Nan Chiau Primary Schoolncps.moe.edu.sg/wp-content/uploads/2017/04/Primary_3_4_Science_and...Nan...
Transcript of Nan Chiau Primary Schoolncps.moe.edu.sg/wp-content/uploads/2017/04/Primary_3_4_Science_and...Nan...
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Science Workshop for ParentsPrimary 3 & 4 (Lower Block)
Nan Chiau Primary School
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ts Objectives of Science Workshop
• Understand how your child learn Science in school
• Science curriculum and syllabus
• Equip you with some skills and techniques to coach your child in the learning of Science
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ts Overview of Workshop1. MOE Science curriculum framework
2. Scientific Inquiry and 5E Model
3. MOE Science Primary Syllabus
4. Topics covered in lower block
5. Examination format and Time management
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ts Overview of Workshop6. Techniques in answering MCQ
7. Techniques in answering open-ended questions
8. Techniques in checking the paper
9. Common misconceptions
10. Support from parents
11. Q and A
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ts 1. Science Curriculum FrameworkMOE Science curriculum nurtures students to
• be curious in exploring their natural and physical world around them with joy.
• develop deep understanding of Science concepts, principles and theories
• Acquire process skills and methodologies to solve problems.
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ts 2. Scientific Inquiry• Scientific inquiry is
defined as the activities and processes which scientists and students engage in to study the natural and physical world around us.
• Learning science as inquiry goes beyond merely presenting facts.
BSCS 5E Instructional
ModelInquiry-based Instructional Strategy
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ts 2. Scientific Inquiry• Students must be
actively engaged in
• collecting and using of evidence;
• formulating and communicating explanations with scientific concepts to new situations.
BSCS 5E Instructional
ModelInquiry-based Instructional Strategy
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2. Nan Chiau Science DepartmentInquiry-based Seamless Learning• Based on the inquiry-based approach
• Uses the Science syllabus 5E Instructional Model
• Re-designed the curriculum to bridge the gap between theory and practice with the affordances of technology
• Enables students to foster self-directed learning, and develop deep learning
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Process Skills• Observing
• Comparing
• Classifying
• Using apparatus and equipment
• Communicating
• Inferring
• Predicting
• Analysing
• Generating possibilities
• Evaluating
• Formulating hypothesis
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Topics Covered (Primary 3)Term Theme Topic
1
Diversity
Classification: Living & Non-living things(D1)Animals (D3)
Plants (D2)Fungi and bacteria (D4)Exploring Materials (D5) 2
3 SystemsYour Amazing Body as a System (S1) Plants and their parts (S2)
4 Cycles
Life cycles of some animals (C1) Life cycle of plants (C2)Revision of P3 topics
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ts Examination Format (Primary 3)
**Each open-ended question carries 2, 3 or 4 marks.
Level Item typeNumber of questions
Number of marks per question
Duration
SA1 Multiple-choiceOpen-ended
156 - 7
3020
1h
SA2 Multiple-choiceOpen-ended
2410 -11
4832
1h 30min
50
80
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Topics Covered (Primary 4)
