# Difference between revisions of "User:Ranjani"

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= Math Fun = | = Math Fun = | ||

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+ | <div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"> | ||

+ | ;;[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ಸಮರೂಪ_ತ್ರಿಭುಜಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div> | ||

+ | |||

+ | <!-- This portal was created using subst:box portal skeleton --> | ||

+ | <!-- BANNER ACROSS TOP OF PAGE --> | ||

+ | {| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;" | ||

+ | |- | ||

+ | |style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | ||

+ | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics] | ||

+ | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics] | ||

+ | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | ||

+ | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics] | ||

+ | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | ||

+ | [http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus] | ||

+ | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | ||

+ | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics] | ||

+ | |||

+ | [http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks] | ||

+ | |||

+ | [http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank] | ||

+ | |} | ||

+ | While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist''']. | ||

+ | |||

+ | = Concept Map = | ||

+ | __FORCETOC__ | ||

+ | [[File:Triangles_.mm |flash]] | ||

+ | |||

+ | = Textbook = | ||

+ | To add textbook links, please follow these instructions to: | ||

+ | ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage]) | ||

+ | #[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter10.pdf Karnataka text book for Class 10, Chapter 10 - Triangles] | ||

+ | |||

+ | =Additional Information= | ||

+ | http://www.mathopenref.com/similartriangles.html | ||

+ | |||

+ | |||

+ | |||

+ | ==Useful websites== | ||

+ | # [http://www.mathsisfun.com/triangle.html All about triangles] :This is a reference website for types and classification off triangles | ||

+ | # http://www.regentsprep.org/regents/math/geometry/GPB/theorems.htm :A good website for quick reference of all theorems in geometry. Suitable for both students and teachers.<br> | ||

+ | # Click [http://karnatakaeducation.org.in/KOER/en/index.php/Classification_of_triangles here] for notes on types of triangles. | ||

+ | # to get the videos on similar triangle in Kannada [http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ಸಮರೂಪ_ತ್ರಿಭುಜಗಳು click here]this is shared by Yakub koyyur GHS Nada. | ||

+ | |||

+ | ==Reference Books== | ||

+ | |||

+ | = Teaching Outlines = | ||

+ | |||

+ | ==Concept #1 A triangle and its basic properties== | ||

+ | ===Learning objectives=== | ||

+ | # A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. | ||

+ | # It is the polygon with the least number of sides. | ||

+ | # A triangle can be defined as a polygon which has 3 sides, 3 angles and 3 vertices. | ||

+ | # The sum of any two sides is always greater than the third side. | ||

+ | # The angle opposite to longest side is the largest. | ||

+ | # The angles inside the triangle are its interior angles. | ||

+ | # The sum of all 3 interior angles in any triangle is always 180 degrees which is called the angle sum property of a triangle. | ||

+ | # The external angle of a triangle is always equal to the sum of its two opposite interior angles. | ||

+ | |||

+ | ===Notes for teachers=== | ||

+ | [''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''] | ||

+ | # A triangle PQR consists of all the points on the line segment PQ,QR and RP. The three line segments, PQ, QR and RP that form the triangle PQ, are called the sides of the triangle PQR.[[File:Screenshot from 2015-08-14 11-40-01.png | 200px | right]] | ||

+ | # A triangle has three angles. In figure, the three angles are ∠PQR ∠QRP and ∠RPQ | ||

+ | # A triangle has six parts, namely, three sides,PQ QRand RP.Three angles ∠PQR ∠QRP and ∠RPQ. These are also known as the elements of a triangle. | ||

+ | # The point of intersection of the sides of a triangle is known as its vertex. In figure, the three vertices are P, Q and R. In a triangle, an angle is formed at the vertex. Since it has three vertices, so three angles are formed. The word triangle =tri + angle ‘tri’ means three. So, triangle means closed figure of straight lines having three angles. | ||

+ | |||

+ | ===Activity No # 1 Make your triangle === | ||

+ | {| style="height:10px; float:right; align:center;" | ||

+ | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | ||

+ | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||

+ | |} | ||

+ | * Estimated Time - 40 minutes | ||

+ | * Materials/ Resources needed; Paper, pencil, and scale. | ||

+ | * Prerequisites/Instructions, if any: | ||

+ | # The students should know points and line segments. | ||

+ | * Multimedia resources | ||

+ | * Website interactives/ links/ Geogebra Applets | ||

+ | * Process (How to do the activity): | ||

+ | # Mark three non-collinear point P, Q and R on a paper. | ||

+ | # Join these points in all possible ways. The segments are PQ, QR and RP. | ||

+ | # A simple close curve formed by these three segments is called a triangle. It is named in one of the following ways. | ||

