Changes

= Introduction =

= Introduction =

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><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><br>

'''Descriptive Statement'''

'''Descriptive Statement'''

<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><br>

<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 best they can be used to describe 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><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>

In summary, the commitment to develop number sense requires a dramatic shift in the way students learn mathematics.

 

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 =

= Mind Map =

6. Recognizing the quantity represented by numerals and discovering how one number is related to another number<br>

6. Recognizing the quantity represented by numerals and discovering how one number is related to another number<br>

7. This number representation is continuous.<br>

7. This number representation is continuous.<br>

=== Lesson 1 :  Quantity and Numbers ===

=== 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).<br><br>

'''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).<br><br>

Separate the two groups again.  Can I add only all of them together? Or can I add 1 at a time, 2 at a time, 3 at a time?   

Separate the two groups again.  Can I add only all of them together? Or can I add 1 at a time, 2 at a time, 3 at a time?   

The ideas to be introduced would be Skip counting and quantity increase is continuous.<br>

The ideas to be introduced would be Skip counting and quantity increase is continuous.<br>

'''Part 2'''

'''Part 2'''

*Pose this question like this – “ I added 5 apples to six apples to make it 11 apples.  What should I do to a bag of 11 apples to make it have 6 apples again”.  I take away 5.  This is called subtraction and is the inverse process of addition.<br>   

*Pose this question like this – “ I added 5 apples to six apples to make it 11 apples.  What should I do to a bag of 11 apples to make it have 6 apples again”.  I take away 5.  This is called subtraction and is the inverse process of addition.<br>   

'''''The “-” is called a mathematical operator.  The subtraction is called an operation.  These operations have some properties and they always hold''.'''

'''''The “-” is called a mathematical operator.  The subtraction is called an operation.  These operations have some properties and they always hold''.'''

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'''Evaluation activities'''

'''Evaluation activities'''

*Create situations where children work in groups and compare collections of items without counting.<br>

*Create situations where children work in groups and compare collections of items without counting.

*Have groups work with 3 groups of fruits, sticks, pencils, etc. The idea that addition can be extended indefinitely can be discussed.<br>

*Have groups work with 3 groups of fruits, sticks, pencils, etc. The idea that addition can be extended indefinitely can be discussed.

*Subtraction with quantities without getting into negative numbers.<br>

*Subtraction with quantities without getting into negative numbers.

*Children must orally and in a written form represent these operations.<br>

*Children must orally and in a written form represent these operations.

*Create different sets of objects and ask the children to add [ to test for the legitimacy of addition]

*Create different sets of objects and ask the children to add [ to test for the legitimacy of addition]

*Adding to quantity in 2's, 3's - Combinations of 2 numbers that will give 10 as an answer.  Can you guess the pattern for combinations of numbers that will give 20 as an answer?  [ Subtraction is an inverse process of addition]   

*Adding to quantity in 2's, 3's - Combinations of 2 numbers that will give 10 as an answer.  Can you guess the pattern for combinations of numbers that will give 20 as an answer?  [ Subtraction is an inverse process of addition]   

*Worksheets of simple problem solving – with just number manipulations

*Worksheets of simple problem solving – with just number manipulations

*Worksheets of simple problem solving – with word descriptions.  Children can either draw these answers or write them in statements.  Evaluate the ability of the child to process written instructions.

*Worksheets of simple problem solving – with word descriptions.  Children can either draw these answers or write them in statements.  Evaluate the ability of the child to process written instructions.

== Part II – Negative Numbers ==

== Part II – Negative Numbers ==

# To understand that negative numbers are numbers that are created to explain situations in such a way that mathematical operations hold<br>

# To understand that negative numbers are numbers that are created to explain situations in such a way that mathematical operations hold<br>

# Negative numbers are opposite of positive numbers; the rules of working with negative numbers are opposite to that of working with positive numbers<br>

# Negative numbers are opposite of positive numbers; the rules of working with negative numbers are opposite to that of working with positive numbers<br>

# Together, the negative numbers and positive numbers form one contiuous number line<br>

# Together, the negative numbers and positive numbers form one continuous number line<br>

# Perform manipulations with negative numbers and express symbolically situations involving negative numbers<br>

# Perform manipulations with negative numbers and express symbolically situations involving negative numbers<br>

#Does this give us the answer to the problem? <br>

#Does this give us the answer to the problem? <br>

#Did we add or subtract to find the answer? <br><br>

#Did we add or subtract to find the answer? <br><br>

'''Activity2  - Sum and product of numbers'''<br>

'''Activity2  - Sum and product of numbers'''<br>

'''Objectives'''

'''Objectives'''