Term Theme Topic
1 CyclesMatter (C3)
2 InteractionsMagnets and their Characteristics (I1)Making Magnets (I2)
3 EnergyHeat and Temperature (E2)Effects of Heat (E3)
4 EnergyLight and Shadow (E1)Revision of P3 and P4 topics
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ts Examination Format
**Each open-ended question carries 2, 3, 4 or 5 marks.
Level Item typeNumber of questions
Number of marks per question
Duration
SA1 Multiple-choiceOpen-ended
2410-11
4832
1h 30min
SA2 Multiple-choiceOpen-ended**
2812-13
5644
1h 45min
80
100
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Examination Format(P3 SA1)
• Time Duration (1 hr)
• Booklet A (15 MCQ) – 20 to 25 minutes
• Booklet B (6 - 7 OE) - 30 – 35 mins
• About 5 to 10 minutes of checking time
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Examination Format(P4 SA1 and P3 SA2)
• Time Duration (1 hr 30 min)
• Booklet A (24 MCQ) – 30 to 35 min
• Booklet B (10 -11 OE) - 45 to 50 min
• About 5 to 10 minutes of checking time
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Examination Format(P4 SA2)
• Time Duration (1 hr 45 min)
• Booklet A (28 MCQ) – 40 to 45 min
• Booklet B (12 – 13 OE) - 50 min – 1 h
• About 5 to 10 minutes of checking time
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ts 6. Techniques in MCQ
• Get your child to identify the contextual clues by circling, underlining or highlighting them.
• The purpose of underlining/highlighting parts of a text is to make the information stand out.
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ts 6. Techniques in MCQRemind your child to • Link the question to the
topic that was taught- What topic is the question from?
• Recall the concepts taught.- What concepts have I
learnt?• Ask your child whether
they understand what the question is asking.- What does the question want from me?
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ts 6. Techniques in MCQ
•Method of elimination•Instead of finding the correct response, it will be easier to eliminate the incorrect distractors to avoid confusion.
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Which of the following are true for all mammals?
A: They have hair.
B: They live on land only.
C: They give birth to their young alive.
D: They feed their young with the mother’s milk.
(1) A and C only
(2) A and D only
(3) B and C only
(4) B and D only
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Which of the following are true for all mammals?
A: They have hair.
B: They live on land only.
C: They give birth to their young alive only.
D: They feed their young with the mother’s milk.
(1) A and C only
(2) A and D only
(3) B and C only
(4) B and D only
Topic P3 Classification of animals
Recall
concepts
Characteristics of mammals
- Have hair
- Give birth to young alive
- Lay eggs
- Feed young with milk
- Live on land and in water
Aim of
Question
True statements for All
mammals
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tsThe diagram below shows the human digestive system.
No digestion takes place in ________.
(1) A and B only
(2) B and D only
(3) C and E only
(4) A, C and E only
C
B
A
E D
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tsThe diagram below shows the human digestive system.
No digestion takes place in ________.
(1) A and B only
(2) B and D only
(3) C and E only
(4) A, C and E only
C
B
A
E D
Topic P3 Digestive System
Recall
concepts
Digestion starts at the
mouth and ends at the small
intestine.
Aim of
Question
Parts that have no digestion
taking place
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7. Answering Science
Open-ended Questions
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7. General Examination Techniques
Do not leave any question unattempted.
Avoid spending too much time on any particular
question.
Advise your child to move on if they find any
question too challenging for him/her.
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Using
TRACCERto answer Science
Open-endedQuestions
7. Techniques in Open-ended
T R A C C E RTopic Recall Aim Compare Claim Evidence Reason
What topicis the
question from?
What conceptshave I learnt?
What does the question want from
me?
Is there a need to makecomparison?
If yes, should I use
comparativeor
superlativeterms?
What is the choice made
to the question?
What can I observe /
gather from the question to support the claim?
Whichconcept(s) help(s) to explain the evidence to support the
claim?
Copyright © 2017 Nan Chiau Primary School
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Examples of Open-ended questions
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TRACCER Framework
Topic P4 Matter and P3 Materials
Recall concepts • Solids and liquids occupy space.• Waterproof objects cannot absorb
water.
Aim of Question
Which beaker has the waterproof ball?
Compare Compare the water level among the 4 beakers, Q, R, S and T (Superlative terms)
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[C] Beaker T.[C] Beaker T.
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TRACCER Framework
Topic P4 Matter and P3 Materials
Recall concepts • Solids and liquids occupy space.• Waterproof objects cannot absorb
water.
Aim of Question
Which beaker has the ball that is made of a material most suited to make towel?
Compare Compare the water level among the 4beakers, Q, R, S and T (Superlative terms)
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TRACCER Framework
Claim Beaker Q.
Evidence Water level at the end of the experiment is the lowest.
Reason • The ball in Beaker Q absorbed the most amount of water.
