This document provides information about volume and capacity, including definitions and examples. It discusses volume as referring to the space an object takes up, while capacity refers to the amount a container can hold. Metric and imperial units of volume are listed. An interactive teaching strategy on calculating fractional volumes is presented, with steps such as demonstrating, providing practice questions, and a recreational game. Differences between interactive and lecture strategies are compared, noting interactive strategies allow more active student participation while lectures risk passive learning.

1. FACULTY OF EDUCATION AND LANGUAGES
JANUARY / 2011
HBMT3203
TEACHING MATHEMATICS IN YEAR FIVE AND SIX
MATRICULATION NO :
IDENTITY CARD NO. :
TELEPHONE NO. :
E-MAIL : znas77@yahoo.com.my
LEARNING CENTRE : JOHOR LEARNING CENTRE

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INTRODUCTION
VOLUME
The word ”volume” has several different meanings. The most common definition
is the magnitude or intensity of a certain sound. Volume may also refer to how much
space a three dimensional object takes up or the amount of three dimensional space
occupied by an object.
For example, the volume is height x base x length = 4 x 5 x 10 = 200 units³. Units
of volume include :
1) Metric thats in cubic centimeters (cm³), cubic meters (m³) and liters.
2) Imperial are in fluid ounce, cubic inch, cubic foot, pints, gallons and bushels.
A cubic centimeter (cm3) is a commonly used unit of volume extending the
derived SI-unit cubic metre, and corresponds to the volume of a cube measuring 1 cm ×
1 cm × 1 cm. One cubic centimetre corresponds to a volume of 1⁄1000000 of a cubic metre,
or 1⁄1000 of a litre, or one millilitre; thus, 1 cm3 ≡ 1 mL. The mass of one cubic centimetre
of water at 3.98 °C (the temperature at which it attains its maximal density) is roughly
equal to one gram.
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CAPACITY
Capacity means the amount that something can hold. Usually it means or in other words,
capacity is the volume of a container given terms of liquid measurement, such as
mililiters (ml) or liters (l) in Metric, or pints or gallons in Imperial. The liter is a unit of
volume equal to 1/1000 cubic meter or 1 cubic decimeter (dm³). The unit has two official
symbols: the Latin letter L in lower and upper case (l and L). If the lower case L is used it
is often written as a cursive ℓ, although this usage has no official approval by any
international bureau.
The word litre is derived from an older French unit, the litron, whose name came from
Greek via Latin. The original French metric system used the litre as a base unit, and it has
been used in several subsequent versions of the metric system and is accepted for use
with the SI, although not an official SI unit, the SI unit of volume is the cubic metre (m3).
The spelling of the word used by the International Bureau of Weights and Measures is
"litre" and this is also the usual one in most English-speaking countries, but in American
English the spelling is "liter", being endorsed by the United States.
One litre of water has a mass of almost exactly one kilogram.
Example, ”the bucket has a capacity of 9 liters”. So, this bucket has the ability or
power to contain or hold.
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CONTENT
COMPARE AND CONTRAST STRATEGIES OF TEACHING MATHEMATICS
a) Example on Volume
INTERACTIVE LEARNING STRATEGY
VOLUME OF LIQUID LESSON PLAN:
Learning Area : Computation of volume of liquid.
Learning objectives : 1. Use and apply fractional computation to problems
involving the volume of liquids.
Learning outcomes : (i) Compute volume of liquid from a situation expressed in
fraction.
Teaching aids : Measuring cylinder, coloured liquids, measuring tape.
Set induction : Teacher shows a jug of coloured liquids to pupils.
Teacher pours half of the liquid into a container.
Step 1 : Pupils to discuss in their own group about amount of the remains
of the liquid.
Pupils’ Activity. Notes To Teachers:
Try to recall the fraction through the names:
Teacher asks
pupils to name the o half,
fraction of the
o one over two
water remains.
o one halve
Teacher asks
pupils to convert
the volume into Guide pupils to say the measurement in correct conversion (basic
liter and mililiter.
knowledge) in liter and mililiter.
Teacher asks Eg:
pupils to write
½ of 1000m l = 500ml
down the
relationship ¼ of 1000m l = 250 ml
between fraction
¾ of 1000m l = 750 ml
and volume.
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Teacher’s Instruction: Expected answers from pupils:
o Can anyone tell me how do you get o They get their answer from the
your answer? previous knowledge and from the
examples given.
