## Monday, March 29, 2010

### Algebra: Introduction

ALGEBRA

Objective:
To have a better understanding of the historical background of Algebra and the fundamental nomenclature used in Algebra.

In groups of 4s please complete the 4-stages of the Introduction: Algebra below. Appoint a scribe to post your findings on-line. Please quote and check the reliability of your sources. Remember to indicate your group members.

Stage 1:
World of
Mathematics on Abu Ja'far Muhammad ibn Musa Al-Khwarizmi
Who is
Abu Ja'far Muhammad ibn Musa Al-Khwarizmi ?
Identify his contributions in Mathematics and Sciences.

Stage 2:
Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was the author of a book entitled Al-jabr w'al muqabala (written in 830 AD) that gave the name al-jabr to the branch of mathematics that is now known by its modern spelling as algebra.

What is Algebra?

Construct a simple mind map to illustrate this. You may refer to sample for inspiration.

source: Mind Map Art info@mindmapart.com

Stage 3:
Use the website or mathematics dictionary and find the definition of the following. Use diagrams or examples to illustrate your explanation. Click here for reference or refer to worksheet 1.

1. variable
2. constant
3. coefficient
4. expression
5. equation

Stage 4:
Watch the following video on Introduction to Algebra and explain the differences between like terms and unlike terms.

1. Stage 1: He was a Persian mathematician, astronomer, geographer and author. He wrote on Hindu-Arabic numerals. He was among the first to use zero as a place holder in positional base notation. The word algorithm was derived from his name. He corrected Ptolemy’s (a geographer and astronomer) research in geography and astronomy/astrology, using his own findings. He made some contributions to the tables of trigonometric functions. His algebra treatise Hisab al-jabr w'al-muqabala gives us the word algebra and can be considered as the first book to be written on algebra.

2. Stage 1 : Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.
His Kitab al-Jabr wa-l-Muqabala presented the first systematic solution of linear and quadratic equations. He is considered the founder of algebra, a credit he shares with Diophantus. In the twelfth century, Latin translations of his work on the Indian numerals, introduced the decimal positional number system to the Western world.He revised Ptolemy's Geography and wrote on astronomy and astrology.

3. Stage 1
He was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.
His Kitab al-Jabr wa-l-Muqabala presented the first systematic solution of linear and quadratic equations. He is considered the founder of algebra.
He introduced the decimal positional number system to the Western world.
He revised Ptolemy's Geography and wrote on astronomy and astrology.
-Wikipedia

Stage 2
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.
-Wikipedia

Stage 3
A variable is a symbol that stands for a value that may vary.
A constant is a non-varying value.
A coefficient is a multiplicative factor in some term of an expression.
An expression is a finite combination of symbols that are well-formed according to the rules applicable in the context at hand.
An equation is a mathematical statement that asserts the equality of two expressions.
-Wikipedia

Naveena

4. Stage 1
He contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing" On the Calculation with Hindu Numerals written about 825, was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. Al-Khwārizmī, rendered as (Latin) Algoritmi, led to the term "algorithm".Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and Greek mathematics.Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and the Middle east. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa.He also wrote on mechanical devices like the astrolabe and sundial and assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers. When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

5. Stage 1
He was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.
He presented the first systematic solution of linear and quadratic equations and is considered the founder of algebra. Latin translations of his work on the Indian numerals, introduced the decimal positional number system to the Western world.
He revised Ptolemy's Geography and wrote on astronomy and astrology.
He systematized and corrected Ptolemy's data for Africa and the Middle east.
He established the basis for innovation in algebra and trigonometry.

Stage 2
Algebra is an Arabic word meaning bringing together broken parts. Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, etc. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

6. Stage 2 :Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics

7. Stage 1:
He was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad. His contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing". He was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe.
He systematized and corrected Ptolemy's data for Africa and the Middle east. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa. He also wrote on mechanical devices like the astrolabe and sundial. He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers. When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

Stage 3:
Variable: A variable is a symbol, usually a letter, which is used to represent an unknown number.

Constant: A symbol that represents a fixed amount.

Coefficient: The number (positive or negative) in the algebraic term is called the coefficient.

Expression: An expression can be a term or a collection of terms separated by addition or subtraction operators.

Equation: A mathematical statement containing an equal sign, to show that two expressions are equal.