• The most absorbent material is needed to be used to make a towel so that we can dry our body the fastest.
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[C] Beaker Q. [E] Its water level at the end of the experiment is the lowest, showing that it absorbed the most amount of water. [R] Towel is the most absorbent material allowing us to dry our body the fastest.
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AnotherOpen-ended question
Topic
Recall concepts
Aim of Question
Compare
Claim
Evidence
Reason
Topic Heat
Recall concepts Good conductors of heat conduct heat away from a
heat source faster.
Aim of Question Which liquid, A or B, is a better conductor of heat?
Explain.
Compare Compare temperature of water in both beakers, A
and B. (Comparative terms)
Claim Liquid A
Evidence Temperature of Liquid A is higher at the end of the
experiment.
Reason Liquid A could conduct heat away from the stove
faster.
Which liquid, A or B, is the better conductor of heat? Explain your answer.
[C] Liquid A. [E] The temperature of Liquid A is higher at the end of the experiment.[R] Liquid A could conduct heat away from the stove faster.
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TRACCER is…Topic
Recall relevant concepts
Aim
Claim (the choice made)
Compare (using either comparative or superlative terms)
Evidence (the data / clues in the question)
Reason (the Science concepts that connects the evidence to support your claim)
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Techniques in Checking Open-ended Questions
READ the written answer again and check whether you have all the points required.
Check if you have answered SPECIFICALLY to what the question is asking. Do not use general statements.
Check if you have USE scientific terms in your Reason
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Common Misconceptions
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Science MisconceptionsA plant needs sunlight, air and water to survive.
A plant needs food, air and water to survive. It needs sunlight to make food.
Fungi are plants.
Both fungi and non-flowering plants reproduce by spores. However, fungi are not plants.
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A chicken has 3 LIFE CYCLES.
A chicken has 3 stages of growth in its life cycle.
A frog has 5 stages of growth in its life cycle.
A frog has 3 stages of growth in its life cycle.
Science Misconceptions
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The number of stages of growth in the life cycle determines the life span of the animal. For instance, a 4-stage life cycle butterfly has a longer life span than a 3-stage life cycle chicken.
The number of stages of growth in the life cycle DOES NOT determine the life span of the animal. The life cycle simply tells us the specific stage of growth of a particular living thing.
Science Misconceptions
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The mass of the object depends on its size.
Mass of object depends on the amount of
substance in the object. For instance, a piece
of A4 size paper is much bigger than a
marble. That does not mean that the paper
has more mass than the marble.
Science Misconceptions
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When more air is pumped into a container, the
volume of air remains constant. Thus, mass of
air in the container is constant too.
When more air is pumped into a container, the
volume of air remains constant as air can be
compressed. Since there is presence of more
air in the container, the total mass of air would
increase.
Science Misconceptions
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When an object expands, the mass increases
too.
When an object expands, the volume
increases but the mass remains the same.
The magnetic object attracts the magnet.
A magnet attracts the magnetic object.
Science Misconceptions
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Amount of heat and temperature is the same.
Heat and temperature are 2 different concepts.
50 ml of water at 100oC has MORE HEAT than
20 ml of water at 100oC.
The ice cubes in a glass melted because they
have lost its coldness.
The ice cubes in a glass melted because they
have gained heat from the glass as well as the
surrounding.
Science Misconceptions
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When I touch a door knob, my hand feels cold
as coldness is transferred to my hands.
When I touch a door knob, my hand feels cold
as heat from my hand is transferred to the
door knob.
Science Misconceptions
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ts 9. Support at Home• Provide a conducive environment for your child
to do work.
• KEEP all P3, P4 resources for revision.
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ts 9. Support at Home• MAKE Science relevant in your daily lives
through observations around him/her and make links to Science .
