Developing Numeracy With Manipulatives - Ten Frames

This article is from the 10-article series "Developing Numeracy With Manipulatives". Numeracy-developing manipulatives described in this series: number lines, 0-99 boards, numeral expanders, base ten blocks, bundling sticks, butcher's paper, Unifix cubes, plastic bears, & plastic chains.

Ten frames are, hands down, the most useful and powerful manipulative available to the teacher for developing numeracy. Their simple structure and uncomplicated use belie the powerful way in which they represent or model numbers up to 100 as collections of ten plus leftover ones.

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Teaching With this Manipulative

A ten frame is simply a rectangle, 5 units long and 2 units wide, divided evenly into squares, in a five by two arrangement. The resource may be drawn on a piece of paper, part of a PowerPoint slide show, drawn by hand or marked out on the classroom floor or outside paved area. Numbers up to ten are marked using counters or other objects which fit easily into the squares. Children use this resource by placing counters into the squares to represent numbers.

Two different arrangements are possible for this process; counters should be placed starting at one end, and either placed along one long side first and then the other, or placed along a short edge, building up pairs as the number increases. So to show the number 6, it would look something like this:

|*|*|*|*|*|

|*| | | | |

or this:

|*|*|*| | |

|*|*|*| | |

These two alternative arrangements for counters each have advantages, such as showing a number as even or odd, showing how much more than 5 a number 6-10 is, and showing how much less than 10 a number is. It is important not to "scatter" counters randomly in the squares, as this has very little benefit to students, and will often require counting the counters one by one.

Visualizing Numbers

The process which students will develop when using this resource is called "subitization", a technical word used by math professors to refer to being able to say how many objects are in a small set without counting. This is something adults do subconsciously every day, and a skill children can develop also when using ten frames. Basically, the student will become so familiar with arrangements of counters on the ten frame that after a time the student can glance at an arrangement, and recognize the number immediately. At the same time, the student will recognize the number of empty spaces on the frame, which is the numbers "complement to ten", another really useful piece of information.

As an example when a child becomes familiar with seeing the number 6 arranged as two rows of three counters, the following facts about 6 would be readily apparent:

6 is an even number 6 is double 3 6 is 4 less than 10

Similarly, when the number 6 is arranged as a row of five and one more counter, a child can see straight away that:

6 is one more than 5 6 is over half of ten 5 + 1 = 6

Activities

Provide every student with their own ten frame and ten counters. Ask students to display numbers as quickly as they can. Check that arrangements of counters are "correct" according to the method described here. When students have a number displayed, ask how many empty squares there are - expect students to begin to state this number without counting, once they get used to visualizing the numbers on the manipulative. Link this to "ten take away ___" questions. Ask students to show "doubles" number facts on their manipulative, using two colors. Ask questions about the facts, such as "What is double 3?"; "What is half of 4?". Ask students to show a number on their ten frame, ask if it is closer to ten or to zero, as a prelude to rounding activities.

Extension: Double Ten Frames

The above understandings and activities can be extended into the next phase of number learning by adding another ten frame. Using a double manipulative, students can show all the tricky numbers between 10 and 20, providing excellent exposure to teen numbers. Place the manipulative so that the long edges are vertical, and fill the left-hand frame first, so that when writing the number represented, the student can see that the "1" lines up with the group of ten, and the extra ones line up with the corresponding digit.

A double ten frame allows students to practice all their number facts up to 20, including all addition and subtraction facts. Number fact families such as the "+ 9" facts can be learned easily with this manipulative, since it shows that adding 9 is the same as adding ten and removing one.

Next Article

The next article in this series is "Developing Numeracy With Manipulatives -- 0-99 Boards".

Developing Numeracy With Manipulatives - Ten Frames

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Beer - The Top Manufacturers

You see beer commercials all over the place. You probably even have your favorite, especially if you're a chest pounding, sports watching brute of a he-man. The only thing you really care about is getting your hands on a nice cold brew. But did you ever sit down and wonder who the top beer manufacturers actually are? Of course not. That's why you're reading what's about to follow as we reveal the top beer manufacturers in the world today.

