it by 2.

Step5:

Take away the number you have thought from the answer, that is, subtract the answer from the number you have thought.

ANSWER: 3

Trick 2: Any Number

Step1:

Think of any number.

Step2:

Subtract the number you have thought with 1.

Step3:

Multiply the result with 3.

Step4:

Add 12 with the result.

Step5:

Divide the answer by 3.

Step6:

Add 5 with the answer.

Step7:

Take away the number you have thought from the answer, that is, subtract the answer from the number you have thought.

ANSWER: 8

FROM MATH MAGIC/TRICKS

Trick 1: Number below 10

Step1:

Think of a number below 10.

Step2:

Double the number you have thought.

Step3:

Add 6 with the getting result.

Step4:

Half the answer, that is divide it by 2.

Step5:

Take away the number you have thought from the answer, that is, subtract the answer from the number you have thought.

ANSWER: 3

Trick 2: Any Number

Step1:

Think of any number.

Step2:

Subtract the number you have thought with 1.

Step3:

Multiply the result with 3.

Step4:

Add 12 with the result.

Step5:

Divide the answer by 3.

Step6:

Add 5 with the answer.

Step7:

Take away the number you have thought from the answer, that is, subtract the answer from the number you have thought.

ANSWER: 8

FROM HTTPS://WWW.EASYCALCULATION.COM/FUNNY/TRICKS/TRIC

 2.https://www.mathsisfun.com/fractions.htm

Fractions

A fraction is a part of a whole

Slice a pizza, and we get fractions:

1/2	1/4	3/8
(One-Half)	(One-Quarter)	(Three-Eighths)

The top number says how many slices we have. 
The bottom number says how many equal slices it was cut into.

Have a try yourself:

Click the pizza →

Slices we have:

Total slices:

"One Eighth"

Slices:

EQUIVALENT FRACTIONS

Some fractions may look different, but are really the same, for example:

4/8	=	2/4	=	1/2
(Four-Eighths)		Two-Quarters)		(One-Half)
	=		=

It is usually best to show an answer using the simplest fraction ( 1/2 in this case ). That is called Simplifying, or Reducing the Fraction

NUMERATOR / DENOMINATOR

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

Numerator

Denominator

You just have to remember those names! (If you forget just think "Down"-ominator)

ADDING FRACTIONS

It is easy to add fractions with the same denominator (same bottom number):

1/4	+	1/4	=	2/4	=	1/2
(One-Quarter)		(One-Quarter)		(Two-Quarters)		(One-Half)
	+		=		=

Another example:

5/8	+	1/8	=	6/8	=	3/4
	+		=		=

ADDING FRACTIONS WITH DIFFERENT DENOMINATORS

But what about when the denominators (the bottom numbers) are not the same? 

3/8	+	1/4	=	?
	+		=

We must somehow make the denominators the same.

In this case it is easy, because we know that 1/4 is the same as 2/8 :

3/8	+	2/8	=	5/8
	+		=

But when it is hard to make the denominators the same, use one of these methods (they both work, use the one you prefer):

• Least Common Denominator, or
• Common Denominator

3.http://www.abcteach.com/free/m/mulitplication_quicktricks_elem.pdf

Quick Tricks for Multiplication 



Why multiply?

A computer can multiply thousands of numbers in less than a second.  A human is lucky to multiply two numbers in less than a minute.  So we tend to have computers do our math. 

But you should still know how to do math on paper, or even in your head.  For one thing, you have to know a little math even to use a calculator.  Besides, daily life tosses plenty of math problems your way.  Do you really want to haul out Trusty Buttons every time you go shopping?

Of course, normal multiplication can get boring.  Here's the secret: shortcuts.  You might think of numbers as a dreary line from 0 to forever.  Numbers do go on forever, but you can also think of them as cycles.  Ten ones make 10.  Ten tens make 100.  Ten hundreds make 1000.  

If numbers were just a straight highway, there'd be no shortcuts.  But they're more like a winding road.  If you know your way around, you can cut across the grass and save lots of time.

Multiply by 10: Just add 0

The easiest number to multiply by is 10.  Just “add 0.”

3 x 10 = 30 140 x 10 = 1400 

Isn't that easy?  This “trick” is really just using our number system.  3 means “3 ones.”  Move 3 once to the left and you get 30, which means, “3 tens.”  See how our numbers cycle in tens?  Whenever you move the digits once to the left, that's the same as multiplying by 10. 

