WELCOMEWELCOME

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

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

I. Contents:I. Contents: TEACHING-LEARNING REQUIREMENTS TEACHING-LEARNING REQUIREMENTS

OF GRADE 3 TO 6.OF GRADE 3 TO 6. CLASS-ROOM ENVIRONMENT OF THIS CLASS-ROOM ENVIRONMENT OF THIS

GRADE LEVEL.GRADE LEVEL. MATHEMATICAL FOUNDATIONS.MATHEMATICAL FOUNDATIONS. OBSTACLES TO QUALITY MATH-OBSTACLES TO QUALITY MATH-

LEARNING.LEARNING. HOW TO ERADICATE THE OBSTACLES.HOW TO ERADICATE THE OBSTACLES. TYPES OF INTELLIGENCES.TYPES OF INTELLIGENCES. HABITS OF HIGHLY EFFECTIVE MATH-HABITS OF HIGHLY EFFECTIVE MATH-

TEACHING.TEACHING.

1.TEACHING-LEARNING 1.TEACHING-LEARNING REQUIREMENTSREQUIREMENTS

Students in the grade 3-6 are intrigued with Students in the grade 3-6 are intrigued with mathematics. To nurture this interest , students at mathematics. To nurture this interest , students at this grade level need to be involved in an active this grade level need to be involved in an active learning process rather than one that only builds learning process rather than one that only builds memorization of concepts and procedures.memorization of concepts and procedures.

Concrete experiences are also important at this Concrete experiences are also important at this stage of development . Such experiences allow stage of development . Such experiences allow students to develop and strengthen the skills students to develop and strengthen the skills needed. needed.

The skills are :The skills are : To communicate , reason, solve mathematical To communicate , reason, solve mathematical

problems and reach to higher level of cognitive problems and reach to higher level of cognitive reasoning.reasoning.

2. CLASS-ROOM ENVIRONMENT 2. CLASS-ROOM ENVIRONMENT FOR THIS GRADE LEVEL.FOR THIS GRADE LEVEL.

An effectiveAn effective class-room environment provides class-room environment provides intellectually stimulating instructions and intellectually stimulating instructions and developmentally appropriate opportunities for the developmentally appropriate opportunities for the students to learn mathematical concepts.students to learn mathematical concepts.

This classroom environment fosters an atmosphere This classroom environment fosters an atmosphere in which students are encouraged to find solutions in which students are encouraged to find solutions through a variety of methods and feel less through a variety of methods and feel less threatened about making and correcting mistakes.threatened about making and correcting mistakes.

Class-room instruction includes opportunities for Class-room instruction includes opportunities for students to communicate them mathematical students to communicate them mathematical thinking by talking , writing and sharing with each thinking by talking , writing and sharing with each other.other.

3. MATHEMATICAL 3. MATHEMATICAL FOUNDATION.FOUNDATION.

Grade contents build a foundation of basic Grade contents build a foundation of basic number-sense , operations , quantitative number-sense , operations , quantitative reasoning , number-patterns , relationships , reasoning , number-patterns , relationships , geometric and spatial reasoning , geometric and spatial reasoning , measurements , probability and statistics. measurements , probability and statistics. This content builds on and expand This content builds on and expand conceptual understanding of math.conceptual understanding of math.

Through interweaving of mathematical Through interweaving of mathematical concepts and process students learn to concepts and process students learn to value math , display confidence in the value math , display confidence in the mathematically solved problems, and make mathematically solved problems, and make connections between math and other connections between math and other subjects .subjects .

4.OBSTACLES TO QUALITY 4.OBSTACLES TO QUALITY MATH-LEARNING.MATH-LEARNING.

Family Family disaster-stories about math disaster-stories about math difficulty.difficulty.

Terror producing teaching.Terror producing teaching. Fuzzier meaning less explanation.Fuzzier meaning less explanation. Lack of link between math and real life.Lack of link between math and real life. A rush into “formal abstract” math A rush into “formal abstract” math

without any concrete physical or without any concrete physical or pictured experience without any pictured experience without any concrete, physical or pictured concrete, physical or pictured experience.experience.

A robotic, imitate, memorized style with little A robotic, imitate, memorized style with little conceptual grounding.conceptual grounding.

A habitual disconnect between a child’s natural A habitual disconnect between a child’s natural style and a superimposed alien math style.style and a superimposed alien math style.

Sometimes the material is meaningless, Sometimes the material is meaningless, monotone , black and white, that leads to monotone , black and white, that leads to boredom.boredom.

