RANCANGAN PENGAJARAN DAN PEMBELAJARAN MI (1)

SKEMA TLO

RANCANGAN PENGAJARAN DAN PEMBELAJARAN MINGGUAN
Program Ijazah Sarjana Muda Perguruan (PISMP) dengan Kepujian
1
3
PROGRAM: ____________________________________________________________________________ SEMESTER: ______ TAHUN: ______
3 (2 + 1)
Kredit: ____________

Teaching of Numbers, Fractions, Decimals and Percentages
MTE3109
Kursus: __________________________________________________________________________________________ Kod: ____________

Minggu

Tajuk dan
Kandungan

M1

Whole numbers

Hasil
Pembelajaran

Kuliah
(jam)

To study early
numbers
development



To explain
number sense





Pre-number
concepts
Counting
strategies
Early
numbers
development and
number sense

Tutorial
(jam)


Amali
(jam)


Reading:

ii. McIntosh,A.J.(1992).
’Two needed
revolutions’ from
Challenging Children
to Think When They
Compute.QUT,
Brisbane
(1 hr)

(a+b):
a represents lecture
and tutorial hours
b represents practical
work

Show 
Make a number
how 201 and 120 would be
expander (Reys, pp176) or
represented with three

arrow cards for use in
different place-value models.
reinforcing reading and
Exami
writing numbers

Make hundred number
ne a primary mathematics
text-book. How many
chart and carry out Lesson
different place-value models
Idea 8-3 (Reys: pp 177) and
are illustrated? Which model
Activity In the Classroom
is used the most? Comment
8-3(reys:pp182)
if the textbook provides a

What have you learnt
good choice of models?

from these two activities?
Defend your answer.
(1 hr)
(2 hrs)

Reading:

Reference:

i. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)
pp.166-192

Booker,at.el.(1997)
Teaching Primary
Mathematics (2nd Ed.).
pp 53-92

(1 hr)

Or refer Booker (2004)

- Illustrate with
examples the
meaning of
number sense
(1 hr)

Whole numbers

To carry out
counting
strategies
To represent
place value in
numbers



Place value
representation of
numbers
- Grouping or
trading
-Developing place
Value
-Regrouping and
renaming
(2 hrs)





Catatan

Prepare a set of
materials that can be helpful
for

- counting
- learning basic
facts (eg. Tenframe)
-writing and
recording numbers
- Try out the resources with
your peers during micro
teaching
(2 hrs)

Discuss:
-what are some
characteristics of
numbers?

(2 hrs)

M2

ISL

(jam)

1

Note:
i.Reys, at. el(2004).
60hrs interaction will be
Helping children learn done in 12 weeks.
Mathematics (7th ed.) 1 week =(a+b)hours
pp.137-163
= 5 hours

SKEMA TLO

Minggu
M3

Tajuk dan
Kandungan
Number

operations and
basic facts

Hasil
Pembelajaran
To construct
models for
addition and
subtraction
To construct
models for
multiplication
and division

Kuliah
(jam)


Models for
addition and

subtraction

Models for
multiplication and
division

Basic facts

Tutorial
(jam)




(1 hr)

Amali
(jam)

Read about basic facts
from pp. 206-224 (Reys) and
discuss questions 1-6 in page
224.
Summarise all the
strategies for teaching basic
facts
(1 hr)

Task 1:
In pairs, choose and prepare
only one card from Activity In
the Classroom 9-5 to 9-98(Reys:pp210-212).

Play with your peers.

Exchange the Activity
Cards with other groups so
that you get a chance to play
all the 4 types.

ISL
(jam)

Catatan

Reading:

Reference:

i. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)
pp.195-225

Cathcart, et al (2006).
Learning Mathematics
in Elementary and
Middle Schools. A
Learner-Centered
Approach (4th Ed). pp.
145-162

(1 hr)

Task 2:

In groups of 4, plan an
activity with teaching material
that can be used to reinforce
basic facts.
Carry out micro-teaching
using the models and aids
prepared
(3 hrs)
M4

Operation sense
and
computations

To calculate by
mental
computations
To make
estimation in
computations





Mental

computation
-The role of mental
computation

Computationa
l estimation
- estimation skills
- why doing

estimations
(1 hr)

Group
presentation of Activity 1:
‘How did you do it?’
Make a
summary of the methods
applied based on the data
collected by the whole class.
Comment on the
findings regarding mental
computation.