Step 2 : Teacher shows pupils how to compute volume from situation
exposed in fraction. Teacher demonstrates how to solve them.
e.g.
3
of 400 
8
In this context, “of ” means multiplication (×) operator, so,
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Step 3 : Teacher shows a few questions on cards and asks the pupils to
solve.
A. Compute the following in litre.
No. Question Answer
1 1
of 800 
8
2 3
of 320 
8
3 6
of 480 
8
4 7
of 560 
8
5 5
of 640 
8
Step 4 : Stress the importance of when to multiply and when to divide by
having each student write down, verbally repeat, and use the rules
in the provided examples.
Step 5 : Recreational Game (BINGO)
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Recreational Game ( BINGO )
Answer Instructions
5. Choose a question from 1 to 12.
6. Solve the question and circle the
correct answer.
7. When a pupil gets 5 straight or
diagonal lines, the game is over.
8. The pupil with the least uncircled
2 3
1) of 150 m  = ………….. m  7) of 45  = ……………. 
3 5
3 4
2) of 720 m  = ………….. m  8) of 250  = …………….. 
4 5
5 3
3) of 420 m  = ………….. m  9) of 104  = …………….. 
6 8
2 3
4) of 370 m  = ………….. m  10) of 126  = …………….. 
5 7
4 1
5) of 630 m  = ………….. m  11) of 100  = ……………… 
7 4
6 5
6) of 560 m  = ………….. m  12) of 108  = ……………… 
7 6
DIFFERENCES BETWEEN INTERACTIVE STRATEGY AND LECTURE
STRATEGY
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INTERACTIVE STRATEGY LECTURE STRATEGY
1. It means “Interactive” is in the sense 1. Teacher have to set overarching goals,
they create a collaborative and dynamic organized content and developed a
set of mechanisms to stimulate their course plan with ideas for how to give
own learning. Initially the interactive students the practice that will make it
teaching processes are shown. The basic possible for them to achieve the learning
presupposition of this process is that outcomes. In this section, teacher will
there is much efficiency in learning if make choices about what students will
the student adopts an active, energetic have to do in order to learn the content
posture during information transmission. of the skills or lesson.
The hardware mechanisms for 2. It also can convey a lot of information to
interactive teaching are then described. many student but only from what teacher
As the software devices for the model, a gives in the classroom.
set of expert systems is considered. 3. It can maximizes staff time.
Finally, the evaluation of the whole 4. This strategy also non-threatening to
experiment is discussed. students.
2. It allows students to get more 5. Students may feel boring and also lacks
information and also allows students to of student’s feedback.
talk, listen, read, write and reflect as 6. Teacher and students may difficult to
they approach course content through meet individual learning needs. It is
problem solving exercises and activities. more to “The talk and chalk method”.
3. It can stimulates critical thinking and
decision making but still with teacher’s
guidance. Without proper teacher
guidance, students may learn incorrect
info.
INTERACTIVE STRATEGY LECTURE STRATEGY
4. Can include others teaching aids such as 7. Encourages one – way communication,
technology systems. Example, the teacher must make a conscious effort
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computer, projector, internet connection to become aware of student problems
system, books, articles, films, and student understanding of content
recordings, experiences, projects and without verbal feedback.
other people. 8. Requires a considerable amount of
5. Students feel more enganged and unguided student time outside of the
empowered to the teaching and learning classroom to enable understanding and
activities. long-term retention of content.
6. Encourage the questioning mind and 9. Requires the teacher to have effective
equip students with skills for finding the speaking skills.
answers.
SIMILARITIES BETWEEN INTERACTIVE STRATEGY AND LECTURE
STRATEGY
Interactive strategy and lecture strategy still have some similarities in both
strategies that teacher will use in their teaching and learning activities especially in the
classroom. From both strategies, the teacher will have the same problems such as some
students may be passive in the classroom. For interactive teaching strategy, assessing
students contribution in active learning environments ca be a problem. Teacher needs to
outline the evaluation criteris for each assignment.