Addition using number line can be demonstrated using Geogebra.<br>

Addition using number line can be demonstrated using Geogebra.<br>

See image below<br>

See image below<br>

Click [http://www.karnatakaeducation.org.in/KOER/Maths/numberlineAddition.html here] for an animation.<br>

Click [http://karnatakaeducation.org.in/KOER/Maths/numberlineAddition.html here] for an animation.<br>

Click [http://www.karnatakaeducation.org.in/KOER/Maths/numberlineAddition.ggb here] to download the Geogebra file.<br>

Click [http://karnatakaeducation.org.in/KOER/Maths/numberlineAddition.ggb here] to download the Geogebra file.<br>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'''How to do the activity - Multiplication'''<br><br>

'''How to do the activity - Multiplication'''<br><br>

parts of the curriculum for reinforcement. For example, when looking at

parts of the curriculum for reinforcement. For example, when looking at

shapes, talk about ‘half a square’ and ‘third of a circle’.  

shapes, talk about ‘half a square’ and ‘third of a circle’.  

A discontinuous whole is a group of items that together make up the whole. To find a fraction part of such a whole, we can divide it up into groups, each with the same number of items. We call such groups "equal-sized groups" or "groups of equal size". It is important that we always mention thathe groups are equal in size to emphasise this aspect of the fraction parts of a whole. Examples of discontinuous wholes are: 15 oranges, 6 biscuits, 27 counters, 4 new pencils, etc.  

A discontinuous whole is a group of items that together make up the whole. To find a fraction part of such a whole, we can divide it up into groups, each with the same number of items. We call such groups "equal-sized groups" or "groups of equal size". It is important that we always mention thathe groups are equal in size to emphasise this aspect of the fraction parts of a whole. Examples of discontinuous wholes are: 15 oranges, 6 biscuits, 27 counters, 4 new pencils, etc.  

Language patterns for a continuous whole To find 1/5  of my circular disc, I first divide the whole circular disc into 5 parts of equal size. Each part is 1/5 of the whole, and if I shade one of these parts, I have shaded of the 1/5 whole.  

Language patterns for a continuous whole To find 1/5  of my circular disc, I first divide the whole circular disc into 5 parts of equal size. Each part is 1/5 of the whole, and if I shade one of these parts, I have shaded of the 1/5 whole.  

find a fraction part of a unit whole, we have to cut/fold/break, etc. because the whole is a  

find a fraction part of a unit whole, we have to cut/fold/break, etc. because the whole is a  

single thing.  

single thing.  

same number as the denominator. It is thus made up of more that one item and is a  

same number as the denominator. It is thus made up of more that one item and is a  

discontinuous whole.  

discontinuous whole.  

denominator. This is also made up of more than one unit and so it is a discontinuous  

denominator. This is also made up of more than one unit and so it is a discontinuous  

whole.  

whole.  

denominator. This is also a multiple unit whole, and so it is a discontinuous whole.  

denominator. This is also a multiple unit whole, and so it is a discontinuous whole.  

   

   

Writing or ordering fractions in pre positioned boxes along number line.  This can illustrate how a number line can be used to represent fractions of distance or length; or support the notion of a fraction being larger or smaller than another.   

Writing or ordering fractions in pre positioned boxes along number line.  This can illustrate how a number line can be used to represent fractions of distance or length; or support the notion of a fraction being larger or smaller than another.   

Marking the fraction on an empty number line - this involves measurement and judgement of a fraction as a proportion of a length or distance.

Marking the fraction on an empty number line - this involves measurement and judgement of a fraction as a proportion of a length or distance.

the fractions with denominator equal to 5 are now displayed as shown:  

the fractions with denominator equal to 5 are now displayed as shown:  

To find equivalent forms of Rational Numbers

To find equivalent forms of Rational Numbers

Principal Roots and Irrational Numbers  

Principal Roots and Irrational Numbers  

Prerequisite Concepts: Set of rational numbers  

Prerequisite Concepts: Set of rational numbers  

Activity to find square root using geoboard

Activity to find square root using geoboard

Construct these triangles on a virtual geoboard. Provide students with the formula for the area of a triangle (A = ½bh) and ask them to determine the areas of the displayed triangles. [12.5 units2 and 4.5 units2.]

Construct these triangles on a virtual geoboard. Provide students with the formula for the area of a triangle (A = ½bh) and ask them to determine the areas of the displayed triangles. [12.5 units2 and 4.5 units2.]

  Tell students that there are more squares that fit on a geoboard than those found during the previous lesson. Today's lesson will focus on finding some atypical squares using geoboards.

  Tell students that there are more squares that fit on a geoboard than those found during the previous lesson. Today's lesson will focus on finding some atypical squares using geoboards.

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_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]]

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_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]]