It was prepared for the staff of our school , in order to guide that how to make, teaching and leaning for Maths, interesting and fun . To reduce boredom for kids and to relate the concepts with the nature and universe.

1. WELCOME

2. •The laws of nature
are but the
mathematical
thoughts of God.
(Euclid)

3. Just think doing
things for others
could really end up
benefiting you in the
long run.

4. I. Contents:
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TEACHING-LEARNING REQUIREMENTS
OF GRADE 3 TO 6.
CLASS-ROOM ENVIRONMENT OF THIS
GRADE LEVEL.
MATHEMATICAL FOUNDATIONS.
OBSTACLES TO QUALITY MATHLEARNING.
HOW TO ERADICATE THE OBSTACLES.
TYPES OF INTELLIGENCES.
HABITS OF HIGHLY EFFECTIVE MATHTEACHING.

5. 1.TEACHING-LEARNING
REQUIREMENTS



Students in the grade 3-6 are intrigued with
mathematics. To nurture this interest , students
at this grade level need to be involved in an
active learning process rather than one that only
builds memorization of concepts and procedures.
Concrete experiences are also important at this
stage of development . Such experiences allow
students to develop and strengthen the skills
needed.
The skills are :
To communicate , reason, solve mathematical
problems and reach to higher level of cognitive
reasoning.

6. 2. CLASS-ROOM ENVIRONMENT
FOR THIS GRADE LEVEL.

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An effective class-room environment provides
intellectually stimulating instructions and
developmentally appropriate opportunities for
the students to learn mathematical concepts.
This classroom environment fosters an
atmosphere in which students are encouraged to
find solutions through a variety of methods and
feel less threatened about making and correcting
mistakes.
Class-room instruction includes opportunities for
students to communicate them mathematical
thinking by talking , writing and sharing with
each other.

7. 3. MATHEMATICAL
FOUNDATION.


Grade contents build a foundation of basic
number-sense , operations , quantitative
reasoning , number-patterns , relationships ,
geometric and spatial reasoning ,
measurements , probability and statistics.
This content builds on and expand
conceptual understanding of math.
Through interweaving of mathematical
concepts and process students learn to value
math , display confidence in the
mathematically solved problems, and make
connections between math and other
subjects .

8. 4.OBSTACLES TO QUALITY
MATH-LEARNING.
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Family disaster-stories about math
difficulty.
Terror producing teaching.
Fuzzier meaning less explanation.
Lack of link between math and real life.
A rush into “formal abstract” math without
any concrete physical or pictured
experience without any concrete,
physical or pictured experience.

9. 
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A robotic, imitate, memorized style with little
conceptual grounding.
A habitual disconnect between a child’s natural style
and a superimposed alien math style.
Sometimes the material is meaningless, monotone ,
black and white, that leads to boredom.
Poor self-image causes constant forgetting, spacing
out, blowing tests and in the end develops hatred for
math.
COMENT : How would you react with a daily
portion of sawdust for your meal?

10. How to help them?
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Youth can leap over any of these obstacles to math
success.
Right approach can make up for a multitude of
assumed impossibilities and disabilities.
Young people or even the adults just need to get the
real scoop behind the method in a clear and fun
way.
They are thirsty for concepts, the number sense, the
number patterns, the calculations , the formulae etc.
At his stage we can lead them to the right direction.
Nine-tenth of education is encouragement.
As soon as we discover the problem we will be able
to resolve it.

11. TYPES OF INTELLEGENCE
1.
2.
3.
4.
5.
6.
7.
8.
9.
There are nine types of intelligences by research, each
has been proved to be equivalent to any other by any
scientific criterion you think of, when we speak they are
intelligent we can actually and accurately mean they are
intelligent nine other ways;
Intrapersonally
(self smart)
Kinesthetically
(mind-body union)
Spatially
(Picture smart)
Interpersonally
(people smart)
Musically
(music smart)
Naturalistically
(nature smart)
Logically/mathematically (number/reason smart)
Linguistically
(word smart)
Existentially
(deep thinking ,questions)
If that is so it stands to reason that if you teach math through
all the intelligence channels, you have a vastly increased
chance of reaching every brain you are working with.