And that's the quick way to multiply by 10.  Move each digit once to the left.  Fill the last place with a 0.   


Math: Quick Tricks for Multiplication

Name: _____________________________________________________


2 ©2005abcteach.com
Exercise A:   1. Give two reasons to get good at doing math in your head.


2. Give two situations where you might need or want to do math in your head, not with a calculator.


3. Explain the quick way to multiply by ten. 


4. Solve these problems without using a calculator. a. 4 x 10

b. 15 x 10

c. 400 x 10

d. 23 x 10

e. 117 x 10 

4.http://nrich.maths.org/5435

Sums of Powers - A Festive Story

Article by Theo Drane

Published November 2006,December 2006,February 2011.

On the twelfth day of Christmas, my true love gave to me.. .

How many gifts?
But that's easy; all you have to do is add up the numbers from one to twelve.

That sounds easy, but what if the last line had been... fifty drummers drumming?
Isn't there a better way than huddling over your calculator?

And a partridge in a pear tree...

On the fifth day 1+2+3+4+5=15 gifts are given. We can visualize this as 15 squares arranged into the shape of a staircase; 1 square on top of 2 squares on top of 3 squares etc.

Two of these staircases can be placed together to form a rectangle. The stair shape is half the area of the rectangle, which is:

5×(5+1)2=15

For the twelfth day we can repeat the process and end up with a new rectangle, as shown on the right. The rectangle is 12 by 12+1=13. We can now say: 

1+2+3+...+12=12×(12+1)2=78

So the true love gets 78 gifts on the twelfth day of Christmas.

How many gifts arrive on the nth day?

The same argument applies and we would end up drawing a rectangle that was nsquares high and n+1 squares wide. We would end up with: 

1+2+3+...+n=n×(n+1)2

Four turtle doves...

That's all well and good but what if the true love went overboard on the whole gift front?

Instead of two turtle doves, he gave four;

instead of three French hens he gave nine ...

More precisely, if instead of giving n gifts on the nth day, n×n (normally written as n2) gifts are given, then what?

Now on the twelfth day there would be 1+4+9+25+…+144 gifts.

Is it time to huddle over our calculator now?

Not quite yet, we can visualize the number of gifts on the third day, for example as 1 cube on top of 4 cubes on top of 9 cubes arranged as in Figure A.

Now treat the object in A as a single building block. If you put two of these building blocks together you get the solid in Figure B.

Adding another building block you get the solid on the left in Figure C. The picture on the right is just a different view of the solid shown on the left.

Figures D and E show two copies of the solid made from three building blocks separately (D) and then placed together (E).

Now what is the point of all this?

Well the task is to work out how many cubes are inside our building block, we can do it two ways.

By direct counting we get:

1+4+9=14.

But we also have shown that six of our building blocks can be arranged into the solid cuboid in Figure E. So, how many cubes are there in Figure E?

Well the cuboid is 3 cubes high, 4 cubes wide and 7 cubes long and the cuboid contains 6 of our building blocks.

So the volume of our building block is: 

1+4+9=3×4×76=14

Now here's a question:

Would the construction have worked if our building block had more layers, e.g. 1 cube on top of 4 cubes on top of 9 cubes on top of 16 cubes?

We can repeat the process, but this time starting with a block with four layers.

The final solid in Figure F is now a cuboid that is 4 cubes high, 5 cubes wide and 9 cubes long and the cuboid contains 6 of our building blocks.

So in this case the volume of the building block is 

12+22+32+42=4×5×96=30

By staring at the images, I hope you would agree that we can start with a building block that has any number of layers and that following the same construction we would end up with a cuboid that is n blocks high, n+1 cubes wide and 2n+1 cubes long and contains 6 our of building blocks.

So then the volume of the building block would be 

12+22+32+…+n2=n×(n+1)×(2n+1)6

So our overzealous gift giver would have bestowed 

12×13×256=650

gifts on his true love on the twelfth day.

N.B. You can find an algebraic proof of this result in the article "Mathematical Induction" on the site.

Twenty-seven French hens ...

You may now have an inkling as to where this is heading:

what if instead of two turtle doves, he gave eight

and three French hens became twenty-seven?

Demonstrations of the following result in this article can be found but are not included here, for example you can look at the problem "Picture Story" .

13+23+…+n3=(1+2+3+…n)2

A very pleasing result which means that ...

