The numeral in modern english

The task when math education leaders made it a priority to make math more meaningful, the excellent idea was to focus more instruction on the purpose and meaning of mathematical principles rather than memorization and practice. At first, teachers created a balance between the why and the how of mathematics. However, after some years, a few argued that the why of mathematics is more important than the how. Many listened, and changes began. Modeling was deemphasized, accuracy was devalued, and practice was limited. To some extent, these changes worked. Student engagement increased, math class was more inviting and exciting, and, as a result, students enjoyed math more than ever before. However, students’ mathematics performance was not maintained.
The novelty of the work over the past few decades, students in the United States, especially those who show difficulties early, have underwhelmed on international mathematics achievement assessments. Statistics from international assessments and reports suggest students from the United States lack the skills to compete in an international arena, especially in fields requiring proficiency in mathematics (National Center for Education Statistics, n.d.; National Mathematics Advisory Panel [NMAP], 2008). In the example above, the great idea of playing in the waves was fun, but the father and son lost their focus. What has been learned about student engagement and activity cannot be lost, but rigor cannot be sacrificed. We have to keep our vision on learning and achievement for all students, even—and maybe especially—those who struggle early.

CHAPTER I. THE NUMERALS IN ENGLISH
1.1. Functions of numerals
This material describes how numbers are expressed by numerals in English and provides examples of cardinal and ordinal numerals, common and decimal fractions, and examples of differences between British and American English in expressing numbers. Some differences in the representation of numbers in English and Russian are also indicated.
For the purposes of studying, numbers in this material are written in words and figures. Recommendations on the use of figures or words for expressing numbers and examples of the use of numbers in various situations are given in Numbers in Situations in the section Miscellany¹.
Functions of numerals
A numeral is a figure, a letter, a word (or their combinations) representing a number. Cardinal numerals indicate number, quantity or amount and are used in counting. Ordinal numerals indicate order, that is, the order of things in a series. Numerals can be written in figures or words (2 or two; 25 or twenty-five; 17th or seventeenth).
Numerals function as nouns and adjectives. In a sentence, a numeral can serve as a subject, attribute, object, predicative complement, or adverbial modifier.
Ten students took part in the competition. Three of them received awards.
Twenty cars were sold on the first day. Five of them were sports cars.
There are 135 employees in this company. We talked to 45 of them.
How many cakes did you buy? – I bought five. I ate two.
Two plus four is six. Three times three is nine.
How old is your grandfather? – He is 72. He was born in 1940.
Note:It is interesting to note that the numeral is not a part of speech in English. The word "numerals" in English sources refers mostly to figures (not words). Words like "three, six, twenty, forty-five, hundred, third, sixth, twentieth, forty-fifth, hundredth" are nouns and adjectives in English.
Compare English and Russian parts of speech:
There are eight parts of speech in English: nouns, pronouns, adjectives, verbs, adverbs, prepositions, conjunctions, and interjections. (In some English sources, articles are included in this list as a part of speech.)
There are ten parts of speech in Russian: nouns, pronouns, adjectives, numerals, verbs, adverbs, prepositions, conjunctions, particles, and interjections.
Numerals: BrE and AmE
Both in British English and in American English groups of three digits in numerals of one thousand and higher are usually separated by a comma, counting from the right: 4,286; 12,345; 378,925; 6,540,210.
Some manuals of style recommend writing four-digit numerals without a comma: 1570; 2358; 5625.
In numbers written as words in British English, the conjunction "and" is used before tens, or before ones if there are no tens, starting with hundreds: one hundred and twenty-three (123); four hundred and seven (407); three thousand five hundred and thirty-eight (3,538); seventy-three thousand and five (73,005); five million three hundred thousand and fifty (5,300,050).
Note the use of more than one conjunction "and" in large numbers in British English: two million six hundred and twenty-five thousand three hundred and ten (2,625,310).
In American English, the conjunction "and" is generally not used before tens or ones: one hundred twenty-three (123); four hundred seven (407); three thousand five hundred thirty-eight (3,538); seventy-three thousand five (73,005); two million six hundred twenty-five thousand three hundred ten (2,625,310); five million three hundred thousand fifty (5,300,050).
In British English, the conjunction "and" is also used before tens or ones in ordinal numerals above one hundred: one hundred and tenth (110th); three thousand and fifth (3005th). But "and" is not used in American ordinals: one hundred tenth (110th); three thousand fifth (3005th).
In this material, numbers expressed in words are written without "and" before tens or ones².
Digits, figures, numerals, numbers
The words "digit, figure, numeral, number" may present some difficulty for language learners. For example, you can say "the digit 3; the figure 3; the numeral 3; the number 3", but the meanings of these word combinations are not the same.
The word "digit" refers to any of Arabic figures from 0 to 9. Examples: the digit 4; the digit 7; a three-digit number; a group of three digits; use digits to write these numbers.
The word "figure" refers to a numerical symbol for a number and can also refer to the numerical value of a number. Examples: the figure 4; Arabic figures; a six-figure number; a figure of 3.5 million; round figures; write these numbers in figures and in words. The word "figures" can also mean "arithmetic": He is good at figures.
A numeral is a name used for denoting a number. Numerals can be in the form of any symbols denoting a number. In texts of general character, numerals are usually written as figures or words. Examples: the numeral 7; the numeral seven; ordinal numerals; Arabic numerals, Roman numerals.
The word "number" refers to quantity or amount (in various fields of application) and is one of the main concepts in mathematics. Examples: whole numbers; natural numbers; prime numbers; even numbers; odd numbers; large numbers; round numbers; negative numbers; the number 12; the number twelve; the number 165.
One of the meanings of the word "number" is "numeral". Because of that, the word "number" can be used in many cases where the word "numeral" is meant, for example, you can say "cardinal numerals" or "cardinal numbers"; "ordinal numerals" or "ordinal numbers".
Not all languages have numeral systems. Specifically, there is not much need for numeral systems among hunter-gatherers who do not engage in commerce. Many languages around the world have no numerals above two to four—or at least did not before contact with the colonial societies—and speakers of these languages may have no tradition of using the numerals they did have for counting. Indeed, several languages from the Amazon have been independently reported to have no specific number words other than 'one'. These include Nadëb, pre-contact Mocoví and Pilagá, Culina and pre-contact Jarawara, Jabutí, Canela-Krahô, Botocudo (Krenák), Chiquitano, the Campa languages, Arabela, and Achuar.[7] Some languages of Australia, such as Warlpiri, do not have words for quantities above two,[8][9][10] as did many Khoisan languages at the time of European contact. Such languages do not have a word class of 'numeral'.
Most languages with both numerals and counting use base 8, 10, 12, or 20. Base 10 appears to come from counting one's fingers, base 20 from the fingers and toes, base 8 from counting the spaces between the fingers (attested in California), and base 12 from counting the knuckles (3 each for the four fingers).