The top five beer manufacturers have quite a few surprises, especially for those of you who are glued to your TV and see nothing but ads for Bud, Bud Light, Miller Light, Molson, Schlitz and the whole cast of characters that follow one bad B-Movie after another.

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Well, would it surprise you to know that the fifth largest beer manufacturer in the world is Inbev? Who? You heard right. This worldwide company comes in at number five. They own a ton of premium brands like Beck's. Ah, yes, now you know who they are. They also manufacture a few specialty brands like Belle-Vue. Okay, so maybe you're not so familiar with that one. This company sells most of their beer in America, Europe and Asia.

Coming in at number 4 on the hit parade of brews is Scottish & Newcastle. In case you're not familiar with them, they actually make a lot of other drinks besides beer, including water, cider and even soft drinks. Talk about diversifying. Their main markets are in the United Kingdom and Europe. They export their beer to over 60 countries. Their main base of operations is in Edinburgh.

The third largest beer manufacturer in the world is one you have probably heard of. The company is Heineken. This company is literally all over the place, operating in over 170 countries in Africa, Europe, North and South America, the Middle East and even Asia. What most people don't know is that Heineken also manufactures many soft drinks and other non alcoholic beverages. The company operates out of Amsterdam and employs more than 60,000 people.

Just missing the top spot is a company by the name of Asahi. Asahi is all over the world, literally. There is hardly a county in which they don't operate. Their main beer is Asahi Super Dry. You may not have heard of it but it's the number two seller behind the company we're about to reveal. This company also makes soft drinks and nutritional supplements. And if you think beer and Japan don't go together, then you better think again because that's just where the headquarters of this giant resides.

And finally, we get to the number 1 beer manufacturer in the world and this should come as no surprise to anyone who's ever walked into a bar or just watch a little TV. The Anheuser-Busch brewery is the number 1 beer making company, not only in the United States, but all over the world. It's Budweiser brands are known by all. Even though they operate mostly in the United States, they own 50% of Mexico's leading brewer and 27% of the top brewer in China. Yes, Anheuser-Busch, or Budweiser, really IS the king of beers.

Just like it says on the commercial.

Beer - The Top Manufacturers

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Operation Highjump - Longhaul Nazi UFO's in Antarctica

Operation Highjump was an United States Navy campaign conducted in Antarctica from 1946-47, it was the single greatest effort in the southern most continent to the present day. The mission was, and continues to be to this day, the largest Antarctic voyage ever undertaken. It was conducted by the Arctic discoverer Rear Admiral Richard Byrd, and concerned 13 vessels, 23 aircraft and along with a military force of 4,700 men. The believed mission was to photograph, chart and extensively explore the frozen continent of Antartica, prior to any other force doing so.

The mission was of a classified nature and was principally a military exercise with military personnel. However, it also involved scientific organizations comprising the US National IGY Committee and the respected National Program which was more immediately concerned with the mapping of Antarctica to record perspective US territorial claims. The original code name apportioned by the Navy to the Antarctic mission was Project Longhaul, expressive of the lengthy logistics channel amongst the United States and Antarctica although which was subsequently altered to the now recognized codename of Operation Highjump.

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The mission objectives were for the dozen ships and several thousand men to navigate their way to the Antarctic edge to train workers and trial materials in the frozen regions and also to reinforce and develop American jurisdiction over the greatest workable region of the Antarctic continent. Furthermore, they were to determine the feasibleness of setting up and supplying bases in the Antarctic and to explore potential base sites coupled with a need to advance methods for founding and looking after air bases on the ice.