Poor self-image causes constant forgetting, Poor self-image causes constant forgetting, spacing out, blowing tests and in the end spacing out, blowing tests and in the end develops hatred for math.develops hatred for math.

COMENTCOMENT:: How would you react with a daily How would you react with a daily portion of sawdust for your meal?portion of sawdust for your meal?

How to help them?How to help them? Youth can leap over any of these obstacles to Youth can leap over any of these obstacles to

math success.math success. Right approach can make up for a multitude of Right approach can make up for a multitude of

assumed impossibilities and disabilities.assumed impossibilities and disabilities. Young people or even the adults just need to get Young people or even the adults just need to get

the real scoop behind the method in a clear and the real scoop behind the method in a clear and fun way.fun way.

They are thirsty for concepts, the number sense, They are thirsty for concepts, the number sense, the number patterns, the calculations , the the number patterns, the calculations , the formulae etc.formulae etc.

At his stage we can lead them to the right At his stage we can lead them to the right direction. direction.

Nine-tenth of education is encouragement.Nine-tenth of education is encouragement. As soon as we discover the problem we will be As soon as we discover the problem we will be

able to resolve it.able to resolve it.

TYPES OF INTELLEGENCETYPES OF INTELLEGENCE There are nine There are nine types of intelligences by research, each types of intelligences by research, each has been proved to be equivalent to any other by any has been proved to be equivalent to any other by any scientific criterion you think of, when we speak they are scientific criterion you think of, when we speak they are intelligent we can actually and accurately mean they are intelligent we can actually and accurately mean they are intelligent nine other ways;intelligent nine other ways;

1.1. IntrapersonallyIntrapersonally (self smart)(self smart)2.2. KinestheticallyKinesthetically (mind-body union)(mind-body union)3.3. SpatiallySpatially (Picture smart)(Picture smart)4.4. InterpersonallyInterpersonally (people smart)(people smart)5.5. MusicallyMusically (music smart)(music smart)6.6. NaturalisticallyNaturalistically (nature smart)(nature smart)7.7. Logically/mathematically (number/reason smart)Logically/mathematically (number/reason smart)8.8. LinguisticallyLinguistically (word smart)(word smart)9.9. Existentially Existentially (deep thinking ,questions)(deep thinking ,questions)

If that is so it stands to reason that if you teach math If that is so it stands to reason that if you teach math through all the intelligence channels, you have a vastly through all the intelligence channels, you have a vastly

increased chance of reaching every increased chance of reaching every brain you are brain you are working with.working with.

FOUR HABITS OF HIGHLY FOUR HABITS OF HIGHLY EFFECTIVE MATH TEACHINGEFFECTIVE MATH TEACHING

1.LETS MAKE 1.LETS MAKE SENSE:SENSE: Dilemma between conceptual vs. procedural Dilemma between conceptual vs. procedural

understanding.understanding. 2.REMEMBER THE GOALS:2.REMEMBER THE GOALS: connect your ultimate goals to sub goals .connect your ultimate goals to sub goals . 3.KNOW YOUR TOOLS:3.KNOW YOUR TOOLS: Learn how to use tools and add to your toolbox.Learn how to use tools and add to your toolbox. 4.LIVING AND LOVING MATH:4.LIVING AND LOVING MATH: You are a teacher. Show the way, with your You are a teacher. Show the way, with your

attitudes.attitudes.

II.CONTENTSII.CONTENTS

1. 1. Number patternsNumber patterns 2.Concept of multiplication2.Concept of multiplication 3.multimlication table.3.multimlication table. 4.division4.division 5.Factors5.Factors 6.prime numbers6.prime numbers 7. integers7. integers 8.fractions8.fractions 9.problem solving.9.problem solving.

NUMBER PATTERNSNUMBER PATTERNS

PREVIOUS KNOWLEDGE:PREVIOUS KNOWLEDGE: Whole numbersWhole numbers Natural numbersNatural numbers

1.EVEN AND ODD NUMBERS1.EVEN AND ODD NUMBERS

Objectives: to identify even and odd Objectives: to identify even and odd numbers.numbers.

Use a hundred chart.Use a hundred chart. Skip-count by two’s, start from 2 ,the Skip-count by two’s, start from 2 ,the

numbers you will land on are even, shade numbers you will land on are even, shade the numbers , by the end of the page we the numbers , by the end of the page we get the shaded numbers which are even.get the shaded numbers which are even.