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ts 9. Support at Home• VISIT the Science centre, nature reserves etc…
• WATCH educational programmes on television
e.g. Animal Planet, Magic School Bus etc…
• READ non-fiction books & publications e.g, Singapore Scientists, National Geographic Kids etc…
Primary 3 & 4 Mathematics
Workshop for Parents24 March 2017
P3/P4 Mathematics Workshop for Parents
Outline
1. Mathematics Framework and Syllabus
2. Polya’s 4-steps to Problem Solving
3. Problem-solving Heuristics
4. Identify your child’s area of concern
5. Supporting your child in the learning of
Mathematics
P3/P4 Mathematics Workshop for Parents
Outline
1. Mathematics Framework and Syllabus
2. Polya’s 4-steps to Problem Solving
3. Problem-solving Heuristics
4. Identify your child’s area of concern
5. Supporting your child in the learning of
Mathematics
Mathematics Framework
Monitoring of one’s own thinking
Self-regulation of learning
Reasoning, communication
and connections
Applications and modelling
Thinking skills and heuristics
Numerical
Algebraic
Geometric
Statistical
Probabilistic
Analytical
Numerical calculation
Algebraic manipulation
Spatial visualisation
Data analysis
Measurement
Use of mathematical tools
Estimation
Beliefs
Interest
Appreciation
Confidence
Perseverance
P3/P4 Mathematics Workshop for Parents
Development of
Comprehensive
Lesson
packages
real-life experiences
to explore
possibilities and
make connections
Use of affordances of
ICT to learn
anywhere anytime
Student-centric activities
to discover, reason &
communicateCustomised videos with
authentic situations to
stimulate thinking
Develops self-directed
learning and collaborative
learning through inquiry-
based approach
New pedagogical
strategies with
integration of 5E
Instructional Model &
Concrete-Pictorial-
Abstract approaches
RC² (Reasoning, Communication, Collaboration)
P3/P4 Mathematics Workshop for Parents
School Math Assessments
• Term 1 (Revision Paper)
• Term 2 (SA1)
• Term 3 (Revision Paper)
• Term 4 (SA2)
Weighting details (Pri 3 – Mathematics)
Percentage for End-Of-Year Overall Assessment
Term Formative Assessment Weighting Final
1 - - Semester 1
40%2
(SA1)
Main Paper = 80 marks 40%
3 - - Semester 2
60%
4
(SA2)
Main Paper = 80 marks 60%
Overall 100%
P3 Mathematics Examination Format
Section Item Type Number of
questions
Number of
marks per
question
Number of
marks
Total
number of
marks
Duration
A Multiple-
choice6 1 6 30 1 h 45 min
12 2 24
B Short-
answer15 2 30 30
C Structured/
Long-
answer
4 3 12 20
2 4 8
39 - 80
Term Formative Assessment Weighting Final
1 - - Semester 1
40%2
(SA1)
Main Paper = 100 marks 40%
3 - - Semester 2
60%
4
(SA2)
Main Paper = 100 marks 60%
Overall 100%
Percentage for End-Of-Year Overall Assessment
Weighting details (Pri 4 – Mathematics)
P4 Mathematics Examination Format
Section Item Type Number of
questions
Number of
marks per
question
Number of
marks
Total
number of
marks
Duration
A Multiple-
choice14 2 28 28 1 h 45 min
B Short-
answer21 2 42 42
C Structured
/ Long-
answer
2 3 6 30
6 4 24
43 - 100
P3/P4 Mathematics Workshop for ParentsTopics P3 sub-topics P4 sub-topics
WHOLE
NUMBERS
- Numbers up to 10 000
- Addition and subtraction
- Multiplication and
division
- Mental calculation
- Numbers up to 100 000
- Multiplication and division
- Four operations
- Factors and multiples
FRACTIONS - Equivalent fractions
- Addition and subtraction
- Mixed numbers and
improper fractions
- Addition and subtraction
- Fraction of a set of objects
DECIMALS - Decimals up to 3 decimal
places
- Addition and subtraction