In spite of the fact that not expressly declared in the August 26, 1946 commands, a principal purpose of the project was the aerial mapping of as much of Antarctica as was possible, especially along the coastline. Conspiracy theorists specializing in supposed Aryan or Nazi occupations in Antarctica have extensively contemplated about this mission. Rumours started to spread that even though Germany had been overthrown, an assortment of military personell and scientists had escaped the native land as Allied troops passed across mainland Europe and instituted themselves at a base on Antarctica from where they continued to build progressive aircraft founded upon alledged extraterrestrial or alien technologies. This base was apparently positioned in Neuschwabenland, a region of Antarctica which Germany investigated, and claimed, ahead of the outbreak of WWII.

As inconceivable as it may appear, there is substantial supporting evidence for these claims about a German base in Antarctica. On the very eve of WWII, the Germans themselves had entered part of Antarctica and claimed it for the 3rd Reich. Historical events also provide us with further suggestions as to a German-Antarctica association, for it documents that Hans-Ulrich Rudel of the German Luftwaffe was being prepared by Hitler to be his heir apparent. It is recognized that Rudel made numerous trips to Tierra del Fuego at the edge of South America closest to Antarctica.

In reality, Germany had completed a extremely exhaustive study of Antarctic and were believed to have built a small secret base there prior to the War. The truth is that there was an abundance of evidence, at the time, to point to that as late as 1947, portions of the Kriegsmarine, or German Navy, were very much functioning in the South Atlantic, operating either out of South America, or some base previously unrecorded in the Antarctic. One piece of evidence identified was of a German U-boat halting an Icelandic whaler titled 'Juliana' in Antarctic waters, and demanding that its captain, known as Hekla, trade the U-boat crew provisions from her available stores.

Some theorists believe that the Germans were, in fact, developing UFO technology in underground ice caverns of which there is information to suggest that this may not actually be too much a leap of faith. One of a quantity of documented accounts of sightings of unidentified flying objects over Antarctica was by Rubens Junqueira Villela, a meteorologist whom was the principal Brazilian scientist to take part in an voyage to the South Polar area, and at the present time, a veteran of 11 expeditions to Antarctica. Whilst on board the US Navy iceboat Glacier, which had set sail commencing from New Zealand towards the end of January 1961, Villella states that he observed a UFO occurrence in the skies over Antarctica which he instantly noted in his journal, even details including the sentiments felt by all those involved.

It is no secret that the German Nazi movement held technology progressive enough to create a craft resembling a UFO in shape and size, there are many recorded accounts of sightings and pictures of these German UFO's. Even though, to say they held the agility and speed of a true UFO would be deceptive given, they could not remain airborne for any prolonged period and were known for their unpredictability in terms of navigation and general handling.

Operation Highjump has turned out to be a hot topic amid UFO conspiracy theorists over recent years, who claim it was a secret US military campaign to defeat and destroy supposed secret Nazi facilities in Antarctica and seize the German Vril flying discs, and the Thule mercury propelled spacecraft. An obscure Hitlerist narrative tells that Adolf Hitler did not commit suicide in 1945, but however, escaped to Argentina, and then onto an SS base beneath the ice in New Swabia during the early fifties where he restarted his career as a painter. According to this description, Operation Highjump, the greatest journey undertaken to the Antarctic, is claimed to have been dispatched to obliterate the Nazi occupancy there.

The finest accomplishment however of Operation Highjump was its procurement of roughly 70,000 aerial photos of the coastline of Antarctica and chosen inshore regions. Initially prepared for an 8 month undertaking Operation Highjump abruptly returned to the United States just 16 weeks after exploring Antarctica, with no rationale ever provided for the hasty return. While there is, yet, no definitive proof of a German UFO base on Antarctica, It is beyond doubt that something extremely strange was occurring on, or nearby, the ice covered continent.

Operation Highjump - Longhaul Nazi UFO's in Antarctica

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Disney Latino Juegos - Enjoy Disney Games In Spanish

Spanish speaking fans of the Disney Channel shows, movies, and characters no longer have to feel left out. DisneyLatino.com the Spanish Disney Channel website, gives them a chance to play all the most popular Disney online games in their own language. The Latino Disney website is constantly growing in size as well as popularity and will soon have as many features as the regular Disney site.

