Multiplication Division
2009
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Multiplication Division
Time Division Multiplexing Layer Concept
Time Division Multiplexing
Bell Laboratories invented time-division multiplexing (TDM) to maximize the amount of voice traffic carried over a medium. Before multiplexing, each telephone call required its own physical link. This was an expensive and unscalable solution. TDM divides the bandwidth of a single link into separate channels or time slots. TDM transmits two or more channels over the same link by allocating a different time interval (time slot) for the transmission of each channel. In effect, the channels take turns using the link.
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Time Division Multiplexing Layer Concept.
Time Division Multiplexing Layer Concept.
TDM is a physical layer concept. It has no regard for the nature of the information that is being multiplexed onto the output channel. TDM is independent of the Layer 2 protocol that has been used by the input channels.
TDM can be explained by an analogy to highway traffic. To transport traffic from four roads to another city, you can send all the traffic on one lane if the feeding roads are equally serviced and the traffic is synchronized. So, if each of the four roads puts a car onto the main highway every four seconds, the highway gets a car at the rate of one each second. As long as the speed of all the cars is synchronized, there is no collision. At the destination, the reverse happens and the cars are taken off the highway and fed to the local roads by the same synchronous mechanism.
This is the principle used in synchronous TDM when sending data over a link. TDM increases the capacity of the transmission link by slicing time into smaller intervals so that the link carries the bits from multiple input sources, effectively increasing the number of bits transmitted per second. With TDM, the transmitter and the receiver both know exactly which signal is being sent.
In our example, a multiplexer (MUX) at the transmitter accepts three separate signals. The MUX breaks each signal into segments. The MUX puts each segment into a single channel by inserting each segment into a timeslot.
A MUX at the receiving end reassembles the TDM stream into the three separate data streams based only on the timing of the arrival of each bit. A technique called bit interleaving keeps track of the number and sequence of the bits from each specific transmission so that they can be quickly and efficiently reassembled into their original form upon receipt. Byte interleaving performs the same functions, but because there are eight bits in each byte, the process needs a bigger or longer time slot.
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What are some creative ways to teach division and multiplication?
We homeschool our 8 yr old - and he is in 3rd grade. He is learning multiplication and division. He knows his tables, but we are having a hard time with teaching him long division and complex mult.
Any ideas, websites, etc would be helpful!
Make sure that he knows his tables (mutliplication and division) very, very well. He should know them instantaneously, without having to think about it; otherwise, he'll spend too much mental energy on figuring out the tables and is likely to not really get the more complicated ideas.
Work on making sure that he really understands that multiplication and division are opposites of each other. Have him give you the other problems in a "fact family" when you give him a simple mutiplication or division problem. For example, if told that 4 x 6 = 24, he should be able to tell you that 6 x 4 = 24; 24 divided by 6 = 4; 24 divided by 4 = 6. Practicing this regularly for a while, will help him with some more complicated concepts.
You can use objects to practice the basic concepts of division and mutiplication, such as taking 24 M & Ms and dividing them evenly amongst 4 imaginary people to act out 24 divided by 4. Make sure that he has really mastered the basic ideas.
Eventually branch out to acting out problems with a remainder. Try to have him divide 13 blocks evenly amongst 4 stuffed animals, to get the idea that 13 divided by 4 = 3 with one extra block left over. Practice this sort of thing a lot with objects; then try doing it with objects and also writing out the division--so that he can see how the reality of dividing translates into writing out the math.
Keep doing it with objects and writing out the math until he tells you that he doesn't need to bother with the objects any more. Some kids will master the notion sooner than others; go at his pace. (And meanwhile, continue working on reviewing the basic facts.)
Don't be afraid to back off for a while and do some other topics in math for a while. Sometimes, a child isn't quite ready for the topic, or needs a break if he's felt frustrated or confused by it. Work on some fun math topics for a while (graphing, Roman numerals, etc.) to give him a break and then come back to it later.
Try practicing basic facts in different ways. In addition to flash cards or copying them or reciting them, try watching the "Multiplication Rock" video.
Or play "Multiplication War"--divide a deck of cards between 2 people (remove the face cards); each player places their pile of cards face down; turn over 2 cards each, at the same time; each player multiplies the 2 cards together; the person with the highest product takes all the cards that were turned over; if a player gives the wrong product, the other automatically wins the cards; the person who ends the game with the most cards wins.
Or get a computer math game.
Or use flashcards and give a small treat for every 5 (or 10) that he can get right instantaneously.
Or use a board game and revise the rules to have moves determined by mutliplying the numbers on the dice together. (Or to practice larger facts, by specialty dice that have more than 6 sides and have numbers past 6 on them.)
Hope this helps...
Multiplication and Division of Power Series
