HBMT 3103

770218-01-5450HBMT 3103: TEACHING MATHEMATICS IN YEAR FOUR

SEMESTER MEI 2010

FAKULTI BAHASA DAN PENDIDIKAN

PROGRAM SARJANA MUDA PENGAJARAN (KOHORT 5)

HBMT 3103

TEACHING MATHEMATICS IN YEAR FOUR

ZAMATUN NASRAH BINTI MARWAN

TUTOR

MRS. TEY KAI WEAN

[email protected]

PUSAT PEMBELAJARAN

Pusat Pembelajaran Wilayah Johor

Semester Mei 2010


SEMESTER MEI 2010

Assalamualaikum warahmatullahiwabarakatuh,

,

Thank god for His permission I have finish my assignment for the Teaching

Mathematics in Year Four that have been given to me. Many thankful to my tutor Mrs. Tey

Kai Wean for her helpness to give me more easier to finish my assignment.

Many challenges that I have to face to finish this assignment and also thank to my

friends that have gave me motivation and also lend their hands to help me and also share their

knowledges.

More thanks and love to my family and also my parents, who gave me support and

pray to give me more strength to finish my assignment.

Hope all of you will be happy and may god bless you.

Thank you.


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TABLE OF CONTENTS

1. Acknowledgements

2. Introductions

3. Definitions of Fractions

4. Compare and Contrast :

(i) Differences

(ii) Similarities

5. Modification and Justification

6. Summary

7. References

INTRODUCTION


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Learning about fractions is one of the most difficult tasks for primary school children.

Children seeing the fractions as a number that have unique factors. It is different with the

whole numbers that they have learnt. These unique factors make the children hard to

understand in learning of fractions especially in addition of fractions in different

denominators. The objective of this article is to describe various ways of teaching fractions,

focus on how to teach fractions with different denominators. These three articles are to

compare and find the differences and also the similarities. One of the articles that have the

best method will be choose and can be modified or justified to get suit with our own students.

DEFINITIONS OF FRACTIONS

There are many definitions of fractions such as part of a whole. In arithmetic, a

number expressed as a quotient, in which a numerator is divided by a denominator. In a

simple fraction, both are integers. A complex fraction has a fraction in the numerator or

denominator. In a proper fraction, the numerator is less than the denominator. If the

numerator is greater, it is called an improper fraction and can also be written as a mixed

number where a whole-number quotient with a proper-fraction remainder. Any fraction can

be written in decimal form by carrying out the division of the numerator by the denominator.

The result may end at some point, or one or more digits may repeat without end.

COMPARE AND CONTRAST


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DIFFERENCES

TEACHING FRACTIONS

{cross-product method}

HELP WITH

FRACTIONS

{Least Common

Denominator (LCD)}

KIDSPIRATION

{Kidspiration Fraction

Boxes}

1) Traditional way to teach

addition of fractions.

1) Using and working with

concrete models.

1) Teaching using resources

and tools in teaching and

learning sessions.

2) It is a traditional algorithm

that requires paper and

pencils and also employs

mental mathematics.

2) Students have to find

‘common denominator’

and also ‘least common

denominator’.

2) It is requires tools to

build fractions and

dynamically search for

equivalent fractions and

common denominators.

3) Steps

a) ½ + 1/3

Find the sum of two

fractions by cross

multiply.

1 x 3 = 3

2 x 1 = 2

b) Add the two cross-

products : 3 + 2 = 5.

The result becomes the

new numerator.

c) The new denominator

is the product of the

denominators:

2 x 3 = 6

d) The sum is 5/6.

3) Steps

a) Build each fractions so

that both denominators

are equal.

Remember, when

adding fractions, the

denominators must be

equal. So, this is the

first step. We have to

find common

denominator.

b) Re-write each

equivalent fraction

using this new

denominator.

3) Steps

Open the lesson by

presenting a situation that

involves the addition of

fractions with different

denominators.

Eg: Nani bought 5/6 of

a kg of fudge and Jerry

bought ½ of a kg of

fudge. Write both

fractions in the board.

First, ask which

students, Nani or Jerry

bought more fudge.

How do they know?

TEACHING FRACTIONS HELP WITH KIDSPIRATION


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{cross-product method} FRACTIONS

{Least Common

Denominator (LCD)}


Boxes}

c) Now, we can add the

numerators and keep

the denominator of the

equivalent fractions.

d) Re-write the answer as

a simplified or reduced

fraction, if needed.

Inform students that

Nani and Jerry would

like to figure out how

much fudge they have

altogether. Does the

situation call for

addition, subtraction,

multiplication or

division? Why? Then

ask students to estimate

much fudge the two

students purchased

altogether.

a) Some students might

suggest that 3/6 can “fit

inside” of 1/2, or that

3/6 of Nani’s kilograms

of fudge can be

“combined with Jerry’s

1/2 kg to make 1 whole

kg.” This concept of

transferring a fractional

quantity to “make a

whole” can be

demonstrated by multi-

selecting 3/6 and



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{Least Common

Denominator (LCD)}


Boxes}

dragging them to the

empty 1/2 cell.

Note: A fraction box will

only “accept” tiles if the

fractional quantity being

moved and the space to

which it is moved are

equivalent.

Does the model help us see

how much fudge Nani and

Jerry have altogether? Allow

students to determine that the

total amount is 1 2/6 kg of

fudge. If they are working on

simplifying fractions, they

can use the arrow buttons to

“re-divide” the top fraction

box and explore fractions

that are equivalent to 2/6.