(2 hrs)

Activity 2:
Reading:
Form groups and each group
Activity 1: For Tutorial
carry out one activity based on
W4
activity 2 to 6 in pp39(Groves).

In groups of

-Record what happens
three, interview at
when you try out the activity
least 6 primary
and comment on what you
school children
have learnt .
based on activity
1 : How did you do

Submit your comments
it?” ( pp. 38 of
through weekly reflective log.
Groves).

Record
Activity 3:
different methods

Try activity
and present to the
3.13 (Qs. A-M) listed in pp48
class.
Reader ‘Computation
Techniques and Number
(1 hr)
Sense.’
(2 hrs)

2

Reference:
i.Groves, S.
(2006)
‘Computation
Techniques and
Number Sense (In
Week 5)
ii. Cathcart, et
al (2006).
Learning
Mathematics in
Elementary and
Middle Schools. A
Learner-Centered
Approach (4th
Ed). pp. 166-169
iii. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)

SKEMA TLO

Minggu

Tajuk dan
Kandungan

Hasil
Pembelajaran

Kuliah
(jam)

Tutorial
(jam)

Amali
(jam)

ISL
(jam)

Catatan
pp.228-249

M5
Operation sense
and
computations

To use
calculators and
abacus in
computations
To construct
teaching aids
for numbers



The 
Make a list of the

In about half a
role of algorithms
standard written algorithm for
page, summarise and
- Children’s use
the whole numbers which you
present your views on
and understanding
believe should be included in
whether or not children in
of
the primary mathematics
primary school should use
algorithm in whole
curriculum.
calculators and the way in
number operations 
which they could be used.
Comment about your list

In groups of suitable
compare with the views put

Calculators
size, design an exercise or
forward by Plunkett’ in his
games where you can use
and abacus
article.
abacus/calculators to teach
operations of numbers.
(1 hr)
(2 hrs)

How far abacus is used
in teaching whole numbers in
Malaysian primary schools?
Discuss with examples

Reading:
i. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)
pp.251-278
ii. Plunkett, S.(1979).
‘Decomposition and all
that rot’, Mathematics
in School, Vol 8 No.
3.pp. 2-5
(prepare Tutorial W5)

(1 hr)

(2 hrs)
M6

Key issues in
teaching whole
numbers


To discuss issues
in knowing basics
facts
To make
recommendations
in the teaching of
place value
To debate the
mathematics
knowledge of
teachers

Issues in

teaching whole
number
Kno
wing basic fact
Teac
hing of place
value
Math
ematics
knowledge of
teachers

Read article X and
summarise the issues raised
in the teaching of
mathematics in primary
school.
(2 hrs)

Acyivity 1:In groups, discuss the
issues related to the teaching of
numbers that exist in our local
school context.

Present your issues
and make recommendations
on how they can be
overcome. Support your
presentation with references.
Activity 2: Debate

Training a
mathematics generalist or a
specialist in handling primary
mathematics in school: Its
impact on children’s learning
of mathematics.

(1 hr)

(2 hrs)

3

References:
iii. Groves, S. (2006)
Computation
techniques and number
sense.
pp 32-35
iv. Groves,S &
Cheeseman, J(1995).’
Beyond expectations:
Using calculators with
young children’
v. Metallo.
(undated)The
abacus: Its history
and applications”

Reading:
Article X:
i. Review: Knowing
and Teaching
Mathematics by
Roger Howe
http://www.ams.org/n
otices/199908/rev.ho
we.pdf
(1 hr)

-

SKEMA TLO

Minggu
M7

Tajuk dan
Kandungan
Fractions,
decimals and
percentages
Fractions

Hasil
Pembelajaran

Kuliah
(jam)