Stage 4:
Like Terms are terms that have the same variables raised to the same powers, but may have different coefficients. Constants are considered as like terms. Terms that are not like terms are unlike terms.

Rayner

8. Stage 2: Algebra was invented by the 9th century Arab mathematician, Mohammed Ibn Musa Al-Khwarizmi. Algebra allows the finding of unknown numbers from information given. In algebra, letters are used to substitute numbers that are not known. These letters are then manipulated in accordance with certain rules until an answer appears.

9. Stage 3 :
Variable:
A variable in mathematics is usually a symbol,letter, that represents a certain number which is unknown.
Example:5 y =5 x ?=?
Variable: y ,but y is a uncertain number.
Constant:
Constant is a fixed quantity that does not change.
Example:1,3,π

Coefficient:
The number whether,positive or negative, in the algebraic term is called the coefficient.
Example:
4x, 4 is the coefficientExpression:
An expression can be a term or a number of terms that is separated by addition and subtraction.
Example: 6π has 1 number of terms
3 y – 8 has 2 number of terms
Equation:
An equation is a mathematical statement that asserts the equality of two expressions. Equations consist of the expressions that are to be equal on opposite sides of an equal sign.
Example: x+3 = 5 9 - a = 2

10. Stage 3:

1) variable - able to assume different numerical values.
2) constant - a quantity or parameter that does not change its value whatever the value of the variables, under a given set of conditions
3) coefficient - a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).
4) expression - a collection of symbols that jointly express a quantity
5) equation - a statement that the values of two mathematical expressions are equal

- Macbook dictionary

11. Stage 4

Like terms are terms with the same variable. Unlike terms are terms with different variable. Example: 5x + 3x both have the same variable “x” hence, this is a like term.
5x + 3 they do not have a common variable and thus is an unlike term.
Like terms can be added and subtracted while unlike terms cannot be simplified further.

12. Stage 4 :
Like terms are two or more terms that have the same variables and powers. The coefficients do not matter. Unlike terms are two or more terms that are not like terms

13. Stage 1) Al'Khwarizmi was an Islamic mathematician who wrote on Hindu-Arabic numerals and was among the first to use zero as a place holder in positional base notation. The word algorithm derives from his name. His algebra treatise Hisab al-jabr w'al-muqabala gives us the word algebra and can be considered as the first book to be written on algebra.
Stage 2) Algebra is the mathematical system used to simplify or generalize a problem. It involves different symbols to represent numbers as constants or variables.
Stage 3)
A variable is a symbol used in Algebra to represent an unknown number which varies.
A constant is a quantity or parameter with a specific and fixed value.
A coefficient is a constant quantity which is placed before and multiplying the variable in an algebraic expression.
An expression is an equation of symbols that give a quantity.
An equation is a line of numbers or symbols that when added, divided, multiplied, subtracted.etc is equivalent to or = or values a quantity.
Stage 4) Terms are any quantity that are separated by plus signs.
Like terms are terms that have the same variables but Unlike terms are terms with different variables.

14. Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.

Algebra is the relation of an expression to a factor.

Variable - a symbol, usually a letter, which is used to represent an unknown number.
Constant - a fixed quantity that does not change.
Coefficient - a number (positive or negative) in the algebraic term.
Expression - term or a collection of terms separated by addition or subtraction operators.
Equation - a mathematical statement that two expressions are equal.

Like terms (or similar terms) have the same variables raised to the same powers, but may have different coefficients. Terms are not like terms are unlike terms.

15. This comment has been removed by the author.

16. Stage 1: Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was a Persian mathematician, astronomer and geographer. He is also a scholar in the House of Wisdom in Baghdad. His Kitab al-Jabr wa-l-Muqabala presented the first systematic solution of linear and quadratic equations. He is considered as the founder of algebra, a credit he shares with another mathematician named Diophantus. In the 20th century, Latin translations of his work on the Indian numerals introduced the decimal positional number system to the Western world. He revised Ptolemy's Geography and wrote on astrology and astronomy. [1] Wikipedia

Stage 2: Algebra is the branch of mathematics concerning the study of the rules of operations and relations, the constructions and concepts arising from them etc. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

Stage 3:
Variable: A variable is a symbol, usually a letter, which is used to represent an unknown number. For example, 3y = 3 x ? = ?. y is an unknown variable where the value is infinite
Constant: A symbol that represents a fixed amount.
Coefficient: The number (positive or negative) in the algebraic term is called the coefficient. For example, in 5x, 5 is the coefficient number.
Expression: An expression can be a term or a collection of terms separated by addition or subtraction operators.
Equation: A mathematical statement containing an equal sign to show that two expressions are equal.

