• Use Mathematical models to represent and understand quantitative relationships.
• Understand patterns, relations, and functions.
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers,
teachers, and others.
symbols.
• Apply and adapt a variety of appropriate strategies to solve problems
Teaching Methods used : Lecture, Discussion, Discovery, Do and Learn, Play and learn
Need to Learn/ Connections :
to represent and understand quantitative relationships, Represent and analyze mathematical situations and structures using algebraic symbols, Apply and adapt a variety of appropriate strategies to solve problems, In Academics in middle grades, plotting of linear equations and simultaneous equations
Such mathematical sentences which may be either True or False but not both are known as Mathematical statements.
(in fact every number is a constant)
Practice Worksheet 1- Based on representing numbers on number line, Constants, Variables, Like and Unlike terms and degree of the term
A symbol which takes on various numerical values is called a variable or literal
Such mathematical sentences containing variables depending upon the value of the variable for their truth or falsity. Such sentences may be true or false depending on particular value of the variable.
(i) x + 7 = 22 (ii) 2x + 13 = 27 (iii) 3y – 6 = 5y – 12
The sign of (=) equality in an equation divides it into two sides, namely left hand side (LHS) and right hand side (RHS) respectively.
Practice Worksheet 2- Based on type of questions: o + 7 = 20, 13 - o = 25
Solving an equation means to find the value(s) of the variable satisfying (making equation true) the given equation.
Practice Worksheet 3- Based on type of questions: o + 7 = 20, o to be replaced with a variable and writing solution of eq.
Practice Worksheet 4- Based on this method.
e.g. x + 7 = 12
x + 7 – 7 = 12 – 7
x = 5
Practice Worksheet 5, 6- Based on the method of Transposing.WS-5- one step transposition, WS-6- more than one step transposition.
Practice Worksheet 7- Solving Linear Equations and representing solution graphically.
Word problems based on linear equation
Evaluation 1
Remedial
Evaluation 1
Evaluation 2
Evaluation 2
Practice Worksheet 1- Based on representing numbers on number line, Constants, Variables, Like and Unlike terms
Practice Worksheet 2- Based on type of questions: o + 7 = 20, 13 - o = 25
Practice Worksheet 3- Based on type of questions: o + 7 = 20, o to be replaced with a variable and writing solution of eq.
Replace o with a variable and write the solution of the equation as shown in 1st sum:
Practice Worksheet 4- Based on method of Subtracting/Adding/Multiplying and Dividing LHS and RHS of the equation.
Solve the following equations to find the value of variable used:
Practice Worksheet 5, 6- Based on the method of Transposing.WS-5- one step transposition, WS-6- more than one step transposition.
WS-5 One step transposition
WS-5 Two or more steps transposition
Practice Worksheet 7- Solving Linear Equations and representing solution graphically.
Solve the following linear equations and represent the solution graphically (on number line):
Evaluation 1
Practice Worksheet 8- Solving Word Problems based on Linear Equations.
-
- Linear Equation/Equation in one variable
- Terminology
- Number line, mathematical statement, Constant, variable, like and unlike terms, degree of the variable, open sentences, solution and equation
- Concept(s)
- Unknown number
- 8 periods of 45 minutes each
- Create and use representations to organize, record, and communicate
• Use Mathematical models to represent and understand quantitative relationships.
• Understand patterns, relations, and functions.
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers,
teachers, and others.
- Analyze and evaluate the mathematical thinking and strategies of others.
symbols.
• Apply and adapt a variety of appropriate strategies to solve problems
Teaching Methods used : Lecture, Discussion, Discovery, Do and Learn, Play and learn
- : Text book, Practice worksheets, Activities,
Need to Learn/ Connections :
to represent and understand quantitative relationships, Represent and analyze mathematical situations and structures using algebraic symbols, Apply and adapt a variety of appropriate strategies to solve problems, In Academics in middle grades, plotting of linear equations and simultaneous equations
- Number line: concept needed to represent solution of the linear equation
- Mathematical Statements:
Such mathematical sentences which may be either True or False but not both are known as Mathematical statements.
