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Presentation Math Workshop#May 25th New            Help our teachers understand the purpose of Math-Teaching.
 

Presentation Math Workshop#May 25th New Help our teachers understand the purpose of Math-Teaching.

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This is presented by a Math teacher,in Army Burn Hall College For Girls ,Abbottabad. ...

This is presented by a Math teacher,in Army Burn Hall College For Girls ,Abbottabad.
The target group was the teachers of school section. There were certain activities also performed an demonstrated in order to introduce new teaching methodologies and to prepare our teachers to meet the need of the day.
Umber

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    Presentation Math Workshop#May 25th New            Help our teachers understand the purpose of Math-Teaching. Presentation Math Workshop#May 25th New Help our teachers understand the purpose of Math-Teaching. Presentation Transcript

      • WELCOME
      • The laws of nature are but the mathematical thoughts of God.
        • (Euclid)
      • Just think doing things for others could really end up benefiting you in the long run.
    • I. Contents:
      • TEACHING-LEARNING REQUIREMENTS OF GRADE 3 TO 6.
      • CLASS-ROOM ENVIRONMENT OF THIS GRADE LEVEL.
      • MATHEMATICAL FOUNDATIONS.
      • OBSTACLES TO QUALITY MATH-LEARNING.
      • HOW TO ERADICATE THE OBSTACLES.
      • TYPES OF INTELLIGENCES.
      • HABITS OF HIGHLY EFFECTIVE MATH-TEACHING.
    • 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.
    • 2. CLASS-ROOM ENVIRONMENT FOR THIS GRADE LEVEL.
      • 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.
    • 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 .
    • 4.OBSTACLES TO QUALITY MATH-LEARNING.
      • 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.
      • 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?
    • How to help them?
      • 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.
    • TYPES OF INTELLEGENCE
      • 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.
    • FOUR HABITS OF HIGHLY EFFECTIVE MATH TEACHING
      • 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.
    • II.CONTENTS
      • 1. Number patterns
      • 2.Concept of multiplication
      • 3.multimlication table.
      • 4.division
      • 5.Factors
      • 6.prime numbers
      • 7. integers
      • 8.fractions
      • 9.problem solving.
    • NUMBER PATTERNS
      • PREVIOUS KNOWLEDGE:
      • Whole numbers
      • Natural numbers
    • 1.EVEN AND ODD NUMBERS
      • 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
    • A HUNDRED CHART 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
      • ACTIVITY :
      • Material: HUNDRED CHART TABLE
      • SKIP-COUNT by 3’s, 4’s, 5’s,….10’s.
      • Which helps to learn and understand table formation.
    • Result;
      • 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, _, ………….
    • 2.CONCEPT OF MULTIPLICATION
      • Objectives:
      • To develop the concept of multiplication through addition.
      • To prepare the multiplication table by skip-count.
      • To stimulate them through different experiences.
    • MULTIPLICATION THROUGH ADDITION
      • Form the arrays of some objects ; how many in all?
      • 4
      • 4
      • 4
      • 12
      • 3 groups of 4 =
    • Connect addition to the multiplication
      • 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.
    • Practice: 4 6 5 4 3 2 1 X 6 6 5 4 3 2 1 X 5 4 3 2 1 0 X
      • STRUCTURED DRILL IS DEMONSRTATED, WHICH IS DESIGNED FOR TABLE LEARNING.
    • The multiplication table 100 90 80 70 60 50 40 30 20 10 0 10 90 81 72 63 54 45 36 27 18 9 0 9 80 72 64 56 48 40 32 24 16 8 0 8 70 63 56 49 42 35 28 21 14 7 0 7 60 54 48 42 36 30 24 18 12 6 0 6 50 45 40 35 30 25 20 15 10 5 0 5 40 36 32 28 24 20 16 12 8 4 0 4 30 27 24 21 18 15 12 9 6 3 0 3 20 18 16 14 12 10 8 6 4 2 0 2 10 9 8 7 6 5 4 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 10 9 8 7 6 5 4 3 2 1 0 X
    • 10 36 0 9 80 8 35 7 12 6 40 5 4 3 14 2 1 0 0 10 9 8 7 6 5 4 3 2 1 0 X
    • 3.CONCEPT OF DIVISION
      • Obj: to develop the concept the concept of division by connecting it to subtraction.
      • To develop the skills by using the multiplication table.
      • 2 x =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.
      • 108
      • 2 216 divide
      • 2 *multiply by 2
      • o 1 *subtract 2-2=0
      • 0 *R: 1<2 (compare the diff
      • 1 6 with divisor)
      • 16 * bring down the new digit.
      • 0 * repeat the same process.
      • This conclusion: R = 0 shows it is completely
      • divisible by 2.
    • practice: 4 24 28 16 20 12 8 Divideby
    • 4.FACTOR AND MULTIPLES
      • 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 .
    • 5.THE CONCEPT OF PRIME NUMBERS
      • 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.
    • THE CHART OF PRIME NUMBERS 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
    • 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.
    • INTEGERS: The directed numbers.
      • 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.
      • Activity:
      • Algebra tiles are introduced in order to make, addition and subtraction of Integers, easy and interesting.
      • Multiplication is illustrated on the 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 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
    • 7.PROBLEM SOLVING. Key words Is, equals, gives, results. = Divided, parts, fractions, half( ÷2), fourth(÷4), etc. ÷ Product, of, into, times, twice(x2), thrice(x3), etc. X Subtract, difference, decrease, less than, more than (comparison), remaining, rest. - Add, sum, total, more, increase, all. Altogether. +
    • STEPS TO SOLVE THE PROBLEM
      • 1.UNDERSTAND the 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.
      • 1. List the given information.
      • 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.
    • 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.
    • Problem: class 3
      • One kilometer equals 1000meters.How many meters are there in 24 kilometer.
    • Problem: class 4
      • A shopkeeper bought 2175 ice-pops. If 15 ice pops were packed in each box. How many boxes did he buy?
    • Problem: class 5
      • Sadaf bought 36 chickens.17 of them are white. What fraction of the chicken are not white?
    • 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.
    • Problem :class 3
      • Order the fraction from least to greater
      • a. 1/2, 1/3, 1/4
      • b. 3/4, 3/6, 3/5
      • Research and presented by
      • Mrs. UMBER TARIQ
      • Assisted by
      • Miss. UNIBA
      • Mrs. FOUSIA SHAHEEN
    • THANK YOU