Tuesday, June 7, 2011
LCM , HCF& Algebraic Fractions
LESSON PLAN
MATHEMATICS
Term: Grade:
Week: Periods:
From:
LESSON TITLE: LCM , HCF& Algebraic Fractions
PERIOD 1 Learning Objectives: The students should be able to: 1. recall the method of finding LCM of numbers. 2. recognize the method of finding LCM of algebraic expression 3. correlate the method of finding LCM of numbers with that of algebraic expression. 4. find the LCM of algebraic expressions . 5. simplify the answer after finding the LCM of algebraic expression. | |
Key Vocabulary: Least Common Multiple, numbers, algebraic expression | |
Key Questions: 1. What does the abbreviation LCM stand for? 2. What is the LCM of 12 and 20? 3. What is the LCM of 100 and 135? | |
TEACHER ACTIVITY | STUDENT ACTIVITY |
Ø Finds the LCM of two numbers. . Ø Finds the LCM of two algebraic expressions. Ø Facilitates in correlating the methods of finding LCM of numbers and algebraic expression. Ø Explains in detail using different examples the method of finding LCM of algebraic expressions. | Ø Recalls the method of finding the LCM of two numbers. Ø Recognizes the method of finding the LCM of two algebraic expressions. Ø Correlates the methods of finding LCM of numbers and algebraic expression. Ø Finds the LCM of different algebraic expressions. |
PERIOD 2 Learning Objectives: The students should be able to: 1. recall the method of finding HCF of numbers. 2. recognize the method of finding HCF of algebraic expression 3. correlate the method of finding HCF of numbers with that of algebraic expression. 4. find the HCF of algebraic expressions . 5. simplify the answer after finding the HCF of algebraic expression. | |
Key Vocabulary: Highest Common Factor, numbers, algebraic expression | |
Key Questions: 1. What does the abbreviation HCF stand for? 2. What is the HCF of 12 and 20? 3. What is the HCF of 100 and 135? | |
TEACHER ACTIVITY | STUDENT ACTIVITY |
Ø Finds the HCF of two numbers. . Ø Finds the HCF of two algebraic expressions. Ø Facilitates in correlating the methods of finding HCF of numbers and algebraic expression. Ø Explains in detail using different examples the method of finding HCF of algebraic expressions. | Ø Recalls the method of finding the HCF of two numbers. Ø Recognizes the method of finding the HCF of two algebraic expressions. Ø Correlates the methods of finding HCF of numbers and algebraic expression. Ø Finds the HCF of different algebraic expressions. |
PERIOD 3 Learning Objectives: The students should be able to: 1. recall the method of finding HCF of numbers. 2. recognize the method of finding HCF of algebraic expression 3. correlate the method of finding HCF of numbers with that of algebraic expression. 4. find the HCF of algebraic expressions . 5. simplify the answer after finding the HCF of algebraic expression. |
Key Vocabulary: Highest Common Factor, numbers, algebraic expression |
Key Questions: 1. What does the abbreviation HCF stand for? 2. What is the HCF of 12 and 20? 3. What is the HCF of 100 and 135? |
TEACHER ACTIVITY | TEACHER ACTIVITY |
Ø Finds the HCF of two numbers. Ø Finds the HCF of two or more algebraic expressions. Ø Facilitates in correlating the methods of finding HCF of numbers and algebraic expression. Ø Explains in detail using different examples the method of finding HCF of algebraic expressions. Ø Gives more examples for practice. | Ø Finds the HCF of two numbers. Ø Finds the HCF of two algebraic expressions. Ø Facilitates in correlating the methods of finding HCF of numbers and algebraic expression. Ø Explains in detail using different examples the method of finding HCF of algebraic expressions Ø Finds the HCF of given algebraic expressions. |
PERIOD 4 Learning Objectives: The students should be able to: 1. Understand the concept of algebraic fractions. 2. Add algebraic fractions with same denominators. 3. Subtract the given algebraic fractions with same denominators. 4. Find out the sum and difference of algebraic fractions with same denominators. | |
Key Vocabulary : Fraction, Algebraic fractions, common denominator, LCM,Sum. | |
