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= Concept Map =
= Concept Map =
[[File:Introduction_to_algebra.mm|Flash]]
__FORCETOC__
__FORCETOC__
=Additional Information=
=Additional Information=
==Useful websites==
==Useful websites==
http://www.math-drills.com/patterning.shtml <br>
http://www.commoncoresheets.com/Patterns.php<br>
http://www.math-aids.com/Algebra/Pre-Algebra/Expressions/Translate.html<br>
==Reference Books==
==Reference Books==
NCERT Book referenced <br>
NCERT Book referenced <br>
===Notes for teachers===
===Notes for teachers===
Activity and lesson 1
[[File:1..png|400px]]<br>[[File:2..png|400px]]<br>
[[File:1.0..png|700px]]<br>[[File:2..png|700px]]<br>
The students must complete the table like the following:
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
No of squares| No of match sticks | Write match sticks (as a number expression) | Write algebraically
(we completed this)
(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 <br>
Go back to the number of squares and triangles and activities and introduce Expressions.<br>
Give Ex-11.2 different problems as homework/ classwork practice problems.<br>
'''Lesson 3'''
(this may take 2 periods)<br>
*http://www.commoncoresheets.com/Math/Patterns%20and%20Function%20Machines/Identifying%20Pattern%20Attributes/English/1.pdf<br>
*Numbers and generalizations – Use the spreadsheet to work with addition and subtraction and multiplication generalization<br>
*Students must make word problems in groups to describe a given expression<br>
*Students can work in groups for this number pyramid also - check file<br>
*See page 232 of NCERT book used. That verbal/ mathematical expression important to build.<br>
*Exercise 11.3 for all students (Do 11.3 with the spreadsheet – discuss some problems)<br>
*In groups have children write out expressions for given situations in Page 234 of the book chapter.<br>
*Exercise 11.4 based on student level <br>
*Introduce equation (based on perimeter of an object) – Show Geogebra file<br>
'''Lesson 4'''
Revisit forming an expression; take the same square example they did above. Extend by making it like this
[[File:3..png|400px]]<br>
See this link very useful - http://nrich.maths.org/8111<br>
-How may different ways can you draw?<br>
-How many down (vertical) lines and how many inverted C?<br>
-How many along (horizontal lines) and and how any downs?<br>
-How many squares and inverted C?<br>
-How many match sticks?<br>
*Exercise 11.4 based on student level
*Exercise 11.5 based on student level
'''Lesson 5'''
Expressions involving square<br>
The objectives of this lesson is to show the difference between 5x2 and (5x)2<br>
Use the attached Geogebra<br>
file and use following questions.<br>
What is the side of small square?<br>
What is the side of large square? Explain in terms of small square<br>
What is the area? Of small square? Of large square? Express in variables<br>
(x)² and (factor*x)². How is this different from factor*x²<br>
For the (5x)2 you should keep drawing squares using polygon tool.<br>
Use the following second NCERT textbook<br>
http://ncert.nic.in/NCERTS/textbook/textbook.htm?gemh1=12-15<br>
Exercise 12.1
===Activity No # ===
===Activity No # ===