12. FOUR HABITS OF HIGHLY
EFFECTIVE MATH TEACHING
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1.LETS MAKE SENSE:
Dilemma between conceptual vs. procedural
understanding.
2.REMEMBER THE GOALS:
connect your ultimate goals to sub goals .
3.KNOW YOUR TOOLS:
Learn how to use tools and add to your toolbox.
4.LIVING AND LOVING MATH:
You are a teacher. Show the way, with your
attitudes.

13. II.CONTENTS
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1. Number patterns
2.Concept of
multiplication
3.multimlication table.
4.division
5.Factors
6.prime numbers
7. integers
8.fractions
9.problem solving.

14. NUMBER PATTERNS
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PREVIOUS KNOWLEDGE:
Whole numbers
Natural numbers

15. 1.EVEN AND ODD NUMBERS
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Objectives: to identify even and odd
numbers.
Use a hundred chart.
Skip-count by two’s, start from 2 ,the numbers
you will land on are even, shade the numbers ,
by the end of the page we get the shaded
numbers which are even.
The remaining numbers are odd numbers.
Activity: use hundred chart and colors

16. A HUNDRED CHART
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100

17. 
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ACTIVITY :
Material: HUNDRED CHART TABLE
SKIP-COUNT by 3’s, 4’s, 5’s,….10’s.
Which helps to learn and understand table
formation.

18. Result;
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

The coloured boxes have even numbers, where 0, 2, 4, 6
and 8 are in ones place.
The boxes not coloured are odd numbers have 1, 3, 5,
7and 9 in ones place.
Practice/exercise; use hundred chart and ask the
students whether the number is even or odd.
a) 7. b) 4. c)8. d) 9. e) 21 f) 54.
Activity: Students can form different patterns e.g, start at
5, skip- count by 5, where do you land after 4 skips?
skip count by 4 ,move 6 skips, what do you land on ?
2, 4, 6, _, _, 12, 14,……..
5, 10, _, 20, _, ………….

19. 2.CONCEPT OF
MULTIPLICATION




Objectives:
To develop the concept of multiplication
through addition.
To prepare the multiplication table by skipcount.
To stimulate them through different
experiences.

20. MULTIPLICATION THROUGH
ADDITION


Form the arrays of some objects ; how
many in all?
4
4
4
12
3 groups of 4 =

21. Connect addition to the
multiplication
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Repeat addition of a number and find:
3 groups of 4 =4+4+4 = 12
Similarly; 2 groups of 5 =___
And 4 groups of 7 =___
3+3+3+3+3 =15
5 Threes
=15
5 times 3
=15
Finally

5 x3
=15
This concept can be related by Number line.

22. Practice:
X
4
1 2 3 4 5 6
X 1
6
X 0
5
2
1
3 4
2
3
5
6
4

23. 
STRUCTURED DRILL IS
DEMONSRTATED, WHICH IS
DESIGNED FOR TABLE LEARNING.

24. X
0
1
2
3
4
5
6
7
8
9
10
The multiplication table
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
10
2
0
2
4
6
8
10
12
14
16
18
20
3
0
3
6
9
12
15
18
21
24
27
30
4
0
4
8
12
16
20
24
28
32
36
40
5
0
5
10
15
20
25
30
35
40
45
50
6
0
6
12
18
24
30
36
42
48
54
60
7
0
7
14
21
28
35
42
49
56
63
70
8
0
8
16
24
32
40
48
56
64
72
80
9
0
9
18
27
36
45
54
63
72
81
90
10
0
10
20
30
40
50
60
70
80
90
100

25. X
0
1
2
0
3
4
5
6
7
8
9
10
0
1
2
14
3
4
5
40
6
12
7
35
8
9
10
80
0
36

26. 3.CONCEPT OF DIVISION

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Obj: to develop the concept the concept of division by
connecting it to subtraction.
To develop the skills by using the multiplication table.
2x
=16
16 / 2 =
____
16
14
12
10
8
6
4
2
-2
-2
-2
-2
-2
-2
-2
-2
14
12
10
8
6
4
2
0
8 times subtraction of 2 from 16 ended at 0
16 /2 =8 or
2x 8 =16
This concept can be illustrated by number line.

27. 
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108
2 216
divide
2
*multiply by 2
o1
*subtract 2-2=0
0
*R: 1<2 (compare the diff
16
with divisor)
16
* bring down the new digit.
0
* repeat the same process.
This conclusion: R = 0 shows it is completely
divisible by 2.