- Algebraic Expressions
- Constants: A symbol having fixed numerical value is called a constant.
(in fact every number is a constant)
- Variables: Explanation with example of perimeter of square
Practice Worksheet 1- Based on representing numbers on number line, Constants, Variables, Like and Unlike terms and degree of the term
A symbol which takes on various numerical values is called a variable or literal
- Like and Unlike Terms: Explanation with examples
- Power/Degree of Variables:
- Open Sentences:
Such mathematical sentences containing variables depending upon the value of the variable for their truth or falsity. Such sentences may be true or false depending on particular value of the variable.
- Solution / Solution Set:
- Equation:
-
- Linear Equation:
(i) x + 7 = 22 (ii) 2x + 13 = 27 (iii) 3y – 6 = 5y – 12
The sign of (=) equality in an equation divides it into two sides, namely left hand side (LHS) and right hand side (RHS) respectively.
- Solution of Linear Equation:
- To Solve an Equation:
Practice Worksheet 2- Based on type of questions: o + 7 = 20, 13 - o = 25
Solving an equation means to find the value(s) of the variable satisfying (making equation true) the given equation.
Practice Worksheet 3- Based on type of questions: o + 7 = 20, o to be replaced with a variable and writing solution of eq.
- Solving Linear Equation
- By method of Subtracting/Adding/Multiplying and Dividing LHS and RHS of the equation
Practice Worksheet 4- Based on this method.
e.g. x + 7 = 12
x + 7 – 7 = 12 – 7
x = 5
- By method of Transposing: Under this process we drop a term from one side of an equation and put it on the other side with sign changed
Practice Worksheet 5, 6- Based on the method of Transposing.WS-5- one step transposition, WS-6- more than one step transposition.
- Solving Linear Equations and presenting the solution graphically
Practice Worksheet 7- Solving Linear Equations and representing solution graphically.
Word problems based on linear equation
Evaluation 1
Remedial
Evaluation 1
Evaluation 2
Evaluation 2
Practice Worksheet 1- Based on representing numbers on number line, Constants, Variables, Like and Unlike terms
- Represent following numbers on different number lines: 3, -5, 8, , 0.5, 0.4, -
- Identify the constants in the following terms: 3x, -54z, -2d, p, 34 xy, 0.8 y
- List down the variables of the terms given in question 2.
- Write down the constants and variables in the following terms:
- Identify the like terms in the following:
- Write the degree of the following terms:
- Say True or False
- 3xy and -5xy are like terms.
- 34x and 54y are like terms.
- 2x2y and 2xy2 are like terms.
- -34x and 34x are unlike terms.
- 9xy and 6yx are unlike terms.
- 4y3x and 7x3y are unlike terms.
Practice Worksheet 2- Based on type of questions: o + 7 = 20, 13 - o = 25
- o + 7 = 20
- o + 13 = 34
- 34 + o = 43
- 56 + o = 100
- 13 - o = 25
- 57 - o = 43
- o – 9 = 30
- o – 45 = 70
- o – 43 = 62
- 8 + o = 15
- o – 5 =8
- 3o = 21
- 5o = 15
- 4o = 56
- 24 = 4o
- 12 = 24o
- 39 = 13o
- 21 + 12 = 30 + o
- 20 + 64 = 50 + o
- 12 + o = 20 - o
- 35 + o = 50 - o
- o + 22 = 30 - o
- o + o = 30 - o
- = 4
- = 7
- = 2
- = 6
- = 14
- 5o + 3 = 23
- 12o – 5 = 1
Practice Worksheet 3- Based on type of questions: o + 7 = 20, o to be replaced with a variable and writing solution of eq.