- Multiplication and division
P3/P4 Mathematics Workshop for Parents
Topics P3 sub-topics P4 sub-topics
MEASUREMENT - Length, mass and
volume
- Time
- Money
- Area and perimeter
- Time
- Money
- Area and perimeter
GEOMETRY - Perpendicular and
parallel lines
- Angles
- Perpendicular and parallel
lines
- Angles
- Rectangle and square
- Symmetry
DATA ANALYSIS - Bar graphs - Tables
- Line graphs
Outline
1. Mathematics Framework
2. Polya’s 4-steps to Problem Solving
3. Problem-solving Heuristics
4. Identify your child’s area of concern
5. Supporting your child in the learning of
Mathematics
P3/P4 Mathematics Workshop for Parents
Polya’s 4-steps to Problem Solving
1. Read & Understand the Problem
2. Devise a Plan
3. Carry out the Plan
4. Reflect on your answer
P3/P4 Mathematics Workshop for Parents
Outline
1. Mathematics Framework
2. Polya’s 4-steps to Problem Solving
3. Problem-solving Heuristics
4. Identify your child’s area of concern
5. Supporting your child in the learning of
Mathematics
P3/P4 Mathematics Workshop for Parents
Thinking Skills & Heuristics
• To give a representation
e.g. draw a diagram, make a systematic list, use
equations
• To make a calculated guess
e.g. guess and check, look for patterns, make
suppositions
• To go through the process
e.g. act it out, work backwards, before & after
• To change the problem
e.g. restate the problem, simplify the problem,
solve part of the problem
P3/P4 Mathematics Workshop for Parents
Problem Solving
Heuristics
Model Drawing
There were 250 apples.
The number of oranges was 36 more than the
number of apples.
How many oranges were there?
Example 1a Understand * Devise a plan * Carry out * Reflect
Apples
250
Oranges
?
36250 + 36 = 286
Answer: 286 oranges
There were 286 oranges.
There were 250 apples.
The number of oranges was 36 more than the
number of apples.
How many fruits were there?
Example 1b Understand * Devise a plan * Carry out * Reflect
Apples
250
Oranges
?
36250 + 36 = 286 (oranges)
Answer: 536 fruits
?250 + 286 = 536 (A + Or)
There were 536 fruits.
There were 250 apples.
There were 4 times as many pears as apples.
The number of oranges was 36 less than the number
of pears. How many fruits were there altogether?
Example 1c Understand * Devise a plan * Carry out * Reflect
250
A
P
Or
?
36
1 unit = 250 (Apples)
4 units = 250 x 4
= 1000 (Pears)
1000 – 36 = 964 (Oranges)
250 + 1000 + 964
= 2214
Answer: 2214 fruits
There were 2214 fruits.
There were 250 apples.
There were 4 times as many pears as apples.
The number of oranges was 36 less than the number
of pears. How many fruits were there altogether?
Example 1c Understand * Devise a plan * Carry out * Reflect
250
A
P
Or
?
36
1 unit = 250
9 units = 250 x 9
= 2250
2250 – 36 = 2214
Answer: 2214 fruits
There were 2214 fruits.
Method 2
36
Mrs Tan paid $32 for a cup and a bowl.
Each bowl cost 3 times as much as each cup.
How much did she pay for each cup?
Example 2a Understand * Devise a plan * Carry out * Reflect
Answer: $8
1 cup
1 bowl$32
4 units = 32
1 unit = 32 4 = 8
?
Each cup cost $8.
Mrs Tan paid $32 for a cup and a bowl.
Each bowl cost 3 times as much as each cup.
How much did she pay for each bowl?
Example 2b Understand * Devise a plan * Carry out * Reflect
Answer: $24
1 cup
1 bowl$32
4 units = 32
1 unit = 32 4 = 8
?Each bowl cost $24.
3 units = 8 x 3 = 24
Mrs Tan paid $72 for 3 cups and 2 bowls.
Each bowl cost 3 times as much as each cup.
How much did she pay for each bowl?
Example 2c Understand * Devise a plan * Carry out * Reflect
Answer: $24
9 units = 72
1 unit = 72 9 = 8
Each bowl cost $24.