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{Least Common

Denominator (LCD)}


Boxes}

Once they see that 2/6 is

equivalent to 1/3, click on the

button that says “3 Parts” to

officially change the top

fraction from sixths into

thirds.

b) A second way to show

5/6 + 1/2 is to use

fraction boxes to model

finding a common

denominator. Begin by

representing each

fraction, as before.

Can we find an

equivalent fraction for

1/2 that would make all

of the pieces the same

size?


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TEACHING FRACTIONS


HELP WITH

FRACTIONS

{Least Common

Denominator (LCD)}

KIDSPIRATION


Boxes}

Show students how they

can explore equivalent

fractions with the up

and down arrow

buttons.

For example, 1/2 of a kg

is equivalent to 2/4 of

kg, but are Nani’s and

Jerry’s pieces all the

same size? Continue

changing the divisions

in the fraction box until

students see that 1/2 is

also equivalent to 3/6,

and that both Nani and

Jerry’s portion can be

thought of in terms of

sixths.


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TEACHING FRACTIONS


HELP WITH

FRACTIONS

{Least Common

Denominator (LCD)}

KIDSPIRATION


Boxes}

To officially re-cut the

bottom fraction into

sixths, instead of halves,

click on the button that

says “6 Parts.” Now that

Nani’s and Jerry’s

portions of fudge are

both in sixths of a kg,

the pieces can be easily

combined. Drag tiles

between fraction boxes

to make 1 whole.

Ask students to determine,

based on the model, how

much fudge Nani and Jerry

have altogether. If the

expectation is that students

also simplify their answers,

for example, from 1 2/6 to 1

1/3 kg, they can use fraction

boxes to model simplification

as described in step 1.


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SIMILARITIES

1) In the Teaching Fractions and Help With Fractions articles have a similar method

especially in finding the equivalent fractions for denominator. Even the Teaching

Fractions article using cross multiply and Help With Fractions using Least Common

Denominator, both are still using multiplication to find equivalent denominators.


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MODIFICATION AND JUSTIFICATION

The best method that I can use to teach my students which is in second class after

streaming is using Kidspiration Fraction Boxes. Teaching addition of fractions with different

denominator using Kidspiration Fraction Boxes is one way of the variety of interesting and

interactive programmes that used to show how to add fractions with different denominators.

This method will provide a graduated and conceptually supported framework for students to

create a meaningful connection among concrete, representational and abstract levels of

understanding.

To justify some of the way, teacher also can use cards with Kidspiration Fraction

Boxes. This is to create an activity with hands-on and learning experience. Beginning with

visual, tactile and kinaesthetic experiences to establish understanding, students expand their

understanding through pictorial representations of concrete objects and move to the abstract

level of understanding. "Hands-on and learning by experience are powerful ideas, and we

know that engaging students actively and thoughtfully in their studies pays off in better

learning (Rutherford, 1993, p. 5).” This activity also provides students with a similar set of

experiences so everyone can participate in discussions on a level playing field regardless of

their socio-economic status. In this way, special benefits are not awarded to those who, by

virtue of their wealth or background, have a greater number of experiences under their belts.

It is also forces student thinking by requiring interpretation of the observed events, rather

than memorization of correct responses.

Let the pupils do as many things by himself or herself. Young children need to be

watched closely. However, they learn to be independent and to develop confidence by doing

tasks. It's important to let them make choices, rather than deciding everything for her.

Encourage them to play with other children and to be with adults who are not family

members. The pupils need social opportunities to learn to see the point of view of others.

Young children are more likely to get along with teachers and classmates if they have had

experiences with different adults and children.


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SUMMARY

The importance of providing children with direct experiences with materials, objects,

and phenomena is supported by experience and understanding of how learning takes place.

While information can be remembered if taught through books and lectures, true

understanding and the ability to use knowledge in new situations requires learning in which

children study concepts in-depth, and over time and learning that is founded in direct

experience. Therefore, the justification for hands-on learning is that it allows students to build

understanding that is functional and to develop the ability to inquire them, in other words, to

become independent learners. There are a plethora of benefits that teachers and curriculum

developers adduce to hands-on learning to justify the approach in science. Benefits for

students are believed to include increased learning; increased motivation to learn; increased

enjoyment of learning; increased skill proficiency, including communication skills; increased

independent thinking and decision making based on direct evidence and experiences; and

increased perception and creativity.


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References

M.Othman.(2010). HBMT3103,Teaching Mathematics in Year Four.Seri Kembangan :

Meteor Doc. Sdn Bhd.

http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1027&context=library_talks

http://www.ehow.com/facts_5192514_hands_on-learning-children.html

http://www.helpwithfractions.com/adding-fractions-different-denominators.html

http://www.inspiration.com/lessonplan/addingfractions

http://www.resourceroom.net/math/denominators.asp

http://74.6.146.127/search/cache?ei=UTF-8&p=teaching+fractions+%3A+rules+and+reason&fr=ffds1&u=www.math.ccsu.edu/mitchell/math409tcmteachingfractionsrulesandreasons.pdf&w=teaching+fractions+fraction+rules+reason+reasoning&d=Y72--rZfVC9u&icp=1&.intl=us&sig=LCfyTi8jM6fvGLIQx0tjVA--




http://www.resourceroom.net/math/denominators.asp

http://www.inspiration.com/lessonplan/addingfractions

http://www.helpwithfractions.com/adding-fractions-different-denominators.html

http://www.ehow.com/facts_5192514_hands_on-learning-children.html

http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1027&context=library_talks

HBMT 3103

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