Key Questions: 1. How can we add two rational numbers with same denominator? 2. How can we find the Sum of two algebraic fractions with same denominator? 3. find 1/x + 2/ x | |
TEACHER ACTIVITY | STUDENT ACTIVITY |
Ø Makes the students to recall the concept of fraction. Ø Correlates the concept of fraction with algebraic fraction Ø Utilizes the knowledge of the students in Algebra and introduces the concept of the sum and difference of two algebraic fractions with same denominator. Ø Illustrates the way to find out the sum and difference of two algebraic expressions with same denominator through solving examples on board. Ø Giving questions to the students for practice. | Ø Recall the concept of fraction. Ø Differentiate an algebraic fraction from a fraction. Ø Link their knowledge on algebra to the new concept . Ø Understand the way to find out the product of two algebraic expressions. Ø With the help of the teacher students find out the answers. |
PERIOD 5&6 Learning Objectives: The students should be able to: 1. Add algebraic fractions. 2. Find out the sum of algebraic fractions. 3. Subtract algebraic fractions. 4. Find out the Difference of two algebraic fractions. 5. Find the sum and difference in a single problem. | |
Key Vocabulary : Fraction, Algebraic fractions, Product, Sum and difference of algebraic fractions, | |
Key Questions: 1. How can we add algebraic expressions? 2. How to find the Sum of two algebraic expressions? 3. How can we find the difference of algebraic expressions? | |
TEACHER ACTIVITY | TEACHER ACTIVITY |
Ø Utilizes the knowledge of the students in Sum and Difference of two of algebraic fractions. Ø Illustrates the way to find out the sun and Difference of two algebraic expressions through solving an example on board. Ø Makes the students to recall and apply it in a single problem. . | Ø Utilizes the knowledge of the students in Sum and Difference of two of algebraic fractions. Ø Illustrates the way to find out the sun and Difference of two algebraic expressions through solving an example on board. Ø Makes the students to recall and apply it in a single problem. |
PERIOD 7 Learning Objectives : The students should be able to: 1. Multiply algebraic fractions. 2. Find out the product of algebraic fractions. 3. Divide algebraic fractions. | |
Key Vocabulary: Expression, Fraction, Algebraic fractions, product, quotient, Reciprocal fraction. | |
Key Questions: 1. How to find the product of two algebraic expressions? 2. How can we divide two rational numbers? 3. How can we divide two algebraic fractions? | |
TEACHER ACTIVITY | STUDENT ACTIVITY |
Ø Correlates the concept of fraction with algebraic fraction Ø Utilizes the knowledge of the students in product of two algebraic expressions and introduces the concept of the division of two of algebraic fractions. Ø Illustrates the way to divide two algebraic expressions through solving an example on board. Ø Giving questions to the students ask them to find the product. | Ø Differentiate an algebraic fraction from a fraction. Ø Link their knowledge in product of two algebraic expressions to the new concept of quotient. Ø Understand the way to find out the quotient of two algebraic expressions. Ø With the help of the teacher find the product of algebraic expressions. |
MATERIALS: IGCSE Mathematics/ Ric Pimentel and Terry Wall
Extended Mathematics for IGCSE/ David Rayner
TEACHING AIDS: Black board, work sheet, calculator
EVALUATION: Oral questions
Class work
Worksheet
Home work
Exercises
REFLECTION:
- Level of student participation: …………………………………
- Level of student understanding: ………………………………..
- Level of the objectives achieved: ………………………………
- Student feedback: ………….……………………………………
- Overall feedback: ……………………………………………….
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(Subject Teacher) (Co ordinator)
Monday, May 30, 2011
sample question
(1)
In order to find the height of a tree, some children walk 50 m from the base of the tree and measure the angle of elevation as 10o. Find the height of the tree.
In order to find the height of a tree, some children walk 50 m from the base of the tree and measure the angle of elevation as 10o. Find the height of the tree.