On the twelfth day our exhausted distributor of gifts would have dispensed:

13+23+…+123=(1+2+3+…12)2=6048gifts.

Two hundred and fifty-six calling birds and more ...

So why stop there?

Well, if you are feeling a bit taxed and want to stop here, I think I have given you enough to think about.

For the rest of you intrepid explorers who want to carry on to the summit, for a whole number n and m, go to the notes for more and more and more...

                                                              Article taken from

                                                                   http://nrich.maths.org/5435

5.http://www.educationworld.com/a_curr/curr148.shtml

Get Real: Math in Everyday Life

How many times have your students asked "When are we ever going to use this in real life?" You'll find the answer here!

Through the years, and probably through the centuries, teachers have struggled to make math meaningful by providing students with problems and examples demonstrating its applications in everyday life. Now, however, technology makes it possible for students to experiencethe value of math in daily life, instead of just reading about it. This week, Education World tells you about eight great math sites (plus a few bonus sites) that demonstrate relevance while teaching relevant skills.

MONEY

Let's begin at the Lemonade Stand, an online version of a classic computer game. At this site, students use $20 dollars in seed money to set up a virtual lemonade stand in a neighbor's yard. Each day, they must decide how many cups of lemonade to prepare, how much money to charge for each cup, and how much to spend on advertising. Their decisions are based on production costs and on the weather forecast -- which isn't always accurate. Students have 25 days to either make a go of the business or go broke. Can they learn enough about the vagaries of business to make a profit? Students of all ages will enjoy the challenge provided by this simple game, which simulates some real business challenges and demonstrates how math fluency can help overcome them.

Older students, especially those with a new or imminent driver's license, will be both fascinated and educated by Calculating a Car Payment. Here, students visit a virtual used-car lot and select a car. Then they use formulas that include complex fractions and large exponents to calculate the monthly payments on their virtual dream car. This is a short lesson, but students may be inspired to use it as a springboard to other automobile-based activities. For example, Online Math Applications' Trips page contains mini-lessons on the costs of leasing, owning, and driving cars. Students can examine such topics as the relationship between the number of stops and the number of possible routes, how to determine the shortest route, and the relationship between speed and braking distance. The site contains formulas and quizzes and provides opportunities for students to create their own quizzes using the math and real life data they've learned.

Your students may not be ready to drive or run their own businesses, but it's never too early for them to begin to save. Several sites can help students get started.

The Mint, a comprehensive site designed for middle- and high-school students, provides lots of financial information and a number of useful tools. In Saving & Investing, students can use a variety of calculators to devise a savings plan, study investment strategies, learn about compound interest, or become millionaires. They learn about the federal deficit and check out the National Debt Clock in The Government, and explore the world of credit cards in Spending. Students can also learn about Making a Budget and discover the relationship between Learning and Earning. The site includes lesson plans and classroom activities, a financial dictionary, quizzes and games, and a little fantasy too. Can students learn enough to earn enough to escape from the planet Knab, where the natives "emit a foul smell and leave a slippery slime trail as they move about"? Only time will tell!

Moneyopolis, a site maintained by the accounting firm of Ernst & Young, provides a simple and effective financial planning curriculum for students in grades 6 through 8. In My Money, students learn that the financial planning process is made up of three steps:

• What do you want?
• What do you have?
• How do you get what you want?

Students are guided through the financial planning process -- first with a series of questions to help them identify their own financial goals and then with a printable spreadsheet that helps them identify their spending habits.

The primary feature of the site, however, is the Moneyopolis(SM) game. Kids need to register to play. In Moneyopolis, "a town where money and math smarts are rewarded," students visit seven town centers. To enter each center, they must solve three puzzles, assemble a lock, and open the door. Once inside, students earn money by correctly answering math-related questions and by investing their earnings wisely. They can also spend money -- on luxuries as well as on necessities. At the end of the town tour, students must have saved at least $1,000 while earning three Community Service Medallions. It's real citizenship -- and it's just plain fun. Students may not even notice that it's also math! Just so YOU do, the site also includes a For Teachers section, featuring suggestions for using Moneyopolis as an educational resource, ideas for off-line educational activities, sample lesson plans, and explanations of the correlation of Moneyopolis math problems to NCTM standards. The site promises a future feature that will allow teachers to review scores and statistics for their own students. (Note: Moneyopolis(SM) requires Flash PPC.)