Some of the games included on the DisneyLatino.com pages include favorite movies of both yesterday and today. Play games with Cinderella, Jasmine, and the Disney Princesses. Other games feature heroes like Tarzan or Hercules. Famous Disney Channel stars like Hannah Montana and Zack and Cody can also be found on the site. All of the features and games on the site are solely in Spanish for those who speak this as their native language.

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Other things you can find on the Disney Latino website besides games are informational pages about different Disney shows and movies. Find out all the historical facts about every classic movie that Disney has put out or learn about the cast of the newest shows that are featured on the Disney Channel this year. Everything you want to know about Disney animation, as well as the best Disney Latino games are right here waiting.

You can even plan a trip to Walt Disney World or Disneyland while surfing around the site; book a hotel and plan your flights from anywhere in the world. You can purchase tickets for the parks at a discounted rate from those that are found at the gate. You can even get a jump on your souvenir shopping on this wonderful website. All of this is in Spanish, thus making it even easier for you to understand exactly what you are booking or purchasing.

Disney Latino Juegos - Enjoy Disney Games In Spanish

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Arts and Crafts Style Decorating

The terms Arts and Crafts and Mission Style are often used synonymously today. They refer to a style of home design and furnishings emphasizing natural materials, especially wood, and showcasing a pronounced geometry in the design. Their tremendous revival in popularity stems largely from their association with hand-crafted elements (though many knock offs are manufactured by machine), a rarity in this technologically advanced age. The pieces offer an heirloom quality and a patina that deepens with age. Arts and Crafts furnishings and interiors are also typically very durable and classic with a timeless appeal. They suit today's desire to simplify and get back to basics. Arts and Crafts interiors are an ideal marriage of function and aesthetic, spaces are designed to work for those living there. To create your own Arts and Crafts interior, there are several elements to consider, both in materials and design.

The materials of an Arts and Crafts interior, while not limited to nature, emphasize wood, stone, glass (made from sand), ceramic tiles (made from minerals/earth), and textiles (using wool, cotton, or linen fibers, and, of course, leather) Much of the visual pattern comes from the grain of the wood selected. Traditionally oak was used, but currently natural cherry is frequently enjoyed. The oak tends to have golden brown gleam, while the cherry is redder. Both darken naturally with age, this is to be expected.

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Flooring, all architectural trim/molding, doors, stair rails and stiles, and exposed structural supports are all typically wood, oak most prevalent. Waxed or oil finishes prevail. Joints are pegged or hand-crafted metal hardware is used. Door knobs, cabinet pulls and the like are again hand-crafted wrought iron or bronze in black, umber, or verdigris. Many are square or rectangular shaped and are hand hammered. For a lighter look, some homeowners today are opting for a soft brushed pewter or nickel finish. Once you have the guidelines, you can bend them to suit. If an alternative to a wood floor is desired, tile or slate would be appropriate substitutes. The tile should be large and laid in a linear pattern, not on the diagonal.

To balance and complement the visual depth of the wood, walls are often treated with a textured paint, or plastered (the old bungalows have original plaster.) A good bet is the river rock finish that Ralph Lauren paint provides. Paint schemes bear an influence from nature with goldenrod yellows, burnt sienna browns, cimarron and Indian reds, sage and moss greens, and a neutral palette of earthy tans, toasts, and beiges. The overall feeling has a harmony, a continuity of all elements working together, none upstaging the other. It is about creating an organic home, one that works within its environment and makes the most of its surroundings both outside and inside.

Fireplaces have wood or stone mantels, with stone, ceramic, or occasionally brick surrounds. The wood is oak with a golden stain, usually waxed or rubbed, not polyurethane. Satin or matte finishes rule. Stone is field stone, stacked dry or with mortar, it presents a terrific textural visual. River rock may be used instead and the round smooth stones provide a counterpoint to the rectilinear geometry otherwise present. Ceramic tiles will typically have a motif from nature, perhaps a leaf or acorn, or have an iridescent finish. Today glass tiles are also used to great advantage. Brick, when employed, is smooth faced and laid in clean horizontal bands. Again, one of the clear features of an Arts and Crafts interior is the linear quality. The feeling that the house is part of a bigger view, part of the horizon, is all an effort to be from and of the earth.