+ | # Triangle PQR or Triangle PRQ or Triangle QRP or Triangle RPQ or Triangle RQP . | ||

+ | * Developmental Questions (What discussion questions): | ||

+ | # What are plane figures ? | ||

+ | # What is a polygon ? | ||

+ | # How many points are needed to make a traingle ? | ||

+ | * Evaluation (Questions for assessment of the child): | ||

+ | # What are the intersecting points of a triangle called ? | ||

+ | # Can you draw a triangle with collinear points. | ||

+ | * Question Corner | ||

+ | # Name the elements of a triangle. | ||

+ | |||

+ | ===Activity No # 2. Angle sum property of a triangle=== | ||

+ | |||

+ | Please click the following link for the proof | ||

+ | # [http://tube.geogebra.org/student/m236907 Please click the following link for the proof] : | ||

+ | |||

+ | {| style="height:10px; float:right; align:center;" | ||

+ | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | ||

+ | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||

+ | |} | ||

+ | * Estimated Time: 40 minutes | ||

+ | * Materials/ Resources needed:Laptop, projector, geogebra file and a pointer. | ||

+ | * Prerequisites/Instructions, if any: | ||

+ | # Basics of triangles should have been covered. | ||

+ | # Angles formed when a traversal cuts a pair of parallel lines and the relationship between them should have been taught. | ||

+ | |||

+ | ====Activity No # 3. Side sum property of a triangle==== | ||

+ | |||

+ | * Estimated Time - 20 minutes | ||

+ | * Materials/ Resources needed; Paper, pencil, and scale. | ||

+ | * Prerequisites/Instructions, if any: | ||

+ | # The students should know to construct triangle. | ||

+ | * Process (How to do the activity): | ||

+ | # Mark three non-collinear point A, B and C on a paper. | ||

+ | # Join these points in all possible ways. The segments are AB, BC & AC | ||

+ | # Measure the sides AB, BC & AC | ||

+ | # Find the relationship between AB + BC with AC | ||

+ | # Find the relationship between AC + BC with AB | ||

+ | # Find the relationship between AB + AC with BC | ||

+ | * Developmental Questions (What discussion questions): | ||

+ | # What relationship do you observe ? | ||

+ | * Evaluation (Questions for assessment of the child): | ||

+ | # Think and try : Is it possible to draw a triangle with the condition (AB + BC) < AC | ||

+ | * '''For Geogebra file''' [[http://tube.geogebra.org/m/1482289/ click here ]] | ||

+ | |||

+ | [[Category:Mathematics]] |

## Revision as of 04:24, 22 October 2018

Philosophy of Mathematics |

While creating a resource page, please click here for a resource creation **checklist**.

## Contents

- 1 Concept Map
- 2 Textbook
- 3 Additional Information
- 4 Teaching Outlines
- 5 Assessment activities for CCE
- 6 Hints for difficult problems
- 7 Project Ideas
- 8 Math Fun
- 9 Concept Map
- 10 Textbook
- 11 Additional Information
- 12 Teaching Outlines

# Concept Map

# Textbook

Please click here for Karnataka and other text books.

# Additional Information

## Useful websites

- Useful number pattern activities| Useful number pattern activities
- To get the videos on polynomials in Kannadaclick here this is shared by Yakub koyyur, GHS Nada.

## Reference Books

# Teaching Outlines

## Concept #1 Basics of polynomial

### Learning objectives

- Defining of a Polynomial
- What is an expression?
- Constants, Variables and Exponenets

### Notes for teachers

*why cant the exponent be a negetive integer? *
*because An expression cannot be divided by a variable*

### Activities

- Activity No #1 .Introduction to Polynomials
- Activity No #2
**Concept Name - Activity No.**

## Concept 2 Types of Polynomials

### Learning objectives

- defining monomial, binomial, trinomial and polynomial

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activities

- Activity No #1 Types of polynomals 1
- Activity No #2 Types of polynomals2

## Concept 3 Operation on polynomial

### Learning objectives

- Additon of polynomial
- Substraction of a Polynomial
- Multiplication of a polynomial
- Product of Monomial and a Binomial
- Product of two binomial
- finding product of binomial as Idenitity
- Expansion of Polynomial using Identities

- Divison of a polynomial
- division algoritham for polynomial
- Zeroes of a Polynomial
- division of a polynomial by linear polynomial
- Remainder theorem
- Factor theorem
- Syntheic divsion

- division of a polynomial by polynomial using long division method

### Notes for teachers

*why cant the exponent be a negetive integer? *
*because An expression cannot be divided by a variable*

### Activities

- Activity No #1 .verifying Zeroes of aQuadratic polynomial using Geogebra Applet
- Activity No #2
**Concept Name - Activity No.**