3 units = 8 x 3 = 24
OR
8 + 8 + 8 = 24
1 cup
1 bowl
1 bowl
1 cup
1 cup
$72
May had 80 mangoes. She sold 𝟏
𝟒of them.
(a) How many mangoes did she sell?
(b) How many mangoes were not sold?
Example 3a Understand * Devise a plan * Carry out * Reflect
Answer: a) 20
b) 60
a) She sold 20 mangoes.
80
sold ?
4 units = 80
1 unit = 80 4
= 20
3 units = 20 x 3
= 60
OR 20 + 20 + 20 = 60
OR 80 – 20 = 60
?
b) 60 mangoes were not sold.
A company has 350 workers. 𝟐
𝟓of the workers are male.
How many female workers are there?
Example 3b Understand * Devise a plan * Carry out * Reflect
Answer: 210 female
There are 210 female workers.
350
male female
?
5 units = 350
1 unit = 350 5
= 70
2 units = 70 x 2 = 140 (Male)
350 – 140 = 210
OR 3 units = 70 x 3
= 210
𝟐
𝟗of Anne’s balloons are yellow and the rest are
pink. She has 147 pink balloons, how many balloons
does she have altogether?
Example 3c Understand * Devise a plan * Carry out * Reflect
Answer: 189 balloons
She has 189 balloons.
147
7 units = 147
1 unit = 147 7 = 21
9 units = 21 x 9 = 189
?
A telephone and a radio cost $210.
The telephone cost 𝟑
𝟒as much as the radio.
How much does the radio cost?
Example 4 Understand * Devise a plan * Carry out * Reflect
Answer: $120
The radio cost $120.
T
R$210
?
7 units = 210
1 unit = 210 7
= 30
4 units = 30 x 4
= 120
Repeated Identity Concept
Repeated Identity Concept
Repeated Identity
• Same quantity is repeated;
the amount of the same
quantity will be the same
Clara, Kenneth and Rauf had a total of 104 stamps.
Clara had 8 more stamps than Kenneth and
Rauf had 40 more stamps than Clara.
How many stamps did Rauf have?
Example 5 Understand * Devise a plan * Carry out * Reflect
Clara
Kenneth
8
Rauf 8 40
104
Make the units equal
40 + 8 + 8 =56
104 – 56 = 48
3 units = 48
1 unit = 48 ÷ 3 = 16
16 + 8 + 40 = 64
Rauf had 64 stamps.
Clara, Kenneth and Rauf had a total of 104 stamps.
Clara had twice as many stamps as Kenneth and
Rauf had 24 more stamps than Clara.
How many stamps did Rauf have?
Example 6 Understand * Devise a plan * Carry out * Reflect
Clara
Kenneth
Rauf 24
104
Make the units equal
104 – 24 = 80
5 units = 80
1 unit = 80 ÷ 5 = 16
2 units = 16 x 2 = 32
32 + 24 = 56
Rauf had 56 stamps.
Answer: 56
At a funfair, there were thrice as many adults as children
and four times as many boys as girls.
There were 88 more adults than boys,
how many people were at the funfair?
Example 7 Understand * Devise a plan * Carry out * Reflect
Adults
Children
boys girls
(Adults) 15 units
(Boys) 4 units
(Girls) 1 unit
15 units – 4 units = 11 units
11 units = 88
1 unit = 88 ÷ 11 = 8
15units + 4units + 1unit = 20units
20 units = 20 x 8 = 160
There were 160 people.Answer: 160
Alice and Bernice saved $75 altogether.
Alice and Carol saved $145 altogether.
Carol saved thrice as much as Bernard.
How much did Alice save?
Example 8 Understand * Devise a plan * Carry out * Reflect
A + B
A + C
1u
1u 1u 1u
$75
$145
?
145 – 75 = 70
2 units = 70
1 unit = 70 ÷ 2 = 35
75 – 35 = 40
Alice saved $40.