28. practice:
Divide 8
by
4
12
20
16
28
24

29. 4.FACTOR AND MULTIPLES
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Objectives: to develop the concept of factors and
multiples by using the multiplication table.
Flash cards for multiples.
Flash card for different factors.
Factor X factor = multiple
6
X
4
= 24
find other factors of 24 by using M.table.
List the factors of :18, 63, 36 and 54.
List the multiples of: 6, 2, 5 and 7.
Drill : flash cards and number patterns .

30. 5.THE CONCEPT OF PRIME
NUMBERS

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The number has only two factors 1 and
itself .
As factors of two are; 1and 2.
Factors of 3; 1 and 3
Factors of 4;1, 2 and 4
2 and 3 are prime numbers but 4 is not.
Is 1 a prime number? Give reason.
The remaining numbers are Composite
numbers
Activity: use the hundred chart and colors.

31. THE CHART OF PRIME
NUMBERS
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100

32. 
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6.INTEGERS
Obj: relate the
integers in practical
situations.
The numbers which
involve direction in
addition to the
magnitude.
Temperature, sea
level, profit and loss
etc.

33. INTEGERS: The directed numbers.
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Z={….,-4,-3,-2,-1,0,+1,+2,+3,+4,….}
0
negative numbers
positive numbers
Order of integers:
-4<-3<-2<-1<0<+1<+2<+3<+4
The numerical value of -2 and +2 is same.
But their direction is opposite.
Explanation: Addition and subtraction on number
lines. Multiplication on number lines.

34. 
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Activity:
Algebra tiles are introduced in order to
make, addition and subtraction of Integers,
easy and interesting.
Multiplication is illustrated on the charts.

35. 6.FRACTIONS
• Equal parts of whole.
•
•
•
Call me
numerato
r, I am the
number of
parts that
are in
fraction
3
5
I am
denominato
r, I tell the
name of
parts into
which the
unit is
divided

36. EQUIVALENT FRACTIONS




Fractions that name
the same amount are
called equivalent
fractions.
3/4 and 6/8 give the
same amount.
1/3 =2/6
Understanding: use
Number line & fraction
bars.

37. FRACTION BARS

38. ADD THE FRACTIONS
Make
the name same
1/3+1/6
=2/6+1/6
Add the numbers of fraction
(2+1)/6
Write the answer
3/6=1/2

39. 7.PROBLEM SOLVING.
Key words

+
X
÷
=
Add, sum, total, more, increase, all.
Altogether.
Subtract, difference, decrease, less
than, more than (comparison),
remaining, rest.
Product, of, into, times, twice(x2),
thrice(x3), etc.
Divided, parts, fractions, half(÷2),
fourth(÷4), etc.
Is, equals, gives, results.

40. STEPS TO SOLVE THE
PROBLEM
1.UNDERSTAND the
1.List the given information.
problem.
 What is given info?
 What is to find?
2.PLAN a strategy.
 Decide the method.
3.SOLVE the problem.
 Apply the method.
4.CHECK your answer.
 Look back, does the
answer make sense.
 If not, what other
strategy can be
used.
state the required info,
whether you need all of
the info.
2.Think about the problem
solving strategies you can
use.
3.Follow your plan, show
your solution.
4.Be sure that you
answered the question
asked.
or use other method to
check your work.

41. EXAMPLE
Q. If two angles of the triangle are 94 ° and
34° then what is the measure of the third
angle?
 Let’s apply the four steps of problem
solving.

42. Problem: class 3

One kilometer equals 1000meters.How
many meters are there in 24 kilometer.

43. Problem: class 4

A shopkeeper bought 2175 ice-pops. If 15
ice pops were packed in each box. How
many boxes did he buy?

44. Problem: class 5

Sadaf bought 36 chickens.17 of them are
white. What fraction of the chicken are not
white?

45. Problem: class 6

The length of a rectangle is x cm and its
width is 4 Cm .If the rectangle is 72 cm ² in
area, find x.

46. Problem :class 3



Order the fraction from least to greater
a. 1/2, 1/3, 1/4
b. 3/4, 3/6, 3/5

47. 


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Research and presented by
Mrs. UMBER TARIQ
Assisted by
Miss. UNIBA
Mrs. FOUSIA SHAHEEN

48. THANK
YOU