Changes

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.

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 =

[[File:Number system -Resource material_html_m1be8b6d7.jpg|400px]]<br>

[[File:Number system -Resource material_html_m1be8b6d7.jpg|400px]]<br>

*Understand meanings of operations and how they relate to one another

*Understand meanings of operations and how they relate to one another

= FLOW CHART  

= FLOW CHART =

[[File:Number system -Resource material_html_m65980570.jpg|400px]]

[[File:Number system -Resource material_html_m65980570.jpg|400px]]

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.

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 ==

== Part 1: Number Sense – Counting and Operations ==

=== Objectives ===

'''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 ===

=== 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)

'''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'''

4. Understand the difference between the ordinal value of a number and the representation of a quantity

4. Understand the difference between the ordinal value of a number and the representation of a quantity

5. Manipulate numbers, perform mathematical operations and express these operations symbolically in mathematical language

5. Manipulate numbers, perform mathematical operations and express these operations symbolically in mathematical language

 

<br>'''Materials needed'''<br>

 

 

Materials needed

1. Apples in two groups (or any other fruit)

1. Apples in two groups (or any other fruit)

2. Small cards for writing down the numbers as well as for writing the operations

2. Small cards for writing down the numbers as well as for writing the operations

3. Pencils, etc

3. Pencils, etc

4. A collection of other objects – stones, sticks, notebooks

4. A collection of other objects – stones, sticks, notebooks<br>

How to do the activity

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

1. This whole activity can be done in groups with different sets of objects

#This whole activity can be done in groups with different sets of objects

 

#Keep two group of apples separately.

2. Keep two group of apples seperately.

#Keep them in physically different arrangements.

 

#Based on visual inspection and counting, determine the number of apples and which group is larger or smaller or if both are equal.

3. Keep them in physically different arrangements.

<br>'''Questions for discussion:'''<br>

 

4. Based on visual inspection and counting, determine the number of apples and which group is larger or smaller or if both are equal.

 

Questions for discussion:

How can you describe the two groups? [ Words – red, large, small, more, less]

How can you describe the two groups? [ Words – red, large, small, more, less]

Which words are being used first – more or less, dozen, kilo

Which words are being used first – more or less, dozen, kilo