Difference between revisions of "Algebraic Expressions"

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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
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= Concept Map =  
 
= Concept Map =  
 
[[File:Algebraic Expression  .mm|Flash]]
 
[[File:Algebraic Expression  .mm|Flash]]
 +
 
__FORCETOC__
 
__FORCETOC__
  
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==Reference Books==
 
==Reference Books==
 +
# NCERT textbook for class 7- [http://ncert.nic.in/textbook/textbook.htm?gemh1=12-15 Chapter 12: Algebraic Expressions]
 +
2. Different approaches to teaching algebraic expressions by using and developing contexts such that students see the purpose in      algebraic expressions. [http://www.tess-india.edu.in/sites/default/files/imported/57356/SM11_AIE_Final.pdf Click here]
  
 
= Teaching Outlines =
 
= Teaching Outlines =
  
−
==Concept #==
+
==Concept 1 - [['''Solution for the Problems of Chapter 8-Polynomials 10 STD'''|Solution for the Problems of Chapter 8-Polynomials 10 STD]]==
 
===Learning objectives===
 
===Learning objectives===
 
===Notes for teachers===
 
===Notes for teachers===
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* '''Question Corner'''
 
* '''Question Corner'''
  
 +
== Concept 2: Generalization; and stating in algebraic terms ==
 +
[[File:algebra1.png|400px]]
 +
 +
The students must complete the table like the following:
 +
 +
No of squares
  
−
==Concept #==
+
No of match sticks Write match sticks (as a number expression) Write algebraically
 +
 
 +
=== Algebraic variables can be “x” or “y” or “a” of “b” ===
 +
# Practice with generalization
 +
# Commutative and distributive properties
 +
# Work with Ex 11.1 (from the textbook referred).  Different children can be given different problems. The important thing is they know variables can be in different letters.They should also know that different phenomena can be generalized.  Mangoes, students, pencils.
 +
# Ask children to talk about (I) did they add (ii) did they multiply?
 +
# For example, when they made “Z” they added three match sticks.  When they made 10 “Z” they added 3 +3+3+..... 10 times  This is also multiplying by 10.  And we simply wrote this as if “n” sticks are needed for a “Z”, then 10n sticks are needed for 10 “Z”.  Multiplication is repeated addition.
 +
# Work with the patterns and let children see generalization is not only addition but subtraction and multiplication.
 +
 
 +
== Concept 3: Combining algebraic terms – commutative and distributive properties ==
 +
 
 +
=== Lesson 1 ===
 +
# Give students simple addition (with carry forward).
 +
# In a group students add in different order and verify
 +
# They should multiply in different order and verify
 +
# Also do the distributive property like this
 +
# Go back to the number of squares and triangles and activities and introduce Expressions.
 +
# Give Ex-11.2 different problems as homework/ classwork practice problems.
 +
 
 +
=== Lesson 2 ===
 +
http://www.commoncoresheets.com/Math/Patterns%20and%20Function%20Machines/Identifying%20Pattern%20Attributes/English/1.pdf
 +
# Numbers and generalizations – Use the spreadsheet to work with addition and subtraction and multiplication generalization
 +
# Students must make word problems in groups to describe a given expression
 +
# Students can work in groups for this number pyramid also - check file
 +
# See page 232 of NCERT book used.  That verbal/ mathematical expression important to build.
 +
# Exercise 11.3 for all students (Do 11.3 with the spreadsheet – discuss some problems)
 +
# In groups have children write out expressions for given situations in Page 234 of the book chapter.
 +
# Exercise 11.4 based on student level
 +
# Introduce equation (based on perimeter of an object) – Show Geogebra file
 +
 
 +
==Concept 4: Making simple expressions (addition, subtraction of multiple algebraic terms)==
 
===Learning objectives===
 
===Learning objectives===
 +
# Revisit forming an expression; take the same square example they did above.  Extend by making it like this
 +
[[:File:algebra2.png]]
 +
# See this link very useful - http://nrich.maths.org/8111
 +
## How may different ways can you draw?
 +
## How many down (vertical) lines and how many inverted C?
 +
## How many along (horizontal lines) and and how any downs?
 +
## How many squares and inverted C?
 +
## How many match sticks?
 +
## Exercise 11.4 based on student level
 +
## Exercise 11.5 based on student level
 +
 
===Notes for teachers===
 
===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.''
 
''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.''
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* '''Evaluation (Questions for assessment of the child)'''
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Question Corner'''
 
* '''Question Corner'''
−
 
−
 
 
===Activity No # ===
 
===Activity No # ===
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
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* '''Evaluation (Questions for assessment of the child)'''
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Question Corner'''
 
* '''Question Corner'''
 +
 +
== Concept 5 : Introduction to terminology called monomial, binomial, etc. ==
 +
# Expressions involving square
 +
# The objectives of this lesson is to show the difference between 5x2  and (5x)2
 +
# Use the attached Geogebra file and use following questions.
 +
# What is the side of small square?
 +
# What is the side of large square? Explain in terms of small square
 +
# What is the area? Of small square? Of large square? Express in variables
 +
(x)² and (factor*x)².  How is this different from factor*x²
 +
# For the (5x)2  you should keep drawing squares using polygon tool.
 +
# Use the following second NCERT textbook
 +
http://ncert.nic.in/NCERTS/textbook/textbook.htm?gemh1=12-15 - Exercise 12.1
  