The remaining numbers are odd numbers.The remaining numbers are odd numbers. Activity:Activity: use hundred chart and colors use hundred chart and colors

A HUNDRED CHARTA HUNDRED CHART11 22 33 44 55 66 77 88 99 1010

1111

1212 1313 1414 1515 1166

1717 1188

1199

2020

2211

2222 2323 2424 2525 2266

2727 2288

2299

3030

3311

3232 3333 3434 3535 3366

3737 3388

3399

4040

4411

4242 4343 4444 4545 4466

4747 4488

4499

5050

5511

5252 5353 5454 5555 5566

5757 5588

5599

6060

6611

6262 6363 6464 6565 6666

6767 6688

6699

7070

7711

7272 7373 7474 7575 7766

7777 7788

7799

8080

8811

8282 8383 8484 8585 8866

8787 8888

8899

9090

9911

9292 9393 9494 9595 9966

9797 9988

9999

101000

ACTIVITYACTIVITY:: Material: HUNDRED CHART TABLEMaterial: HUNDRED CHART TABLE SKIP-COUNT by 3’s, 4’s, 5’s,….10’s.SKIP-COUNT by 3’s, 4’s, 5’s,….10’s. Which helps to learn and understand Which helps to learn and understand

table formation.table formation.

Result;Result; The colouredThe coloured boxes have even numbers, where 0, boxes have even numbers, where 0,

2, 4, 6 and 8 are in ones place.2, 4, 6 and 8 are in ones place. The boxes not coloured are odd numbers have 1, The boxes not coloured are odd numbers have 1,

3, 5, 7and 9 in ones place.3, 5, 7and 9 in ones place. Practice/exercisePractice/exercise;; use hundred chart and ask the use hundred chart and ask the

students whether the number is even or odd.students whether the number is even or odd.a) 7. b) 4. c)8. d) 9. e) 21 f) 54.a) 7. b) 4. c)8. d) 9. e) 21 f) 54.

Activity:Activity: Students can form different patterns e.g, Students can form different patterns e.g, start at 5, skip- count by 5, where do you land start at 5, skip- count by 5, where do you land after 4 skips? after 4 skips? skip count by 4 ,move 6 skips, what do you land skip count by 4 ,move 6 skips, what do you land on ?on ?

2, 4, 6, _, _, 12, 14,……..2, 4, 6, _, _, 12, 14,……..5, 10, _, 20, _, …………. 5, 10, _, 20, _, ………….

2.CONCEPT OF MULTIPLICATION2.CONCEPT OF MULTIPLICATION

Objectives: Objectives: To develop the concept of To develop the concept of

multiplication through addition.multiplication through addition. To prepare the multiplication table by To prepare the multiplication table by

skip-count.skip-count. To stimulate them through different To stimulate them through different

experiences.experiences.

MULTIPLICATION THROUGH MULTIPLICATION THROUGH ADDITIONADDITION

Form the arrays of some objects ; Form the arrays of some objects ; how many in all?how many in all?

44

44

44

1212 3 groups of 4 = 3 groups of 4 =

Connect addition to the Connect addition to the multiplicationmultiplication

Repeat addition of a number and find:Repeat addition of a number and find: 3 groups of 4 =4+4+4 = 12 3 groups of 4 =4+4+4 = 12 Similarly; 2 groups of 5Similarly; 2 groups of 5=___=___ AndAnd 4 groups of 74 groups of 7 =___ =___ 3+3+3+3+3 3+3+3+3+3 =15=15 5 Threes 5 Threes =15=15 5 times 35 times 3 =15=15

FinallyFinally 5 x35 x3 =15=15 This concept can be related by This concept can be related by Number line.Number line.

Practice:Practice:

XX 11 22 33 44 55 66

44

XX 11 22 33 44 55 66

66

XX 00 11 22 33 44

55

STRUCTURED DRILLSTRUCTURED DRILL IS IS DEMONSRTATED, WHICH IS DEMONSRTATED, WHICH IS DESIGNED FOR TABLE LEARNING.DESIGNED FOR TABLE LEARNING.

The multiplication tableThe multiplication tableXX 00 11 22 33 44 55 66 77 88 99 1010

00 00 00 00 00 00 00 00 00 00 00 00

11 00 11 22 33 44 55 66 77 88 99 1010

22 00 22 44 66 88 1010 1212 1144

1616 1818 2020

33 00 33 66 99 1212 1515 1818 2211

2424 2727 3030

44 00 44 88 1212 1616 2020 2424 2288

3232 3636 4040

55 00 55 1010 1515 2020 2525 3030 3355

4040 4545 5050

66 00 66 1212 1818 2424 3030 3636 4422

4848 5454 6060

77 00 77 1414 2121 2828 3535 4242 4499

5656 6363 7070

88 00 88 1616 2424 3232 4040 4848 5566

6464 7272 8080

99 00 99 1818 2727 3636 4545 5454 6633

7272 8181 9090

1010 00 1010 2020 3030 4040 5050 6060 7700

8080 9090 100100

XX 00 11 22 33 44 55 66 77 88 99 1010

00 00

11

22 1414

33

44

55 4040

66 1212

77 3535

88 8080

99 00 3636

1010

3.CONCEPT OF DIVISION3.CONCEPT OF DIVISION

Obj: to develop the concept the concept of division Obj: to develop the concept the concept of division by connecting it to subtraction.by connecting it to subtraction.