Replace o with a variable and write the solution of the equation as shown in 1st sum:
- o + 5 = 24 x + 5 = 24 x = 19
- o + 13 = 34
- 34 + o = 43
- 56 + o = 100
- 13 - o = 25
- 57 - o = 43
- o – 9 = 30
- o – 45 = 70
- o – 43 = 62
- 8 + o = 15
- o – 5 =8
- 3o = 21
- 5o = 15
- 4o = 56
- 24 = 4o
- 12 = 24o
- 39 = 13o
- 21 + 12 = 30 + o
- 20 + 64 = 50 + o
- 12 + o = 20 - o
- 35 + o = 50 - o
- o + 22 = 30 - o
- o + o = 30 - o
- = 4
- = 7
- = 2
- = 6
- = 14
- 5o + 3 = 23
- 12o – 5 = 1
Practice Worksheet 4- Based on method of Subtracting/Adding/Multiplying and Dividing LHS and RHS of the equation.
Solve the following equations to find the value of variable used:
- x + 23 = 35
- 5x – 5 = 30
- 9z – 35 = 46
- 3 + p = 13
- 3 + 9z = 39
- 8 – 4w = 4
- x + =
- x + 3 =
- 5x + = 9
- 3x - = x – 3
- x + 8 = 90 – x
- x + 26 = 3( x+ 2)
- 5p + 20 = 35
- 3(x + 4) = 21
- 3y + 5 = 5y – 11
- 2(z – 2.5) = 0.3
- 0.5x – 1.6 = 0.3x + 0.8
- 3x + 6 = 51
- x - = 12
- 8x + (27 – x) = 150
Practice Worksheet 5, 6- Based on the method of Transposing.WS-5- one step transposition, WS-6- more than one step transposition.
WS-5 One step transposition
- x + 22 = 33
- 8 – x = 4
- 2x = 82
- 144 = 4x
- 4x =
- 11y = 165
- 27 – x = 25 – x
- = 2
- = 6
- 118 x = 2950
WS-5 Two or more steps transposition
- 3x + 17 = 23
- 7y – 32 = 17
- 5(3 – x) + 1 = 3(x + 4)
- + 4x = 42
- 2(3y – 2) – 4(2y – 5) = 9
- x – 24%of x = 38
- =
- + = 21
- + = 20
- 2(2x + 17) = 178
Practice Worksheet 7- Solving Linear Equations and representing solution graphically.
Solve the following linear equations and represent the solution graphically (on number line):
- 4x + 31 = 91
- =
- – = 1
- 6(3x + 2) – 5(6x – 1) = 3(x – 8) – 5(7x - 6) + 9x
- 3x - = 8
- x + 1 = 5
- + x = 16
- 2y + = y + 2
- x - 25% of x = 15
- - = - 25
Evaluation 1
- Find the solution of x + 4 = 6. Show the solution on a number line.
- Solve: 5(y – 3) =15. Show the solution graphically.
- A number exceeds its four sevenths by 18. Find the number.
- The sum of three consecutive even numbers is 48. Find the numbers.
- If x – 24% of x = 38, find x.
- Solve: - = - 25
- 6(3x + 2) – 5(6x – 1) = 3(x – 8) – 5(7x - 6) + 9x. Find solution for x.
- The denominator of a fraction is 3 more than the numerator. If 2 is added to the numerator and 5 is added to the denominator, the fraction becomes . Find the fraction.
Practice Worksheet 8- Solving Word Problems based on Linear Equations.
- Five times a number increased by 4 equals to 19. Find the number.
- A number increased by 9 gives 43. Find the number.
- Thrice a number increased by 6 equals 39. Find the number.
- A number when diminished by 11 gives 57. Find the number.
- A number exceeds one-fifth of it by 18. Find the number.
- The sum of two consecutive odd numbers is 32, find the numbers.
- In a class of 40 pupils, the number of girls is three-fifths of the number of boys. Find the number of boys in the class.
- Two supplementary angles differ by 440. Find the angles.
- A man is twice as old as his son. 20 years ago, the age of the man was 12 times the age of the son. Find their present ages.
- The length of rectangular park is three times its breadth. If the perimeter of the park is 192 meters, find the dimensions of the park.