Stage 4: Like terms are terms with the same variable. For example, 5y+3y. Both of them have the same variable. That makes ‘y’ a like term. However, the coefficient number does not affect. Unlike terms are the total opposites. For example, 5y+3. The variable is not the same. Thus, making it an unlike term.

~Jia Le~

17. Stage 2
Algebra was invented by Mohammed Ibn Musa Al-Khwarizmi. Algebra allows the finding of unknown numbers from informations given to them. In algebra, letters are used to substitute numbers that are unknown. These letters are then manipulated until an answer appears.

Si Yuan

18. Stage 3
1) variable - A symbol that stands for a value that may vary .
2) constant - A special number, usually a real number, that arises naturally in mathematics.
3) coefficient - a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the expression.
4) expression - A finite combination of symbols that are well-formed according to the rules applicable in the context at hand.
5) equation - A mathematical statement that asserts the equality of two expressions.
Stage 4
Terms are any quantity that are separated by plus signs.
Like terms mean terms with the same variable. Unlike terms mean terms that have different variables.

Si Yuan

19. Stage 3
1) Variable: A variable is a symbol, usually a letter, which is used to represent an unknown number.
2) Constant: A quantity that remains at a fixed value throughout.
3) Coefficient: The coefficient is the number (positive or negative) the algebraic term is called.
4) Expression: An expression can be a term or a collection of terms separated by addition or subtraction operators.
5) Equation: a mathematical statement that two expressions are equal

20. Stage 1 :
Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad. Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing".

Stage 2:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

Stage 3:

A variable is a symbol, usually a letter, which is used to represent an unknown number.

A constant is a quantity or parameter that does not change its value whatever the value of the variables, under a given set of conditions.

The number (positive or negative) in the algebraic term is called the coefficient.

An expression can be term or a collection of terms separated by addition or subtraction operators.

An equation is a statement that the values of two mathematical expressions are equal.

-Michelle Dapito

21. Stage 2: Algebra is an Arabic word meaning 'bringing together broken parts'. This useful tool of mathematics was invented by a 9th century Arab mathematician whose name was Mohammed Ibn Musa Al-Khwarizmi (from whose Europeanised name comes the word, algorithm).
Algebra allows the finding of unknown numbers from information given.

22. Stage 1:
Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was a persian mathematician, astronomer, and geographer, a scholar in the house of wisdom in Baghdad. His systematic approach to solving linear and quadratic equations led to algebra. He had also systematized and corrected Ptolemy's data for Africa and Middle East. He wrote on mechanical devices like the astrolabe and sundial. He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers. He introduced arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

Preston Ngoui

23. 1) Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.
His Kitab al-Jabr wa-l-Muqabala presented the first systematic solution of linear and quadratic equations. He is considered the founder of algebra, a credit he shares with Diophantus. In the twelfth century, Latin translations of his work on the Indian numerals, introduced the decimal positional number system to the Western world. He revised Ptolemy's Geography and wrote on astronomy and astrology.
-Wiki
2)The word, Algebra is an Arabic word meaning bringing together broken parts. This useful tool of mathematics was invented by the 9th century Arab mathematician, Mohammed Ibn Musa Al-Khwarizmi (from whos Europeanised name comes the word, algorithm).
3)Variable is a number that may vary.
Constant is a number that remains the same.
Coefficient of a term in an expression is the number which is multiplied by one or more variables or powers of variables in the term.
An algebraic expression is a collection of algebraic terms connected by mathematical symbols with no equal or inequality sign.
An equation is the answer to the expression.

24. Stage 1: He was a Persian mathematician, astronomer and geographer and author. He established algebra and trigonometry and responsible for spreading theIndian system of numeration throughout the Middle East and Europe.
He also wrote on mechanical devices like the astrolabe and sundial.He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma’mun, the caliph, overseeing 70 geographers.

Stage 2: Algebra is about finding the unknown in he number statement.