Answer: $40
Equal Concept
‘equal’ can be from the beginning
or at the end
Equal Concept
There were an equal number of sweets in Bag A and Bag B.
After 8 sweets were taken out from Bag A and put into Bag B,
there were 36 sweets in Bag B in the end. How many sweets
were there in each bag at first?
Example 9a Understand * Devise a plan * Carry out * Reflect
Answer: 28 stamps
A
B
36
8
88
?
8
36 – 8 = 28
There were 28 sweets in
each bag at first.
There were an equal number of sweets in Bag A and Bag B.
After 8 sweets were taken out from Bag A and put into Bag B,
there were 36 sweets in Bag B in the end.
(a) How many more sweets were there in Bag B than Bag A in
the end?
(b) How many sweets were there in Bag A in the end?
Example 9b Understand * Devise a plan * Carry out * Reflect
Answer: a) 16 sweets
b) 20 sweets
A
B
36
8
88
?
8 + 8 = 16
a) There were 16 more sweets
in Bag B than Bag A in the end.
36 – 16 = 20
b) There were 20 sweets in Bag
A in the end.
?
Jack and Vin had the same amount of money at first.
After Jack spent $48 and Vin received $12,
Vin had 4 times as much money as Jack in the end.
How much money did each of them have at first?
Example 10 Understand * Devise a plan * Carry out * Reflect
Answer: $68
Jack
Vin
4 units
48
1248
1 unit 4 units – 1 unit = 3 units
48 + 12 = 60
3 units = 60
1 unit = 60 ÷ 3 = 20
20 + 48 = 68
OR
4 units = 20 x 4 = 80
80 – 12 = 68
Each of them had $68 at first.
1 unit
1 unit
3 units
May had 5 times as many stickers as Jane.
After May gave away 88 stickers and
Jane lost 8 stickers, they had the same number of stickers left.
How many stickers did each of them have in the end?
Example 11 Understand * Devise a plan * Carry out * Reflect
Answer: 12
May
Jane
88 – 8 = 80
4 units = 80
1 unit = 80 ÷ 4 = 20
20 – 8 = 12
Each of them had 12 stickers
in the end.
8
88 gave away
8 1u 1u 1u 1u
Before & After
Identify the changes when 1
quantity remains the same.
Solve word problems involving
one unchanged quantity concept.
Before & After:
One Unchanged Quantity Concept
Jane had 12 more pies than Clara at first.
After Jane had eaten 4 pies,
she had twice as many pies as Clara in the end.
How many pies did Clara have?
Example 12
Jane
Clara
1 unit = 12 – 4 = 8
Clara had 8 pies.
1 unit
1 unit
12
Understand * Devise a plan * Carry out * Reflect
\ 4
1 unit
Answer: 8 pies
8
Andy had twice as many stamps as Ben at first.
After Ben had used 15 stamps,
Andy had 4 times as many stamps as Ben.
How many stamps did Andy have?
Example 13 Understand * Devise a plan * Carry out * Reflect
Answer: 60 stamps
Andy
Ben
2 big units = 4 small units
(Ben) 1 big unit = 2 small units
2 small units – 15 = 1 small unit
1 small unit = 15
4 small units = 15 x 4 = 60 OR 15 + 15 + 15 + 15 = 60
Andy had 60 stamps at first.
Andy had 2 big units at first
Andy had 4 small units in the end
1 unit
Change End
A: no change 4 units
B – 15 1 unit
What remains the SAME?
Andy remains the same
1 quantity remains the SAME
1 unit 1 unit 1 unit 1 unit
15
Andy had twice as many stamps as Ben at first.
After Ben had used 15 stamps,
Andy had 4 times as many stamps as Ben.
How many stamps did Andy have?
Example 13 Understand * Devise a plan * Carry out * Reflect
Answer: 60 stamps
Andy
Ben
1 small unit = 15
4 small units = 15 x 4 = 60 OR 15 + 15 + 15 + 15 = 60
Andy had 60 stamps at first.
