Types of Numbers MTH 212 E-Lesson 2 PDF

Types of numbers  Whole numbers As mathematics teachers, we need to know about the different types of numbers that we are dealing with. There are numbers like 1, 2, 3,... etc., ones like 0.33333... , or ones like 5/7. We introduce students to these gradually, and each new type comes...

Types of numbers  Whole numbers As mathematics teachers, we need to know about the different types of numbers that we are dealing with. There are numbers like 1, 2, 3,... etc., ones like 0.33333... , or ones like 5/7. We introduce students to these gradually, and each new type comes with its own uses, and its own challenges. The main types of numbers used in school mathematics are listed below:  Natural Numbers (N), (also called positive integers, counting numbers); They are the numbers {1, 2, 3, 4, 5, …}  Whole Numbers (W). This is the set of natural numbers, plus zero, i.e., {0, 1, 2, 3, 4, 5, …}.  Integers (Z). This is the set of all whole numbers plus all the negatives (or opposites) of the natural numbers, i.e., {…, ⁻2, ⁻1, 0, 1, 2, …}  Rational numbers (Q). This is all the fractions where the top and bottom numbers are integers, e.g., 1/2, 3/4, 7/2, ⁻4/3, 4/1 [Note: The denominator cannot be 0, but the numerator can be].  Real numbers (R), (also called measuring numbers or measurement numbers). This includes all numbers that can be written as a decimal. This includes fractions written in decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0.3333, or 2.142857  Constructing numbers The numbers we meet at school are generally represented by using combinations of ten number symbols (also called numerals or digits) plus the symbols ".", "+", and "–" (e.g., 5, 27; 35.8, ⁻4) The ten number symbols we use are: 1 2 3 4 5 6 7 8 9 as well as 0. All these symbols also represent the numbers one, two, three,... up to nine; as well as zero.0 is itself a number, and a very important one. It is called zero, nil, nought etc. It is also a placeholder. It is first used in this sense in the number ten (10). The 0 denotes that there is nothing in the units’ place, and therefore distinguishes 10 from 1. The concept of place holder is best interpreted as there being zero (0) of the units in the place where the 0 is. For example, in 1025 there are zero hundreds. Students need to meet the number 0 before they meet the number 10.  OTHER TYPES OF NUMBERS  Odd numbers are those numbers that cannot be divided into two equal parts, whereas even numbers are those numbers that can be divided into two equal parts. Examples of odd numbers are 3, 5, 7, 9, 11, 13, 15… Examples of even numbers are 2, 4, 6, 8, 10, 12, 14…  FACTORS AND MULTIPLES  Factors are whole numbers which divide exactly into the number with no remainder, for example, factors of 8 are { 1, 2, 4,and 8}  Multiples of a number can be found in the multiplication table of that number, for example, multiples of 8 are 1×8= 8, 2×8= 16, 3×8= 24 etc. The first three multiples of 8 are: 8,16, and 24.  Factors and multiples List the factors of 12 = { Multiples List the multiples of 12 = {  PRIME AND COMPOSITE NUMBERS  Prime numbers have only two factor factors- itself and one, for example, the number 2 has only two factors, 1 and 2, and therefore it is a prime number. These are the following sets of prime numbers {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…etc.}  Composite numbers have more than two factors, for example, the number 4 has more than two factors, 1, 2, and 4, and therefore it is composite number. These are the following sets of composite numbers {4, 6, 8, 9, 10, 12, 14, 15, 16, 18…etc.}  Define the concepts and give examples to show your understanding: Composite number Examples = { Prime numbers Examples = {  SQUARE NUMBERS AND CUBE NUMBERS  Square numbers are made by multiplying a number by itself once, for example, 9×9= 81, therefore 81 is a square number.  Cube numbers are made by multiplying a number by itself twice, for example, 4×4×4=64 therefore 64 is a cube number. Define the concepts and give examples to show your understanding Square number Examples = { Cube number Examples = {  SQUARE ROOTS AND CUBE ROOTS  The square root of a number is which, when multiplied by itself, is equal to that number. The sign used is √. Example √64 is read ‘the square root of 64’ which is 8, because 8×8 = 64.  The cube root of a number is which, when multiplied by itself twice, is equal to that number. The sign used is 3√. Example 3 √125 is read as ‘the cube root of 125’ which is 5, because 5×5×5= 125 Define the concepts and give examples to show your understanding: Square root Examples Cube root Examples  Introducing a problem solving element ( Task for discussion) What is the only even number that is also prime number? How many prime numbers end in 5? Give a reason. Why there are no primes that are multiples of 10? The sum of two prime numbers is always a prime number. True/False. Give a reason for your answer. The sum of three numbers is 18. If every number is a prime number, what are those numbers? Is there a natural number that is neither a composite number nor a prime? Give a reason for your answer. Playing games using numbers in the classroom Guess my number: How to play: One player chooses (secretly) a whole number within a certain range, eg 1-100 The other players take it in turns to try and discover the number by asking “Yes/No” answer questions: e.g. Is the number greater than 50? Yes is It between 50 and 75? No Is it less than 85? Yes Is the number an even number?etc