Stage 3:
A variable is a symbol which is used to represent an unknown number.
A constant is non-varying value
An expression is a term or a collection of terms separated by addition or subtraction operators.
The number is the algerbic term is a coefficient.
An equation a mathematical statement that two expressions are equal.

25. Stage 1:He was a Persian, mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.
He wrote on astronomy and astrology. He introduced algebra and trigonometry.

Stage 2:Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time.

Stage 3:A variable is a symbol that represents a number.

A constant is a fixed quantity that does not change.

The coefficient of a variable is the number that is placed in front of a variable.

An expression is made up of one or more terms.

An equation consists of two expressions separated by an equal sign. The expression on one side of the equal sign has the same value as the expression on the other side.

26. Stage 2:
Algebra is an Arabic word meaning "bringing together broken parts". It allows the finding of unknown numbers from the information given.

Preston Ngoui

27. Stage 3:
a) Variable: It is a symbol, which is usually a letter, which is used to represent an unknown number. Eg. x, y, z, b, etc.
b) Constant: It is a number that arises naturally in mathematics. Eg. π, e, etc.
c) Coefficient: It is the number (positive or negative) in the algebraic term. Eg. 4, -7, etc.
d) Expression: It is a term or a collection of terms separated by addition or subtraction operations. Eg. 1x=1 term, 1x+2y=2 terms
e) Equation: It is a mathematical statement that asserts the equality of 2 expressions. They consists of expressions that are to be equal on opposite sides of an equal sign. Eg. x+3=5

Preston Ngoui

28. Stage 1: He was an Arabic mathematician who contributed to Algebra, Arithmetic, Trigonometry, Astronomy and Geography.
Stage 2: Algebra the the field of mathematics concerning the study of the rules of operations and relations, allowing the finding of unknown numbers from information given.
Stage 3:
1: A variable is a symbol whose value may vary.
2: A constant is a symbol whose value cannot change.
3: A coefficient is a term in which a variable is multiplied with a constant.
4: A expression is a finite combination of terms.
5: A equation is a statement which expresses the equality of the expressions on opposite sides of the equal sign.
Stage 4: Like terms are combinations of 2 or more terms that have the same powers and variables while unlike terms are the same as above except the terms do not have the same variables and powers.

29. Stage 1: He was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.He contributed the first systematic solution of linear and quadratic equations,algebra, trigonometry and corrected Ptolemy's data.
Stage 2: The word, Algebra is an Arabic word meaning bringing together broken parts. This useful tool of mathematics was invented by the 9th century Arab mathematician, Mohammed Ibn Musa Al-Khwarizmi.
Stage 3:
1.A variable is a symbol, usually a letter, which is used to represent an unknown number.
2.A constant is a quantity or parameter that does not change its value whatever the value of the variables, under and given set of conditions.
3.A coefficient is the number (positive or negative) in the algebraic term.
4.An expression can be a term or a collection of terms separated by addition or subtraction operators.
5.An equation is a statement that the values of two mathematical expressions are equal.
Stage 4:
Like terms- are terms that have the same variable, raised to the same powers, but may have different coefficient.
Unlike terms- are terms that may have the same variable but raised to different power or terms that may have the same power but have different variable.

30. Stage 1:
Musa Al-Khwarizmi was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad. He contributed to mathematics, geography, astronomy, and cartography, established the basis for innovation in algebra and trigonometry.
Stage 2:
Algebra is an Arabic word meaning bringing together broken parts.

31. Stage 4:
Like terms are terms that have the same variables raised to the same powers, but may have different coefficients.
Unlike terms are terms that are not like terms.

Preston

32. Step1:
He is a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad. He is considered the founder of algebra. He introduced the decimal positional number system to the Western world.He was among the first to use zero as a place holder in positional base notation.His contributions had a great impact on language.
~Wikipedia~

Step 2:
Algebra is an Arabic word meaning bringing together broken parts.Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. Simply put, Algebra is about finding the unknown or it is about putting real life problems into equations and then solving them.

Step 3:
1.) A VARIABLE is a a symbol, usually a letter, which is used to represent an unknown number.

2.) A CONSTANT is a term that does not contain a variable. It represents a number that is independent which does not change.

3.) A COEFFICIENT is a number (positive or negative) in the algebraic term.
Example for 4x, 4 is the coefficient.
And for -7y, -7 is the coefficient.