To develop the skills by using the To develop the skills by using the multiplication multiplication table.table.

2 x =162 x =16 16 / 2 =16 / 2 = ________ 1616 1414 1212 1010 88 66 44 22 -2-2 -2-2 -2-2 -2-2 -2-2 -2-2 -2-2 -2-2 1414 1212 1010 8 8 6 6 44 22 00 8 times subtraction of 2 from 16 ended at 08 times subtraction of 2 from 16 ended at 0 16 /2 =8 or 2x 8 =1616 /2 =8 or 2x 8 =16 This concept can be illustrated by This concept can be illustrated by number line.number line.

108108 22 216216 dividedivide 22 *multiply by 2*multiply by 2 oo11 *subtract 2-2=0*subtract 2-2=0 00 *R: 1<2 (compare the diff*R: 1<2 (compare the diff 1166 with divisor)with divisor) 1616 * bring down the new digit.* bring down the new digit. 00 * repeat the same process.* repeat the same process. This conclusion: R = 0 shows it is completely This conclusion: R = 0 shows it is completely divisible by 2.divisible by 2.

practice:practice:

DividDivideby eby

88 1212 2020 1616 2828 2424

44

4.FACTOR AND MULTIPLES4.FACTOR AND MULTIPLES

Objectives: to develop the concept of factors Objectives: to develop the concept of factors and multiples by using the multiplication and multiples by using the multiplication table.table.

Flash cards for multiples.Flash cards for multiples. Flash card for different factors.Flash card for different factors. Factor Factor X X factorfactor = = multiplemultiple 66 XX 44 = 24= 24 find other factors of 24 by using M.table.find other factors of 24 by using M.table. List the factors of :18, 63, 36 and 54.List the factors of :18, 63, 36 and 54. List the multiples of: 6, 2, 5 and 7.List the multiples of: 6, 2, 5 and 7. DrillDrill: flash cards and number patterns .: flash cards and number patterns .

5.THE CONCEPT OF PRIME5.THE CONCEPT OF PRIME NUMBERSNUMBERS

The number has only two factors 1 and The number has only two factors 1 and itselfitself..

As factors of two are; 1and 2.As factors of two are; 1and 2. Factors of 3; 1 and 3Factors of 3; 1 and 3 Factors of 4;1, 2 and 4Factors of 4;1, 2 and 4 2 and 3 are prime numbers but 4 is not.2 and 3 are prime numbers but 4 is not. Is 1 a prime number? Give reason.Is 1 a prime number? Give reason. The remaining numbers are Composite The remaining numbers are Composite

numbersnumbers Activity:Activity: use the hundred chart and colors. use the hundred chart and colors.

THETHE CHART OF PRIMECHART OF PRIME NUMBERSNUMBERS

11 22 33 44 55 66 77 88 99 1010

1111 1212 1313 1414 1515 1616 1717 1818 1919 2020

2121 2222 2323 2424 2525 2626 2727 2828 2929 3030

3131 3232 3333 3434 3535 3636 3737 3838 3939 4040

4141 4242 4343 4444 4545 4646 4747 4848 4949 5050

5151 5252 5353 5454 5555 5656 5757 5858 5959 60606161 6262 6363 6464 6565 6666 6767 6868 6969 7070

7171 7272 7373 7474 7575 7676 7777 7878 7979 8080

8181 8282 8383 8484 8585 8686 8787 8888 8989 9090

9191 9292 9393 9494 9595 9696 9797 9898 9999 100100

6.INTEGERS6.INTEGERS Obj: relate the Obj: relate the

integers in integers in practical situations.practical situations.

The numbers which The numbers which involve direction in involve direction in addition to the addition to the magnitudemagnitude..

Temperature, sea Temperature, sea level, profit and level, profit and loss etc.loss etc.

INTEGERS: The directed INTEGERS: The directed numbers.numbers.