To explain the
meaning of
fraction and
equivalent
To relate mixed
number and
improper fraction



Conceptual
development of
fractions and
equivalent
fractions
Mixed
number and
improper fraction

Tutorial
(jam)


(2 hrs)

Amali
(jam)

In groups:
Based on Reys (2004)
 prepare suitable models for
Helping Children Learn
Mathematics 7th ed. pg 282 –
introducing fractions,
296, discuss and do activities,
including word and symbol
“In the classroom 12-1, 12-2,
cards(Refer Reys: pp. 289)
12-3”.
 prepare suitable models for
teaching equivalent fractions,
(1 hr)
mixed numbers & improper
fractions
 plan a teaching activity and
carry out micro-teaching
using the models and aids
prepared

ISL
(jam)
Readings:.
i. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)
pp.282-296
(Compulsory)

Fractions
To carry out
fraction
operations
(+,-,x,/)



Fractions
operations addition of
fractions
- subtraction of
fractions



Design an
assessment task or a game
[refer Kennedy et al (2004)
page 474] that will help you
understand whether or not
your students understand
operations with fractions.

(1 hr)


Discuss with
your peers the effectiveness
or suitability of your
assessment task /game

In groups:

Make
teaching aids suitable for
addition and subtraction of
fraction

iii.Booker,at.el.
(1997).Teaching
Primary Mathematics
(2nd ed.). pp 97-117
iv. Kennedy et al.
(2004). Guiding
Children’s Learning of
Mathematics (10th ed)
pg 401 – 420
Reading:

iii. Kennedy et al.
(2004). Guiding
Children’s Learning of
Mathematics (10th Ed)

Plan and carry out pg 457 - 477
teaching steps using the aids
(1 hr)
you have prepared and use
the assessment task you
have designed in your tutorial
(3 hrs)

(1 hr)
M9

Fractions
To construct
teaching aids for
fraction



Fractions
operations
– multiplication of
fractions
- division of

 Discuss the following
questions:
o How is multiplication of
fractions different from
multiplication of whole

4

In groups create four story
problems that involve:

multiplication
of fraction with:
- whole numbers

Reference:
ii. Cathcart, et al (2006).
Learning Mathematics
in Elementary and
Middle Schools. A
Learner-Centered
Approach (4th Ed)
Pg 201-225

(1 hr)

(2 hrs)

M8

Catatan

Reference:
i. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)
pp.296-302
ii.Cathcart, et al (2006).
Learning Mathematics
in Elementary and
Middle Schools. A
Learner-Centered
Approach (4th Ed)
Pg 227-238

Reading:

Reference:

i. (Refer to Week 17)

ii. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)
pp.296-302

Askey, R. (1999).

SKEMA TLO

Minggu

Tajuk dan
Kandungan

Hasil
Pembelajaran

Kuliah
(jam)
fractions
(1 hr)

Tutorial
(jam)

Amali
(jam)

numbers?

and fractions;
division of fraction with:
o How do you illustrate the
- whole numbers
multiplication and division of:
and fraction

fractio  Prepare a relevant lesson
n with a whole number, e.g.
plan, the required models and
teaching aids and carry out
3
3
2  ,
x5 =
micro-teaching using the four
5
4
story problems above

fractio
n with a fraction, e.g.
(3 hrs)


3 1
  ,
4 2

3 1
x =
4 2

ISL
(jam)
Knowing and Teaching
Elementary
Mathematics,
American Educator,
American Federation
of Teachers, retrieved
from:
http://www.aft.org/pubs
reports/american_educ
ator/fall99/amed1.pdf
(1 hr)

Catatan

iii. Cathcart, et al
(2006). Learning
Mathematics in
Elementary and Middle
Schools. A LearnerCentered Approach (4th
Ed)
pp 238-249
iv. Kennedy et al.
(2004). Guiding
Children’s Learning of
Mathematics (10th Ed)
pg 478 - 502

