Tag Archives: numeracy

Zero

“The mathematical sages of India conceived of this concept, and started on the path of the creation of zero back in the ninth century BC. The root of the word is in the Sanskrit Shoonya, meaning ‘it is a void’, which got passed on to the Arabs, who knew the symbol as ‘Safira.’

The Western world came to the concept extraordinarily late, when Venetian merchants stumbled across it and brought it back to their homeland, where it was known as ‘zefiro‘–later corrupted to ‘zero.’ The concept gradually spread through Europe, reading such far-flung outposts as the British Isles in the late sixteenth century.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.

8 Trigrams of the I-Ching

“Ch’ien * Tui * Li * Chen * Sun * K’an * Ken * Kun

The I-Ching or Zhouyi, or the Book of Changes is the oldest of the Chinese classics, going back to oral traditions and observations of mankind at least 4,000 years old. It is essentially a collection of six-line hexagrams which are arranged in a textual eightfold pattern, which come with a set of linked values, such as an image in nature, a compass direction and an associated animal. By the use of chance (the casting of coins, dice, yarrow stalks or whatever), the sequences can be changed so that different groups of six-line hexagrams are read together, which gives it the force of a horoscope, managing questions with a cryptic and ever-changing set of responses.

The eight trigrams each have an association with a form of male or female energy, a place, a direction of the compass and a characteristic animal. For instance, the Ch’ien trigram is associated with creative force, with Heaven, the northwest, and the horse; the Tui with joyous openness, lake, west, sheep; Li, with beauty and radiant awareness, fire, south, and pheasant; Chen, with action and movement, thunder, east and dragon; Sun, with following and penetration, with wind, the south-east, and the fowl; K’an, with danger and peril, water, north, and the pig; Ken, with stopping and resting still, with mountains, the north-east and the wolf/dog; Kun with receptive, earth, southwest and the cow.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.

Word Root Exercise: Deca, Dec, Deka, Deci

This worksheet on the Latin roots deca, dec, deka, and deci can assist students in a number of ways I think. These mean, as you probably already recognized, ten; be aware though, that deci actually means tenth. In any case, this is a vocabulary builder, but contains words primarily from  mathematics, so it’s probably best used there to assist students in developing their own understanding and using words growing from these  roots.

If you find typos in this document, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

The Weekly Text, April 5, 2019: A Lesson Plan on the Concept and Act of Simplifying in Mathematics

Several years ago, the school administration under which I then served tasked me with developing math and science vocabulary in a group of struggling students. I wrote a unit on the fly, and then never used it because that fall I was summoned to jury duty (a stint which ended up lasting two months) in Bronx County.

This complete lesson plan on the word simplify and the concept of simplifying is one of the fruits of my labor. As I say, I never had a chance to actually deliver this lesson in the classroom. In any case, I envisioned starting the lesson with this extended context clues worksheet on the transitive verb simplify. The center of this lesson is this worksheet on simplifying numbers that a math teacher and I collaborated on to develop–he actually ended up teaching this lesson in my absence, and so provided some revisions after he’d had a crack at it. Finally, here is a learning support with definitions of the verbs simplify and solve.

If you find typos in these documents, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

Word Root Exercise: Circum-

Here is a worksheet on the Latin word root circum. It means, unsurprisingly, around. This root is at the base of at least two key words–circumference and circumstance–from the high school lexicon. Moreover, because it derives from the Latin, it forms the basis of a number of cognates in the Romance languages, particularly Spanish.

-If you find typos in this document, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

Power of 100

“A hundred is a ubiquitous element of power and finance. If ancient Greek gods were angered the could be appeased with the bloodbath of hetacomb—the sacrifice of 100 oxen. A hundred was also long considered the largest group able to be governed by the command of one man. So there were 100 soldiers under the command of a Roman centurion; 100 slave-soldiers under the command of a mameluke emir; and, following the Roman model, there were 100 senators (two for each of the fifty states) in the US Senate. More prosaically, 100 units comprise all the major currencies of the world—be the yuan, yen, dollars, euros, rials, rupees, dinars, or pounds.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.

Love Game

Scratch * Duck * Love * Nil

“Sport makes much use of the concept of zero, loading it with a multitude of names. There is scratch in golf, coined from ‘scratching out’ any trace on a score card. In cricket, a batsman who gets zero scores a duck–the slang for a bird that lays an egg, the shape of a zero. And that is the origin, too, of the word ‘love’ in tennis, corrupted from the English trying to copy the French for egg–oeuf. Football, meanwhile, favours the Latin nil, from nihil–nothing.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.

Paradigm (n)

Alright, here is another one of Merriam-Webster’s Words of the Day rendered as a context clues worksheet on the noun paradigm. This word, means “a philosophical and theoretical framework of a scientific school or discipline within which theories, laws, and generalizations and the experiments performed in support of them are formulated; broadly : a philosophical or theoretical framework of any kind.”

Needless to say, this is a very important word and concept for learning and for categorizing knowledge. Students, especially college-bound students, really must know this word by the time they don their mortarboards and walk across the stage at graduation.

If you find typos in this document, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

4 Voices and String Quartets

“Soprano * Alto * Tenor * Bass

The four voices required by a chorus are (descending in pitch) soprano, alto, tenor, and bass. The voices have their instrumental counterparts in the string quartet–one of the abiding images of Western high culture, as if a group of four musicians can aspire to express something beyond our humanity. It was Mozart (who wrote twenty-one string quartets) who perfected the form, using violin, two violas, and a cello, though some argue that with the addition of a third viola and the composition of his six string quintets he perfected the form.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.

19 at a Table–and the 13th Month

“Thirteen is a famously unlucky number in the Western world. I certainly grew up with the belief that to invite thirteen guests to sit around the table doomed the last to some nameless dread–so, to avoid that fate, out table was always laid to include fourteen. It was a belief shared by Napoleon, F.D. Roosevelt and John Paul Getty, and concern over the number 13 is the most common form of Western superstition. Hotels often have no room 13, tower blocks tend to avoid a 13th floor, and travel agents know that the thirteenth of a month (especially if it falls on a Friday) will be short of bookings.

The most common explanation of unlucky thirteen is the Last Supper, where thirteen sat down to eat, one of whom was a traitor plotting the arrest and judicial murder of his host and master. But similar stories can be found in many other cultures, such as the Viking Norse, who remembered how Loki stumbled into a gathering of twelve gods (from which he had been excluded) and in his envy started plotting the events that would lead to the end of the world.

Robert Graves enthusiastically listed in The White Goddess the various mythological companies of thirteen that tend to lead to the betrayal, if not sacrificial death, of one of their members: be they Arthur and his twelve nights, Odysseus and his twelve companions, Romulus and the twelve shepherds, Roland and the twelve peers of France, Jacob and his twelve sons, of Danish Hrolf and his twelve Berserks. Not to mention the thirteen dismembered portions of Osiris’s body recovered by Isis from the Nile.

The ultimate cause of our attitude to thirteen may be that the thirteenth month of the year was always weak and withered. For, although twelve lunar months almost fill up our solar year (to produce 360 days from twelve sets of 29 and a half days), there was always the issue a left-over period of five days. This was considered in ancient cultures to be the thirteenth month, a five-day oddity, often believed to be a period of immensely bad luck where the world was not policed by the normal powers, and evil spirits held brief reign. Some cultures made this into a Saturnalia-like carnival, where the norman roles of society were reversed; others deemed it a needful time for sacrifice.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.