## Concept 4 Degree of a polynomial

- this video helps to know the degree of polynomial

### Learning objectives

- Degree of polynomial with one variable
- constant polynomial
- Linear polynomial
- Quadratic polynomial
- Cubic Polynomial
- Quatric polynomial

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activities

- Activity No #1
**Concept Name - Activity No.** - Activity No #2
**Concept Name - Activity No.**

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activities

- Activity No #1
**Concept Name - Activity No.** - Activity No #2
**Concept Name - Activity No.**

# Assessment activities for CCE

Evaluates the zero of a polynomial by graphical representation

# Hints for difficult problems

'''Solution for the Problems of Chapter 8-Polynomials 10 STD'''

# Project Ideas

# Math Fun

Philosophy of Mathematics |

While creating a resource page, please click here for a resource creation **checklist**.

# Concept Map

# Textbook

To add textbook links, please follow these instructions to: (Click to create the subpage)

# Additional Information

http://www.mathopenref.com/similartriangles.html

## Useful websites

- All about triangles :This is a reference website for types and classification off triangles
- http://www.regentsprep.org/regents/math/geometry/GPB/theorems.htm :A good website for quick reference of all theorems in geometry. Suitable for both students and teachers.
- Click here for notes on types of triangles.
- to get the videos on similar triangle in Kannada click herethis is shared by Yakub koyyur GHS Nada.

## Reference Books

# Teaching Outlines

## Concept #1 A triangle and its basic properties

### Learning objectives

- A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments.
- It is the polygon with the least number of sides.
- A triangle can be defined as a polygon which has 3 sides, 3 angles and 3 vertices.
- The sum of any two sides is always greater than the third side.
- The angle opposite to longest side is the largest.
- The angles inside the triangle are its interior angles.
- The sum of all 3 interior angles in any triangle is always 180 degrees which is called the angle sum property of a triangle.
- The external angle of a triangle is always equal to the sum of its two opposite interior angles.

### Notes for teachers

[

- A triangle PQR consists of all the points on the line segment PQ,QR and RP. The three line segments, PQ, QR and RP that form the triangle PQ, are called the sides of the triangle PQR.
- A triangle has three angles. In figure, the three angles are ∠PQR ∠QRP and ∠RPQ
- A triangle has six parts, namely, three sides,PQ QRand RP.Three angles ∠PQR ∠QRP and ∠RPQ. These are also known as the elements of a triangle.
- The point of intersection of the sides of a triangle is known as its vertex. In figure, the three vertices are P, Q and R. In a triangle, an angle is formed at the vertex. Since it has three vertices, so three angles are formed. The word triangle =tri + angle ‘tri’ means three. So, triangle means closed figure of straight lines having three angles.

### Activity No # 1 Make your triangle

- Estimated Time - 40 minutes
- Materials/ Resources needed; Paper, pencil, and scale.
- Prerequisites/Instructions, if any:

- The students should know points and line segments.

- Multimedia resources
- Website interactives/ links/ Geogebra Applets
- Process (How to do the activity):

- Mark three non-collinear point P, Q and R on a paper.
- Join these points in all possible ways. The segments are PQ, QR and RP.
- A simple close curve formed by these three segments is called a triangle. It is named in one of the following ways.
- Triangle PQR or Triangle PRQ or Triangle QRP or Triangle RPQ or Triangle RQP .

- Developmental Questions (What discussion questions):

- What are plane figures ?
- What is a polygon ?
- How many points are needed to make a traingle ?

- Evaluation (Questions for assessment of the child):

- What are the intersecting points of a triangle called ?
- Can you draw a triangle with collinear points.

- Question Corner

- Name the elements of a triangle.

### Activity No # 2. Angle sum property of a triangle

Please click the following link for the proof

- Estimated Time: 40 minutes
- Materials/ Resources needed:Laptop, projector, geogebra file and a pointer.
- Prerequisites/Instructions, if any:

- Basics of triangles should have been covered.
- Angles formed when a traversal cuts a pair of parallel lines and the relationship between them should have been taught.

#### Activity No # 3. Side sum property of a triangle

- Estimated Time - 20 minutes
- Materials/ Resources needed; Paper, pencil, and scale.
- Prerequisites/Instructions, if any:

- The students should know to construct triangle.

- Process (How to do the activity):

- Mark three non-collinear point A, B and C on a paper.
- Join these points in all possible ways. The segments are AB, BC & AC
- Measure the sides AB, BC & AC
- Find the relationship between AB + BC with AC
- Find the relationship between AC + BC with AB
- Find the relationship between AB + AC with BC

- Developmental Questions (What discussion questions):

- What relationship do you observe ?

- Evaluation (Questions for assessment of the child):

- Think and try : Is it possible to draw a triangle with the condition (AB + BC) < AC

**For Geogebra file**[click here ]