Interactive strategy and lecture strategy also can get the teacher give the reward or
compliments for students if they can give cooperation in answering the questions and also
after give the correct result in the groups activities.
b) Difficulties and misconceptions
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EVALUATION
LITERATURE REVIEW
CONCLUSION
I would say that volume refers to the space taken up by an object itself, while capacity
refers to the amount of a liquid or other pourable substance a container can hold. That
more or less parallels what you have seen. I have never, however, seen both terms used of
the same object without clarification, where you would not talk of the volume of a
pitcher, meaning the amount of plastic it is made of, without carefully saying so, since it
is so common to use the two terms interchangeably.
The first thing to realize about interactive teaching is that it is not something
new or mysterious. If you are a teacher and you ask questions in class, assign and check
homework, or hold class or group discussions, then you already teach interactively.
Basically, interactive teaching is just giving students something to do, getting back what
they have done, and then assimilating it yourself, so that you can decide what would be
best to do next.
But, almost all teachers do these things, so is there more to it? To answer this
question, one has to step away from teaching and think about learning. Over the last
twenty years, the field of cognitive science has taught us a lot about how people learn. A
central principle that has been generally accepted is that everything we learn, we
"construct" for ourselves. That is, any outside agent is essentially powerless to have a
direct effect on what we learn. If our brain does not do it itself, - that is, take in
information, look for connections, interpret and make sense of it, - no outside force will
have any effect. This does not mean that the effort has to be expressly voluntary and
conscious on our parts. Our brains take-in information and operate continuously on many
kinds of levels, only some of which are consciously directed.
But, conscious or not, the important thing to understand is that it is our brains
that are doing the learning, and that this process is only indirectly related to the teacher
and the teaching. For example, even the most lucid and brilliant exposition of a subject
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by a teacher in a lecture, may result in limited learning if the students' brains do not do
the necessary work to process it. There are several possible causes why students' learning
may fall short of expectations in such a situation. They may,
not understand a crucial concept partway into the lecture and so what follows is
unintelligible,
be missing prior information or not have a good understanding of what went
before, so the conceptual structures on which the lecture is based are absent,
lack the interest, motivation, or desire to expend the mental effort to follow the
presentation, understand the arguments, make sense of the positions, and validate
the inferences.
However, whatever the cause, without interacting with the students (in the simplest case
by asking questions), a teacher has no way to know if his or her efforts to explain the
topic were successful.
This brings me to the first of three distinct reasons for interactive teaching. It is an
attempt to see what actually exists in the brains of your students. This is the "summative"
aspect. It is the easiest aspect to understand and it is well described in the literature. But,
it is far from being the only perspective! The second reason is "formative", where the
teacher aims through the assigned task to direct students' mental processing along an
appropriate path in "concept-space". The intent is that, as students think through the
issues necessary in traversing the path, the resulting mental construction that is developed
in the student's head will possess those properties that the teacher is trying to teach. As
Socrates discovered, a good question can accomplish this result better than, just telling
the answer.
The third may be termed "motivational". Learning is hard work, and an injection
of motivation at the right moment can make all the difference. One motivating factor
provided by the interactive teacher is the requirement of a response to a live classroom
task. This serves to jolt the student into action, to get his brain off the couch, so to speak.
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Additional more subtle and pleasant events follow immediately capitalizing on the
momentum created by this initial burst. One of these is a result of our human social
tendencies. When teachers ask students to work together in small groups to solve a
problem, a discussion ensues that not only serves in itself to build more robust knowledge
structures, but also to motivate. The anticipation of immediate feedback in the form of
reaction from their peers, or from the teacher is a very strong motivator. If it is not
embarrassing or threatening, students want to know desperately whether their
understanding is progressing or just drifting aimlessly in concept space. Knowing that
they are not allowed to drift too far off track provides tremendous energy to continue.
VOLUME OF LIQUID WORKSHEETS
NAME: _______________________________ DATE: _______________
YEAR: _____________________
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INSTRUCTIONS
 Do not copy the assignment question and instructions to your answer.
 Prepare your assignment answer following the layout of the ASSESSMENT
CRITERIA shown in the RUBRICS provided for the course. Where RUBRICS are
not provided, follow the instructions/guidelines specified by the Faculty for the
assignment concerned.
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 Your assignment should be between 2500 to 3000 words EXCLUDING references.
 Type your answer using 12 point Times New Roman font and 1.5 line spacing.
 Show the number of words at the end of your assignment.
 Tables and figures where provided, should be appropiately titled.
 List your references separately in the APPENDIX page.
ATTACHMENT
REFERENCES
Author’s name (year). Book, Title, Publication
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