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Line 1: − + − + + + + + + + + + + − our daily life is based on numbers. We use it for shopping, reckoning the time, counting distances and so on. Simple calculations seem effortless and trivial for most of our necessities.So we should know about numbers.+ − Numbers help us count concrete objects. They help us to say which collection of objects . + − In this we are learning about Basic operations of numbers Different types of numbers,Representation,.... − How can math be so universal? First, human beings didn't invent math concepts; we discovered them. Also, the language of math is numbers, not English or German or Russian. If we are well versed in this language of numbers, it can help us make important decisions and perform everyday tasks. Math can help us to shop wisely, understand population growth, or even bet on the horse with the best chance of winning the race. − Mathematics expresses itself everywhere, in almost every face of life - in nature all around us, and in the technologies in our hands. Mathematics is the language of science and engineering - describing our understanding of all that we observe.Mathematics has been around since the beginnings of time and it most probably began with counting.Many, if not all puzzles and games require mathematical logic and deduction. This section uses the fun and excitement of various popular games and puzzles, and the exhilaration of solving them, to attract and engage the students to realise the mathematics in fun and games. − Descriptive Statement − Number sense is defined as an intuitive feel for numbers and a common sense approach to using them. It is a comfort with what numbers represent, coming from investigating their characteristics and using them in diverse situations. and how they can best be used odescribe a particular situation. Number sense is an attribute of all successful users of mathematics. Our students often do not connect what is happening in their mathematics classrooms with their daily lives. It is essential that the mathematics curriculum build on the sense of number that students bring with them to school. Problems and numbers which arise in the context of the students world are more meaningful to students than traditional textbook exercises and help them develop their sense of how numbers and operations are used. Frequent use of estimation and mental computation are also important ingredients in the development of number sense, as are regular opportunities for student communication. Discussion of their own invented strategies for problem solutions helps students strengthen their intuitive understanding of numbers and the relationships between numbers. − IN SUMMARY, the commitment to develop number sense requires a dramatic shift in the way students learn mathematics. Our students will only develop strong number sense to the extent that their teachers encourage the understanding of mathematics as opposed to the memorization of rules and mechanical application of algorithms. Every child has the capability to succeed as a user of mathematics, but the degree of success is directly related to the strength of their number sense. The way to assure that all students acquire a good sense − of number is to have them consistently engage in activities which require them to think about numbers and number relationships and to make the connection with quantitative information encountered in their daily lives. − MIND MAP + + + + + + + − How a teacher can use this resource+ − A mathematics teacher focuses on classroom activities and strategies for grades 8-12, deepening mathematical understanding, and linking resource to practice.The Resource explains the language of numbers. and can be used for Teacher Resources or Student Projects.Always it is a great challenge for a Maths teacher to build the basic concept of number when a child enters high school. So teacher has to bridge the gap with the basics which a child may lack. High school students should extend their meaning of number to the real number system and recognize that still other number systems exist. They should have + − + − the opportunity to develop intuitive proofs of the fundamental properties of closure, commutativity, associativity, and distributivity. One way to achieve such an understanding in the classroom is through the identification and description of number patterns and the use of pattern-based thinking .Activities promoting pattern-based thinking can assist students in making similar generalizations about other number forms and their relationships, as well as build initial notions of still other types of important number concepts such as odd and even,prime numbers, and factors and multiples. − − − Objectives − − . understand numbers, ways of representing numbers, relationships amongnumbers, and number systems − − . understand meanings of operations and how they relate to one another − − FLOW CHART − − Sub Theme : Bridge course in Class 8 − Introduction − − − − Line 47:
Line 38: − + − (There could be a few more lessons in this section. For example, for representing collections and making a distinction between 1 apple and a dozen apples. This idea could be explained later to develop fractions. Another activity that can also be used to talk of units of measure. Addition and subtraction have been discussed here – extend this to include multiplication and division)+ − + Line 932:
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Series of Activities on Number Systems (view source)
Revision as of 11:38, 26 January 2013
, 11:38, 26 January 2013no edit summary
[[File:Number system -Resource material_html_m489198fe.png|400px]]
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TOPIC:NUMBER SYSTEM[[File:Number system -Resource material_html_m21619cb9.png|400px]][[File:Number system -Resource material_html_m6187dae0.png|400px]][[File:Number system -Resource material_html_m763a208c.png|400px]][[File:Number system -Resource material_html_m614b607b.png|400px]][[File:Number system -Resource material_html_m330e2a.png|400px]][[File:Number system -Resource material_html_m77c360a2.png|400px]][[File:Number system -Resource material_html_m7b853267.png|400px]][[File:Number system -Resource material_html_m7b853267.png|400px]][[File:Number system -Resource material_html_m6f20bce3.png|400px]][[File:Number system -Resource material_html_m3cabb6c3.png|400px]][[File:Number system -Resource material_html_m3aee68a.png|400px]][[File:Number system -Resource material_html_m1f589acc.png|400px]][[File:Number system -Resource material_html_m1be8b6d7.jpg|400px]][[File:Number system -Resource material_html_54627769.png|400px]][[File:Number system -Resource material_html_39498010.png|400px]][[File:Number system -Resource material_html_360ba54.png|400px]][[File:Number system -Resource material_html_60f99847.png|400px]][[:File:Number system -Resource material_html_58f2d11d.png]][[File:Number system -Resource material_html_33f3ff3f.png|400px]][[File:Number system -Resource material_html_4df41ad.png|400px]][[File:Number system -Resource material_html_4b50dacc.png|400px]][[File:Number system -Resource material_html_1de463c.jpg|400px]]
TOPIC:NUMBER SYSTEM[[File:Number system -Resource material_html_m21619cb9.png|400px]][[File:Number system -Resource material_html_m6187dae0.png|400px]][[File:Number system -Resource material_html_m763a208c.png|400px]][[File:Number system -Resource material_html_m614b607b.png|400px]][[File:Number system -Resource material_html_m330e2a.png|400px]][[File:Number system -Resource material_html_m77c360a2.png|400px]][[File:Number system -Resource material_html_m7b853267.png|400px]][[File:Number system -Resource material_html_m7b853267.png|400px]][[File:Number system -Resource material_html_m6f20bce3.png|400px]][[File:Number system -Resource material_html_m3cabb6c3.png|400px]][[File:Number system -Resource material_html_m3aee68a.png|400px]][[File:Number system -Resource material_html_m1f589acc.png|400px]][[File:Number system -Resource material_html_54627769.png|400px]][[File:Number system -Resource material_html_39498010.png|400px]][[File:Number system -Resource material_html_360ba54.png|400px]][[File:Number system -Resource material_html_60f99847.png|400px]][[:File:Number system -Resource material_html_58f2d11d.png]][[File:Number system -Resource material_html_33f3ff3f.png|400px]][[File:Number system -Resource material_html_4df41ad.png|400px]][[File:Number system -Resource material_html_4b50dacc.png|400px]][[File:Number system -Resource material_html_1de463c.jpg|400px]]
INTRODUCTION
= INTRODUCTION =
<br> Our daily life is based on numbers. We use it for shopping, reckoning the time, counting distances and so on. Simple calculations seem effortless and trivial for most of our necessities.So we should know about numbers.
Numbers help us count concrete objects. They help us to say which collection of objects . In this we are learning about basic operations of numbers - different types of numbers, representation,etc. <br>
How can math be so universal? First, human beings didn't invent math concepts; we discovered them. Also, the language of math is numbers, not English or German or Russian. If we are well versed in this language of numbers, it can help us make important decisions and perform everyday tasks. Math can help us to shop wisely, understand population growth, or even bet on the horse with the best chance of winning the race. <br>
Mathematics expresses itself everywhere, in almost every face of life - in nature all around us, and in the technologies in our hands. Mathematics is the language of science and engineering - describing our understanding of all that we observe.Mathematics has been around since the beginnings of time and it most probably began with counting. Many, if not all puzzles and games require mathematical logic and deduction. This section uses the fun and excitement of various popular games and puzzles, and the exhilaration of solving them, to attract and engage the students to realise the mathematics in fun and games. <br?