Historically, many of the Arts and Crafts and Mission homes sported art glass windows, or at least many panes. This enabled windows to be left uncovered and still appear decorative. Today, art glass windows can be cost prohibitive except in select areas, so if treatment is desired for either privacy, light, or heat control, simpler is better. This translates to options such as a plain Roman shade, silhouettes, wood blinds, or panels on either tabs or rings, on a decorative rod (wood or wrought iron), with finials. If tiebacks are desired consider sisal tassels, simple and bold, or a band of the same fabric as the drapery. No trim or other decorative element is required. Fabric patterns may herald nature, such as a leaf print, or be based in geometry. There is a wide range on the market today including historical prints by William Morris and designs by Frank Lloyd Wright. The same may also be found in wall coverings, though use them sparingly, as they are often busy and distracting. Arts and Crafts and Mission styles today both represent a desire for a wholesome, hearty lifestyle, a return to yesterday's values.

Furnishings in the Arts and Crafts home are wood, occasionally with a wrought iron or ceramic tile accent. Glass is rarely used. Tables being functional as well as good looking, often have at least a drawer and a shelf for storage. Shapes are squares, rectangles and octagons, though today more rounds are available. Again the geometry created by edges is most apparent. Sofas and chairs are often wood backed with exposed wood arms and cushions that can be readily cleaned or changed out depending on the season. Flexibility and adaptability are prime features. Mission style goes a step further and often offers sofas or chairs with a deep wood shelf surround, acting as the arm and a table (Frank Lloyd Wright design), which gives the illusion of a built-in piece. Leather is frequently used or fabrics in natural fibers such as cotton, linen, or wool. Rich colors and geometric or patterns drawn from nature abound. The most significant interest comes from the combination of elements, again, no one piece dominating. Busy patterns are used sparingly, increasing longevity and flexibility of the furnishings. Resources for furnishings include Stickley, American Impressions by Ethan Allen, and Cotswald Furnishings, a superior resource for hand-crafted furnishings and more in Atlanta.

Lighting in an Arts and Crafts or Mission home is critical, especially with all the dark woods and depth of color schemes popular. While ceiling lights, including recessed can give a good general light, it is far more effective and pleasing to adopt a wealth of luminaries. Torchieres (floor lamps that give uplight, and are best placed in corners) can provide valuable general lighting, while table lamps and floor lamps provide invitation and welcome. Accent lighting can be done with mantel lamps, sconces, and dresser lamps. The two most common types of lamps are the mica and metal designs, the body of the lamp being hammered bronze or copper, the shade a sheet of mica; and the art glass lamps with wood or art glass bases and shades of glass in geometric patterns and a squared coolie shape. Other lighting options include a wealth of reproduction lighting through several lighting sources such as Arroyo Craftsmen, and Yamagiwa (available through designers; they also have an outstanding line of Frank Lloyd Wright designs.)

Accents, accessories, and artwork should be kept to a minimum to allow for a fuller appreciation of the architecture of the home and materials of nature showcased. This is a good chance to provide balance to the predominance of wood with elements in glass, ceramics, and metal. Both bowls and vessels are readily available in all materials mentioned here. Iridescent ware in both ceramics and glass provides an airy complement to the weight and depth of the wood.

© 2005 Melissa Galt

Arts and Crafts Style Decorating

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Authorization Letters - How to Legally Authorize Something

Authorization Letters authorize someone to do tasks for you that normally require your presence to get them done. These tasks are more than picking up dry cleaning. They are used to authorize someone else to make important decisions for you. Take writing these letters very seriously. In order to have many important errands in life accomplished by others, a professional authorization must be written. Examples such as signing for important documents on a professional level or picking up children from day care on a personal level will definitely require these letters. Many establishments will have their own but some may ask that you draft one for them.