4.)An EXPRESSION can be term or a collection of terms separated by addition or subtraction operators.

5.)An equation is a mathematical statement that asserts the equality of two expressions. Equations consist of the expressions that are to be equal on opposite sides of an equal sign.
Source: http://www.onlinemathlearning.com/algebraic-expressions.html

Step 4:
Like Terms: Terms that have the same variables raised to the same powers, but may have different coefficients.
Unlike Terms: Terms that does not have the same variables or not raised to the same powers.

33. Stage 1:
World of Mathematics on Abu Ja'far Muhammad ibn Musa Al-Khwarizmi
Who is Abu Ja'far Muhammad ibn Musa Al-Khwarizmi ?
Identify his contributions in Mathematics and Sciences.

1. Who is Abu Ja'far Muhammad ibn Musa Al-Khwarizmi ?

Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was a Persian mathematician, astronomer and geographer. He is also a scholar from the House of Wisdom in Baghdad.

2. Identify his contributions in Mathematics and Sciences.

His contributions include :

1. Establishing the basis for innovation in algebra and trigonometry.

2. Spreading the Indian system of numeration throughout the Middle East and Europe.

3. Systematized and corrected Ptolemy's data for Africa and the Middle east.

4. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa.

5. He also wrote on mechanical devices like the astrolabe and sundial.
He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers.

6. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.

See To Yu Xiang

34. Stage 4:

Like Terms are terms that have the same variables raised to the same powers, but may have different coefficients.

Unlike terms are terms that do not have the same variable or not raised to the same power.

-Michelle Dapito

35. Stage 1: Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was a Persian mathematician, astronomer and geographer, a scholar in the House of Wisdom in Baghdad.
He presented the first systematic solution of linear and quadratic equations. He is considered the founder of algebra.

36. Stage 2:
Abu Ja'far Muhammad ibn Musa Al-Khwarizmi was the author of a book entitled Al-jabr w'al muqabala (written in 830 AD) that gave the name al-jabr to the branch of mathematics that is now known by its modern spelling as algebra.
What is Algebra?

A branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. Algebra can include real numbers, complex numbers, matrices, vectors etc. The letters can also represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.

In a nutshell :
Algebra is replacing numbers with letters.

37. Stage 3:
Use the website or mathematics dictionary and find the definition of the following. Use diagrams or examples to illustrate your explanation. Click here for reference or refer to worksheet 1.

variable
constant
coefficient
expression
equation

1. Variable - A quantity capable of assuming any of a set of values or a symbol representing such a quantity.

2. Constant - A symbol representing an unspecified number that remains invariable throughout a particular series of operations.

3. Coefficient - A numerical or constant factor in an algebraic term or the product of all the factors of a term excluding one or more specified variables.

4. Expression - A symbol or combination of symbols that represents a quantity or a relationship between quantities.

5. Equation - A mathematical statement that two expressions are equal: it is either an identity in which the variables can assume any value, or a conditional equation in which the variables have only certain values (roots).

38. Stage 2:Algebra is about finding the unknown. A branch of mathematics that substitutes letters for numbers.

39. Stage 4:
Watch the following video on Introduction to Algebra and explain the differences between like terms and unlike terms.

Like terms are :

a) All the variables are represented with the same letters.

b) All the variables represented with the same letters have the same index.

c) All the coefficients are different, but the variables have the same index and letters.

Unlike terms :

a) the variables are different.

b) Even though both variables are the same, one variable has an index whilst the other does not, or both indexes are different.

From this, we can conclude that like terms are different from unlike terms as for an expression consisting of like terms, all the variables are of the same value, but for an expression consisting of unlike terms, all the variables will represent a different value.

40. Stage 3:
Variable- It is a symbol which is usually used to represent a unknown number. A Variable is usually a letter.
Constant- It is a symbol that is fixed throughout
Coefficient- It is a number (positive or negative) in the algebraic term
Expression- An expression can be term or a collection of terms separated by addition or subtraction operators.
Equation- An equation is a statement that the values of two mathematical expressions are equal.

41. Stage 4: Like terms are terms that have the same variable raised to the same power, but may have different coefficient. The difference is in the variable being different. So if lets say the variable between two numbers are the same and they are raised to the same number, it is a like term. If the variable is same, but it is raised to the a different number it is consider a unlike term. The opposite is the same.