(1 hr)
M10

Decimals

To relate and
convert fractions
and decimals
To represent
place value in
decimals





Common
fractions and
decimals
:relationship and
conversion
Place value,
ordering and
rounding
(1 hr)

Briefly outline the steps that
explain the meaning of the
commonly used rule ‘divide the
numerator by the denominator’


Discuss how rounding the
divisor can assist in making
an initial estimate in division
with larger numbers.
(1 hr)

5



Prepare teaching materials
to introduce children to
decimal notation of tenths ,
hundredths and
thousandths.
(3 hrs)

Readiing:

Reference:

i. Booker G. at el
(1997)
Teaching Primary
Mathematics (2nd Ed)
pg 247 – 249, 250-252

ii. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)
pp.303-309

(2 hrs)

iii.Cathcart, et al (2006).
Learning Mathematics
in Elementary and
Middle Schools. A
Learner-Centered
Approach (4th Ed)
Pg 252-269

SKEMA TLO

Minggu
M11

Tajuk dan
Kandungan
Decimals

Hasil
Pembelajaran

Kuliah
(jam)

Tutorial
(jam)


To arrange
decimals in order



To round up
decimals
To construct
teaching aids for
decimals

Amali
(jam)

Decimal operations



Discuss the use of place
value chart to help children
understand decimal
computation.

Write a lesson
plan to introduce decimal
computation (for an
operation of your choice) by
linking this topic to fraction
computation.
(1 hr)

(1 hr)

ISL
(jam)

Catatan

Readings:
i. Cathcart, et al
(2006). Learning
Mathematics in
Elementary and Middle
Schools. A LearnerCentered Approach
(4th Ed)
Pg 261-269
Refer to article week
10 pg 261 – 269
(1 hr)

Percentage

To find the
relationship
between
fraction,
decimals
To construct
teaching aids for
percentages





Construct models that Reading: .
can be used to help children
iii. Cathcart, et al
understand percentages.
(2006). Learning

Try out the model with Mathematics in
Elementary and Middle
your peers.
Schools. A LearnerApproach

Discuss with examples Centered
(4th ed) pp. 271-281
the use of percentages in

Percentage
- Relationship
between
fractions,
decimals and
percentages
(1 hr)

daily lives.
(2 hrs)

6

iv. Kennedy et al.
(2004). Guiding
Children’s Learning of
Mathematics (10th Ed)
pp. 443-450, 508-513
(1 hr)

Reference:
ii. Reys, at.el(2004).
Helping Children Learn
Mathematics (7th ed.)
pp.312-329

SKEMA TLO

Minggu
M12

Tajuk dan
Kandungan
Key issues in
teaching
fractions,
decimals and
percentages

Hasil
Pembelajaran
To discuss key

issues in
teaching, fraction,
decimals, and
percentages

Kuliah
(jam)

Tutorial
(jam)

Amali
(jam)

Key issues in 
Discuss the differences 
Refer to
teaching of
between pedagogical issues &
Askey, R. (1999). Knowing
fractions, decimals
content pedagogical issues
and Teaching Elementary
and percentage : 
Mathematics
Discuss why teachers’

In groups:
content pedagogical

Stud
knowledge is crucial to
Create real-life stories related
ent related
effective and meaningful
to the practical applications of
 Teacher
teaching of elementary
the concepts and operations
mathematics [Read: Askey, R.
learned in Fractions,
related
(1999). Knowing and Teaching
Decimals & Percentages.
 Environmenta
Elementary Mathematics]

Share the
lly related
(Socialstories with peers and
(1 hr)
economic
discuss the merits of these
demands)
stories.

Comment and
(1 hr)
discuss how the stories can
be used in class instructions.
(3 hrs)

M13

Revision

M14

Revision

M15

Examination

7

ISL
(jam)
Reading:
i. Askey, R. (1999).
Knowing and Teaching
Elementary
Mathematics
http://www.aft.org/pubs
reports/american_educ
ator/fall99/amed1.pdf
(2 hrs)

Catatan