'''Descriptive Statement'''''Italic text''
<br>Number sense is defined as an intuitive feel for numbers and a common sense approach to using them. It is a comfort with what numbers represent, coming from investigating their characteristics and using them in diverse situations. and how they can best be used odescribe a particular situation. Number sense is an attribute of all successful users of mathematics. Our students often do not connect what is happening in their mathematics classrooms with their daily lives. It is essential that the mathematics curriculum build on the sense of number that students bring with them to school. Problems and numbers which arise in the context of the students world are more meaningful to students than traditional textbook exercises and help them develop their sense of how numbers and operations are used. Frequent use of estimation and mental computation are also important ingredients in the development of number sense, as are regular opportunities for student communication. Discussion of their own invented strategies for problem solutions helps students strengthen their intuitive understanding of numbers and the relationships between numbers.<br>
In summary, the commitment to develop number sense requires a dramatic shift in the way students learn mathematics. Our students will only develop strong number sense to the extent that their teachers encourage the understanding of mathematics as opposed to the memorization of rules and mechanical application of algorithms. Every child has the capability to succeed as a user of mathematics, but the degree of success is directly related to the strength of their number sense. The way to assure that all students acquire a good sense of numbers is to have them consistently engage in activities which require them to think about numbers and number relationships and to make the connection with quantitative information encountered in their daily lives. <br><br>
== How a teacher can use this resource ==
A mathematics teacher focuses on classroom activities and strategies for grades 8-12, deepening mathematical understanding, and linking resource to practice.The Resource explains the language of numbers. and can be used for Teacher Resources or Student Projects.Always it is a great challenge for a Maths teacher to build the basic concept of number when a child enters high school. So teacher has to bridge the gap with the basics which a child may lack. High school students should extend their meaning of number to the real number system and recognize that still other number systems exist. They should have the opportunity to develop intuitive proofs of the fundamental properties of closure, commutativity, associativity, and distributivity. One way to achieve such an understanding in the classroom is through the identification and description of number patterns and the use of pattern-based thinking .Activities promoting pattern-based thinking can assist students in making similar generalizations about other number forms and their relationships, as well as build initial notions of still other types of important number concepts such as odd and even,prime numbers, and factors and multiples.
= MIND MAP =
[[File:Number system -Resource material_html_m1be8b6d7.jpg|400px]]<br>
= Objectives =
The students should be able to<br>
*Understand numbers, ways of representing numbers, relationships among numbers and number systems<br>
*Understand meanings of operations and how they relate to one another
= FLOW CHART
[[File:Number system -Resource material_html_m65980570.jpg|400px]]
= What are numbers - A Bridge course in Class 8 =
This unit on number systems is in three parts. The first part will be to develop in children a sense of numbers, the idea of quantity, counting and mathematical manipulation, collections of quantities and developing a unit of measure. The second would be to develop the ideas of the negative numbers and build an understanding based on the manipulations of numbers. The third part would be to introduce the number line as a continuum and to introduce ideas of fractions and rational numbers.While this is for classes 7and 8, we understand that students may come with very limited sense of the numbers. So the activities are designed in such a way as to help such students also.
== Part 1: Number Sense – Counting and Operations ==
=== Objectives ===
This unit on number systems is in three parts. The first part will be to develop in children a sense of numbers, the idea of quanity, counting and mathematical manipulation, collections of quantities and developing a unit of measure. The second would be to develop the ideas of the negative numbers and build an understanding based on the manipulations of numbers. The third part would be to introduce the number line as a continuum and to introduce ideas of fractions and rational numbers.
While this is for classes 7and 8, we understand that students may come with very limited sense of the numbers. So the activities are designed in such a way as to help such students also.
Part 1: Number Sense – Counting and Operations
Objectives
1. Understand that there is an aspect of quantity that we can develop with disparate objects
1. Understand that there is an aspect of quantity that we can develop with disparate objects
2. Comparison and mapping of quanties (more or less or equal)
2. Comparison and mapping of quanties (more or less or equal)
6. Recognizing the quantity represented by numerals and discovering how one number is related to another number
6. Recognizing the quantity represented by numerals and discovering how one number is related to another number
7. This number representation is continuous.
7. This number representation is continuous.
Lesson 1 : Quantity and Numbers (this is not one period – but a lesson topic)
===Lesson 1 : Quantity and Numbers ===
'''Teacher Note''' - this is not one period – but a lesson topic. There could be a few more lessons in this section. For example, for representing collections and making a distinction between 1 apple and a dozen apples. This idea could be explained later to develop fractions. Another activity that can also be used to talk of units of measure. Addition and subtraction have been discussed here – extend this to include multiplication and division)
Objectives of the activity
'''Objectives of the activity'''
1. To develop an understanding that quantity is something we associate with objects and there are different ways of representing this
1. To develop an understanding that quantity is something we associate with objects and there are different ways of representing this
2. Different objects have different measures of quantity
2. Different objects have different measures of quantity
7. Now, with radius AC and centre A, mark a point on the number line.
7. Now, with radius AC and centre A, mark a point on the number line.
Let the marked point is M. M represents √2 on the number line.
Let the marked point is M. M represents √2 on the number line.