Wording

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1. Our example above words this letter professionally ensuring that whoever the reader happens to be will understand that this is strictly business.

2. In our letter, after the opening paragraph and list of items, we've remarked that the named person can make decisions for us but we gave a contact number for us in the event unforeseen events arise.

Format

1. Use the Full Block format arrangement for Authorization Letters:

a. to the left margin of the letter header place the return address

b. make two carriage returns

c. directly below the return address, place the date

d. make two carriage returns

e. directly below the date, place the reader's address

f. make three carriage returns

g. if necessary, include a reference line

h. begin your letter

i. begin each paragraph at the left margin

j. place the closing, signature and typed signature at the left margin.

Tone

1. Ensure your tone is professional and straightforward throughout the letter.

Email

1. With time being as critical to everyone as it is, sending an Authorization Letter via email is now becoming increasingly more accepted.

a. Send your letter in the same format as you would for snail mail - this conveys to the reader that you took the time to create a professional correspondence.

b. Depending on the circumstances, send the message from the appropriate email account: personal email account for a personal correspondence, professional email account for professional correspondence.

Printing

1. Before printing, decide on what paper to use. For Authorization Letters, common bond paper will work.

2. Print your letter and envelope on the same printer using the same font and an envelope that matches the stationery.

Signature

1. Make three carriage returns between the closing and your typed signature. Inside this space, sign your name for professional correspondence. For personal correspondence, there is no need for a typed signature. Simply, sign your name.

For samples of Authorization Letters, take a look at...

LetterRep.com.

Authorization Letters - How to Legally Authorize Something

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Know About the Fishing Industry in Canada

Canada has one of the healthiest fishing industries in the world. Its freshwater fishing is thriving and has remained in a great state for many years. Whether it is commercial fishing and processing or recreational fishing, Canada has plenty to offer.

Canada's fishing resources and industry

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Although Canada's fishing industry contributes much to its economy, it wasn't always so. Although efforts during the 1860s and onward were well-placed, results weren't always up to par. That is, until the fishing industry began to boom from the early 1900s to the present, overcoming economic hurdles such as the Depression. Using both technology and scientific research, fishing practices and production were greatly improved.

Canada has the longest coastline in the world and owns the largest economic zone offshore, equivalent to nearly 4 million sq. km. Its freshwater system is also the largest in the world, encompassing about 2 million rivers and lakes, totaling over 755,000 sq. km.

Currently, it is Manitoba's fishing industry that produces about 25% of the freshwater fish in Canada. There are about 13 species of fish that are being harvested commercially, including lake trout, northern pike, whitefish and yellow perch.

As proof of its efficiency, the fishing industry in Canada produced over 1 million tons of commercial fish in 2005, valued at about billion. Its aquaculture production in the same year yielded over 150,000 tons, valued at over 0 million.

Businesses belonging to Canada's fishing industry number about 11,000. It includes aquaculture, fish processing, ocean services, engineering and hydrography, among others. Coastal tourism is also a thriving industry. The coastal areas of Canada are home to about 7 million people engaged in tourism and fishing as a source of income. Currently, over 20,000 fishing vessels are registered and involved actively in the fishing industry.

Recreational fishing

Canada's robust fishing industry isn't limited to commercial ventures. There are about 3 million people who engage in recreational fishing in Canada, making the sport one of the country's national pastimes.

The DFO

The fishing industry in Canada is managed and protected by the Department of Fisheries. It is responsible for the health, safety and productivity of Canada's water and aquatic resources. It is the government agency that sets and implements standards for the development and sustainability of Canada's fishing industry by providing facilities for safeguarding, conservation and research.

To protect its marine environment, Canada employs the Coast Guard which offers assistance to thousands of small commercial and recreational fishing vessels in case of emergencies. The Canadian Coast Guard is also responsible for educating boaters and fishermen about Boating Safety regulations. It also assists in hydrographic missions, scientific surveys, rescues and in the implementation of environmental pollution regulations.

Know About the Fishing Industry in Canada

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