Introduction to Algebra

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

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Concept Map

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Textbook

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Additional Information

Useful websites

http://www.math-drills.com/patterning.shtml
http://www.commoncoresheets.com/Patterns.php
http://www.math-aids.com/Algebra/Pre-Algebra/Expressions/Translate.html

Reference Books

NCERT Book referenced
http://ncert.nic.in/NCERTS/textbook/textbook.htm?femh1=11-14

Teaching Outlines

Concept - algebra lessons

Learning objectives

Generalization; and stating in algebraic terms
Algebraic variables can be “x” or “y” or “a” of “b”

Notes for teachers

Activity and lesson 1

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 (we completed this)

Lesson 2

Practice with generalization Commutative and distributive properties

(Part1 - Practice with generalization)

• Work with Ex 11.1. 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.

• Check the following document for Shapes patterns students to understand patterns more.

(Part 2 - Commutative and distributive properties)

• 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 3 (this may take 2 periods)

• 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
  

Lesson 4

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

Lesson 5

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

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