 
= Hints for difficult problems =
 
= Hints for difficult problems =
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Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 +
 +
[[Category:Class 8]]
 +
[[Category:Algebraic expressions]]

Latest revision as of 15:37, 11 November 2019

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

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

Concept Map

[maximize]


Textbook

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

Additional Information

This video is related to writing and evaluating algebraic expression and translate the algebraic expression into word

Useful websites

  1. videos related to algebraic expressionclick here

Reference Books

  1. NCERT textbook for class 7- Chapter 12: Algebraic Expressions

2. Different approaches to teaching algebraic expressions by using and developing contexts such that students see the purpose in algebraic expressions. Click here

Teaching Outlines

Concept 1 - Solution for the Problems of Chapter 8-Polynomials 10 STD

Learning objectives

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.

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ Geogebra Applets
  • Process (How to do the activity)
  • Developmental Questions (What discussion questions)
  • Evaluation (Questions for assessment of the child)
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ Geogebra Applets
  • Process (How to do the activity)
  • Developmental Questions (What discussion questions)
  • Evaluation (Questions for assessment of the child)
  • Question Corner

Concept 2: Generalization; and stating in algebraic terms

Algebra1.png

The students must complete the table like the following:

No of squares

No of match sticks Write match sticks (as a number expression) Write algebraically

Algebraic variables can be “x” or “y” or “a” of “b”

  1. Practice with generalization
  2. Commutative and distributive properties
  3. Work with Ex 11.1 (from the textbook referred). Different children can be given different problems. The important thing is they know variables can be in different letters.They should also know that different phenomena can be generalized. Mangoes, students, pencils.
  4. Ask children to talk about (I) did they add (ii) did they multiply?
  5. For example, when they made “Z” they added three match sticks. When they made 10 “Z” they added 3 +3+3+..... 10 times This is also multiplying by 10. And we simply wrote this as if “n” sticks are needed for a “Z”, then 10n sticks are needed for 10 “Z”. Multiplication is repeated addition.
  6. Work with the patterns and let children see generalization is not only addition but subtraction and multiplication.

Concept 3: Combining algebraic terms – commutative and distributive properties

Lesson 1

  1. Give students simple addition (with carry forward).
  2. In a group students add in different order and verify
  3. They should multiply in different order and verify
  4. Also do the distributive property like this
  5. Go back to the number of squares and triangles and activities and introduce Expressions.
  6. Give Ex-11.2 different problems as homework/ classwork practice problems.

Lesson 2

http://www.commoncoresheets.com/Math/Patterns%20and%20Function%20Machines/Identifying%20Pattern%20Attributes/English/1.pdf

  1. Numbers and generalizations – Use the spreadsheet to work with addition and subtraction and multiplication generalization
  2. Students must make word problems in groups to describe a given expression
  3. Students can work in groups for this number pyramid also - check file
  4. See page 232 of NCERT book used. That verbal/ mathematical expression important to build.
  5. Exercise 11.3 for all students (Do 11.3 with the spreadsheet – discuss some problems)
  6. In groups have children write out expressions for given situations in Page 234 of the book chapter.
  7. Exercise 11.4 based on student level
  8. Introduce equation (based on perimeter of an object) – Show Geogebra file

Concept 4: Making simple expressions (addition, subtraction of multiple algebraic terms)

Learning objectives

  1. Revisit forming an expression; take the same square example they did above. Extend by making it like this

File:algebra2.png

  1. See this link very useful - http://nrich.maths.org/8111
    1. How may different ways can you draw?
    2. How many down (vertical) lines and how many inverted C?
    3. How many along (horizontal lines) and and how any downs?
    4. How many squares and inverted C?
    5. How many match sticks?
    6. Exercise 11.4 based on student level
    7. Exercise 11.5 based on student level

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.

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ Geogebra Applets
  • Process (How to do the activity)
  • Developmental Questions (What discussion questions)
  • Evaluation (Questions for assessment of the child)
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ Geogebra Applets
  • Process (How to do the activity)
  • Developmental Questions (What discussion questions)
  • Evaluation (Questions for assessment of the child)
  • Question Corner

Concept 5 : Introduction to terminology called monomial, binomial, etc.

  1. Expressions involving square
  2. The objectives of this lesson is to show the difference between 5x2 and (5x)2
  3. Use the attached Geogebra file and use following questions.
  4. What is the side of small square?
  5. What is the side of large square? Explain in terms of small square
  6. What is the area? Of small square? Of large square? Express in variables

(x)² and (factor*x)². How is this different from factor*x²

  1. For the (5x)2 you should keep drawing squares using polygon tool.
  2. Use the following second NCERT textbook

http://ncert.nic.in/NCERTS/textbook/textbook.htm?gemh1=12-15 - Exercise 12.1

Hints for difficult problems

Project Ideas

Math Fun

Usage

Create a new page and type {{subst:Math-Content}} to use this template

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