Reverse percentages
Reverse percentages
1. Arham thinks his goldfish got chickenpox. He lost 70% of his collection of goldfish. If he has 60
survivors, how many did he have originally?
2. When heated an iron bar expands by 0.2%. If the increase in length is 1 cm, What is the original
length of the bar?
3. A one year old car is worth $11250. If its value had depreciated by 25% in that first year, calculate its price when new.
4. A sterio system is sold for $1998 and an 11% profit made. Find the original cost of the stereo.
5. A dealer gains5% by selling a washing machine for $950. Find the original cost of the washing machine.
6. A dealer bought a second hand car and spent $650 on repairs. He made a profit of 20% by selling the car for $18 650. For how much did he purchase it?
7. By selling a set of Biology books for $408, the book seller suffers a loss of 4%. What was the cost price of the books?
8. A television has a sale price of $180. This is a saving of 25% on the original price. Find the original price.
9. A company increased its productivity by10% each year for the last two years. If it produced 56 265 units this year, how many units did it produce two years ago?
10. This year a farmer’s crop yielded 50 000 tonnes. If this represents a 25% increase on last year, what was the yield last year?
Angles of elevation and depression
Grade 9 Angles of elevation and depression work sheet
(1) In order to find the height of a tree, some children walk 50 m from the base of the tree and measure the angle of elevation as 10o. Find the height of the tree.
(2) A man standing on top of a mountain 1200 m high observes the angle of depression of a steeple to be 43o. How far is the steeple from the mountain?
(3) A ladder is placed on horizontal ground with its foot 2 m from a vertical wall. If the ladder makes an angle of 50o with the ground, find (a) the length of the ladder,
(b) the height of the wall. Give answers correct to 1 d.p.
(4) The length of the shadow of a vertical pole is 3.42m long when the rays of the sun are inclining at an angle of 40.5o to the horizontal. What is the height of the pole?
Give answer to 2 d.p.
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above Y and Z is 40m. Calculate the horizontal distance:
(i) between X and Z. (ii) between X and Y
(iii) between Y and Z.
(6) A radio mast of 30m high is supported by two cables as shown.
From the diagram:
(i) find the distance between the two points A and B.
(1) The height of a tower is 15 m. A man looks at the tower from a distance of 120m. What is the angle of elevation of the top of the tower from man? | |||||
(2) Find the angle of depression ao of the structure. | |||||
(3) The height of a tree is 25 m. The shadow of the tree has a length of 30 m. Calculate the size of the angle marked po in the diagram | |||||
(4) A hot air balloon, M, is 900m vertically above a point N on the ground. A boy stands at a point O, 1200m horizontally from N. (a) Calculate the distance, OM, of the boy from the balloon. (b) Calculate the angle MON. | |||||
(5) A and B are two villages. If the horizontal distance between them is 12km and the vertical distance between them is 2 km, calculate: (i) the shortest distance between the two villages, (ii) the angle of elevation of B and A. | |||||
(6) A man at the top of a vertical cliff observes a boat (B) at sea. From the diagram, (i) State the angle of depression of the boat from the man. (ii) How far is the boat from the cliff? | |||||
(7) Two planes A and B are flying directly above each other. A person (P) can see both of them. The vertical height between B and P is 5 km. if the angles of elevation of the planes from person are 65o and 75o, calculate: (i) horizontal distance of P from the two planes. (ii) the vertical distance between A and B. | |||||
(8) Two people A and B are standing either side of a transmission mast.
A is 130m away from the mast and B is 200m away.
If the angle of elevation of the top of the mast from A is 60o.
Calculate
(i) the height of the mast
(ii) the angle of elevation of the top of the mast from B.
(9) A girl standing on a hill at A, overlooking a lake, can see a small boat at a point B on the lake.
If the girl is at a height of 50m above B and at a horizontal
distance of 120m away from B, calculate:
(i) the angle of depression of the boat from the girl,
(ii) the shortest distance between the girl and the boat.
# Note : Teachers are required to provide suitable diagrams for the questions
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