Z={….,-4,-3,-2,-1,0,+1,+2,+3,+4,….}Z={….,-4,-3,-2,-1,0,+1,+2,+3,+4,….} 00 negative numbersnegative numbers positive numberspositive numbers Order of integers:Order of integers: -4<-3<-2<-1<0<+1<+2<+3<+4-4<-3<-2<-1<0<+1<+2<+3<+4 The numerical value of -2 and +2 is same.The numerical value of -2 and +2 is same. But their direction is opposite.But their direction is opposite. Explanation: Explanation: Addition and subtraction on Addition and subtraction on

numbernumber lines. Multiplication on number lines. Multiplication on number lines.lines.

Activity:Activity: Algebra tilesAlgebra tiles are introduced in order are introduced in order

to make, addition and subtraction of to make, addition and subtraction of Integers, easy and interesting.Integers, easy and interesting.

Multiplication is illustrated on the Multiplication is illustrated on the charts.charts.

6.FRACTIONS• Equal parts of whole.

• • 3• 5

I am

denominator, I tell the name of parts

into which the unit is

divided

Call me numerator, I am

the number of parts that are

in fraction

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.

FRACTION BARS

ADD THE FRACTIONSADD THE FRACTIONSMake

the name same1/3+1/6

=2/6+1/6

Add the numbers of fraction(2+1)/6

Write the answer3/6=1/2

7.PROBLEM SOLVING.7.PROBLEM SOLVING.Key wordsKey words

++ Add, sum, total, more, increase, Add, sum, total, more, increase, all. Altogether.all. Altogether.

-- Subtract, difference, decrease, Subtract, difference, decrease, less than, more than less than, more than (comparison), remaining, rest.(comparison), remaining, rest.

XX Product, of, into, times, twice(x2), Product, of, into, times, twice(x2), thrice(x3), etc.thrice(x3), etc.

÷÷ Divided, parts, fractions, half(Divided, parts, fractions, half(÷2), ÷2), fourth(÷4), etc.fourth(÷4), etc.

== Is, equals, gives, results.Is, equals, gives, results.

STEPS TO SOLVE THESTEPS TO SOLVE THE PROBLEMPROBLEM1.UNDERSTAND1.UNDERSTAND the the

problem.problem. What is given info?What is given info? What is to find?What is to find?2.PLAN 2.PLAN a strategy.a strategy. Decide the method.Decide the method.3.SOLVE3.SOLVE the problem. the problem. Apply the method.Apply the method.4.CHECK4.CHECK your answer. your answer. Look back, does the Look back, does the

answer make sense.answer make sense. If not, what other If not, what other

strategy can be used.strategy can be used.

1.1.List theList the given given information.information.state the required info,state the required info,whether you need all of whether you need all of the info.the info.

2.2.Think about the Think about the problem solving problem solving strategies you can use.strategies you can use.

3.3.Follow your plan, show Follow your plan, show your solution.your solution.

4.4.Be sure that you Be sure that you answered the question answered the question asked.asked.or use other method to or use other method to check your work.check your work.

EXAMPLEEXAMPLE

Q.Q. If two angles of the triangle are 94 If two angles of the triangle are 94° ° and 34° then what is the measure of and 34° then what is the measure of the third angle?the third angle?

Let’s apply the four steps of problem Let’s apply the four steps of problem solving. solving.

Problem: class 3Problem: class 3

One kilometer equals One kilometer equals 1000meters.How many meters are 1000meters.How many meters are there in 24 kilometer.there in 24 kilometer.

Problem: class 4Problem: class 4

A shopkeeper bought 2175 ice-pops. A shopkeeper bought 2175 ice-pops. If 15 ice pops were packed in each If 15 ice pops were packed in each box. How many boxes did he buy?box. How many boxes did he buy?

Problem: class 5Problem: class 5

Sadaf bought 36 chickens.17 of them Sadaf bought 36 chickens.17 of them are white. What fraction of the are white. What fraction of the chicken are not white?chicken are not white?

Problem: class 6Problem: class 6

The length of a rectangle is The length of a rectangle is x x cm and cm and its width is 4 Cm .If the rectangle is its width is 4 Cm .If the rectangle is 72 cm72 cm²² in area, find in area, find x.x.

Problem :class 3Problem :class 3

Order the fraction from least to Order the fraction from least to greatergreater

a. 1/2, 1/3, 1/4a. 1/2, 1/3, 1/4 b. 3/4, 3/6, 3/5b. 3/4, 3/6, 3/5

Research and presented byResearch and presented by Mrs. UMBER TARIQMrs. UMBER TARIQ Assisted byAssisted by Miss. UNIBAMiss. UNIBA Mrs. FOUSIA SHAHEENMrs. FOUSIA SHAHEEN

THANK THANK YOUYOU