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Line 59: − + − − === Objectives === − # To extend the understanding and skill of representing symbolically numbers and manipulating them.<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> − # Together, the negative numbers and positive numbers form one contiuous number line<br> − # Perform manipulations with negative numbers and express symbolically situations involving negative numbers<br> − − ===Notes for teachers=== − Negative numbers are to be introduced as a type of number; they do the opposite of what positive numbers do.<br> − Read the activity for more detailed description. − − ===Activities=== − #Activity 1 -[[What are negative numbers|What are negative numbers]] − − ==Concept #4 The Number Line== Line 88:
Line 72: − Sub Theme:Fractions − Introduction: − Fractions are defined in relation to a whole—or unit amount—by dividing the whole into equal parts. The notion of dividing into equal parts may seem simple, but it can be problematic. Although we use pairs of numbers to represent fractions, a fraction stands for a single number, and as such, has a location on the number line. Number lines provide an excellent way to represent improper fractions, which represent an amount that is more than the related whole. Instruction in fractions that focuses only on the mechanics of procedures and not on reasoning misses valuable opportunities to guide students in developing this core mathematical skill. This section explains the meaning of fractions, reviews some of the common difficulties in understanding the meaning of fractions, and describes how to use simple pictures to represent fractions.Fractions arise naturally whenever we want to consider one or more parts of an object or quantity that is divided into pieces. Consider how fractions are used in the following ordinary situations: − In this section, we define what we mean by a fraction is part of of an object, collection or quantity. − The five meanings listed below serve as conceptual models or tools for thinking about and − working with fractions and serve as a framework for designing teaching activities that engage students in sense making as they construct knowledge about fractions. − − 1.Part of a whole − 2.Part of a group/set − 3.Measure (name for point on number line) − 4.Ratio − 5.Indicated divisionInterpreting fractions − − Given their different representations, and the way they sometimes refer to a − number and sometimes an operation, it is important to be able to discuss − fractions in the many ways they appear. A multiple representation activity, − including different numerical and visual representations, is one way of doing − this. − Sharing food is a good way to introduce various concepts aboput − fractions. For example, using a chocolate bar and dividing it into pieces. − This can be highly motivating if learners can eat it afterwards. − A clock face shows clearly what halves and quarters look like, and can be − extended to other fractions with discussion about why some are easier to − show than others. We can find a third of an hour, but what about a fifth? − − A paper tape measure is a valuable illustration of+ − different fractions. For example, learners can write on 1/2m, 0.50m and − 50cm for their own portable equivalence chart. − − Folding of paper also can illustrate fractions − − − − I have ten bars of chocolate, and I share them equally − between four people. How much will they each get? − − − We recommend that teachers explicitly use thelanguage of fractions in other − parts of the curriculum for reinforcement. For example, when looking at − shapes, talk about ‘half a square’ and ‘third of a circle’. − − Line 213:
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no edit summary
= Teaching Outlines =
= Teaching Outlines =
==Concept #1 - History of Numbers==
==Concept #1 - History of Numbers: Level 0 ==
===Learning objectives===
===Learning objectives===
#What is the story of numbers?
#What is the story of numbers?
#Activity 2
#Activity 2
==Concept #2 Number Sense and Counting==
==Concept #2 Number Sense and Counting : Level 0==
=== Objectives ===
=== Objectives ===
#Activity 2 - [[Cardinal and Ordinal Numbers]]
#Activity 2 - [[Cardinal and Ordinal Numbers]]
==Concept #3 Negative numbers are the opposite of positive numbers==
==Concept #3 The Number Line :Level 1-2 ==
===Objectives===
===Objectives===
#Numbers can be represented on a continuum called a number line
#Numbers can be represented on a continuum called a number line
#Activity 2 - [[Operations_on_number_lines_1|Sum and product of numbers 1]]
#Activity 2 - [[Operations_on_number_lines_1|Sum and product of numbers 1]]
#Activity 3 - [[Building_the_number_line|Classroom number line]]
#Activity 3 - [[Building_the_number_line|Classroom number line]]
==Concept #4 Number Bases==
==Concept #3 Number Bases==
===Learning objectives===
===Learning objectives===
===Notes for teachers===
===Notes for teachers===
#Activity 1 [http://karnatakaeducation.org.in/KOER/en/index.php/Place_value_activity_1 Activity-1]
#Activity 1 [http://karnatakaeducation.org.in/KOER/en/index.php/Place_value_activity_1 Activity-1]
#Activity 2 [http://karnatakaeducation.org.in/KOER/en/index.php/Place_value_activity_2 Activity-2]
#Activity 2 [http://karnatakaeducation.org.in/KOER/en/index.php/Place_value_activity_2 Activity-2]
==Concept #3 Negative numbers are the opposite of positive numbers - ==
=== Objectives ===
# To extend the understanding and skill of representing symbolically numbers and manipulating them.<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>
# Together, the negative numbers and positive numbers form one contiuous number line<br>
# Perform manipulations with negative numbers and express symbolically situations involving negative numbers<br>
===Notes for teachers===
Negative numbers are to be introduced as a type of number; they do the opposite of what positive numbers do.<br>
Read the activity for more detailed description.
===Activities===
#Activity 1 -[[What are negative numbers|What are negative numbers]]
Sub Theme:Fractions
Introduction:
Fractions are defined in relation to a whole—or unit amount—by dividing the whole into equal parts. The notion of dividing into equal parts may seem simple, but it can be problematic. Although we use pairs of numbers to represent fractions, a fraction stands for a single number, and as such, has a location on the number line. Number lines provide an excellent way to represent improper fractions, which represent an amount that is more than the related whole. Instruction in fractions that focuses only on the mechanics of procedures and not on reasoning misses valuable opportunities to guide students in developing this core mathematical skill. This section explains the meaning of fractions, reviews some of the common difficulties in understanding the meaning of fractions, and describes how to use simple pictures to represent fractions.Fractions arise naturally whenever we want to consider one or more parts of an object or quantity that is divided into pieces. Consider how fractions are used in the following ordinary situations:
In this section, we define what we mean by a fraction is part of of an object, collection or quantity.
The five meanings listed below serve as conceptual models or tools for thinking about and
working with fractions and serve as a framework for designing teaching activities that engage students in sense making as they construct knowledge about fractions.
1.Part of a whole
2.Part of a group/set
3.Measure (name for point on number line)
4.Ratio
5.Indicated divisionInterpreting fractions
Given their different representations, and the way they sometimes refer to a
number and sometimes an operation, it is important to be able to discuss
fractions in the many ways they appear. A multiple representation activity,
including different numerical and visual representations, is one way of doing
this.
Sharing food is a good way to introduce various concepts aboput
fractions. For example, using a chocolate bar and dividing it into pieces.
This can be highly motivating if learners can eat it afterwards.
A clock face shows clearly what halves and quarters look like, and can be
extended to other fractions with discussion about why some are easier to
show than others. We can find a third of an hour, but what about a fifth?
A paper tape measure is a valuable illustration of
different fractions. For example, learners can write on 1/2m, 0.50m and
50cm for their own portable equivalence chart.
Folding of paper also can illustrate fractions
I have ten bars of chocolate, and I share them equally
between four people. How much will they each get?
We recommend that teachers explicitly use thelanguage of fractions in other
parts of the curriculum for reinforcement. For example, when looking at
shapes, talk about ‘half a square’ and ‘third of a circle’.
= Assessment activities=
= Assessment activities=