1 unit
1 unit 1 unit 1 unit 1 unit
15
Students’
Solution
Sally had thrice as many sweets as May.
After May gave away 12 sweets to her brother,
Sally had 7 times as many sweets as May in the end.
How many sweets did Sally have?
Example 14 Understand * Devise a plan * Carry out * Reflect
Answer: 63 sweets
Sally
May
1 unit
12
12 12 12
1 unit 1 unit 1 unit
7 units
1u 1u 1u
Sally end 1u 1u 1u 1u 1u 1u 1u
1u 1u 1u 12 12 12
7 units – 3 units = 4 units
12 + 12 + 12 = 36
4 units = 36
1 unit = 36 ÷ 4 = 9
7 units = 7 x 9 = 63
Sally had 63 sweets.Regrouping
Sally at first
Guess & Check
Guess & Check
• Organise information using a
Table
• Heading for each column
• Logical Guess
• Check
P3/P4 Mathematics Workshop for Parents
There was a total of 10 cows and chickens in a
farm. The farmer counted a total of 32 legs. How
many cows and how many chickens were there?
Example 16 Understand * Devise a plan * Carry out * Reflect
Answer: 6 cows and 4
chickens
No. of
cows
Cows’ legs No. of
chickens
Chickens’
legs
Total no. of legs Check
5 55 x 4 = 20 5 x 2 = 10 20 + 10 = 30
6
X
4 6 x 4 = 24 4 x 2 = 8 24 + 8 = 32
There was a total of 10 cows and chickens in a
farm. The farmer counted a total of 32 legs. How
many cows and how many chickens were there?
Example 17 Understand * Devise a plan * Carry out * Reflect
Answer: 6 cows and 4
chickens
No. of
cows
Cows’ legs No. of
chickens
Chickens’
legs
Total no. of legs Check
10 010 x 4 = 40 0 x 2 = 0 40 + 0 = 40
9
X
X1 9 x 4 = 36 1 x 2 = 2 36 + 2 = 38
6 4 6 x 4 = 24 4 x 2 = 8 24 + 8 = 32
Reduced
by 2
By supposition/ assumption method,
If all are cows,
10 x 4 = 40
4 – 2 = 2
40 – 32 = 8
8 ÷ 2 = 4 (cows chickens)
10 – 4 = 6 (cows)
There was a total of 10 cows and chickens in a
farm. The farmer counted a total of 32 legs. How
many cows and how many chickens were there?
Example 18 Understand * Devise a plan * Carry out * Reflect
Answer: 6 cows and 4
chickens
By supposition/
assumption method,
If all are cows,
10 x 4 = 40
4 – 2 = 2
40 – 32 = 8
8 ÷ 2 = 4 (cows chickens)
10 – 4 = 6 (cows)
By supposition/ assumption
method,
If all are chickens,
10 x 2 = 20
4 – 2 = 2
32 – 20 = 12
12 ÷ 2 = 6 (chickens cows)
10 – 4 = 6 (chickens)
Lily packed some cupcakes for her friends.
If she gave each of them 4 cupcakes, she would have 2 cupcakes left.
If she gave each of them 6 cupcakes, she would need 2 more
cupcakes. How many cupcakes did Lily have?
Example 19a Understand * Devise a plan * Carry out * Reflect
Answer: 10 cupcakes
No. of
friends
Each 4 cupcakes with 2 left Each 6 cupcakes and
need 2 more
Check
11 x 4 = 4
4 + 2 = 6
1 x 6 = 6
6 – 2 = 4
2
X
2 x 4 = 8
8 + 2 = 102 x 6 = 12
12 – 2 = 10
Lily packed some cupcakes for her friends.
If she gave each of them 4 cupcakes, she would have 2 cupcakes left.
If she gave each of them 6 cupcakes, she would need 2 more
cupcakes. How many cupcakes did Lily have?
Example 19b Understand * Devise a plan * Carry out * Reflect
Answer: 10 cupcakes
Multiples of 4
2
4
X
By listing,
1
8
+ 2 (left) 4 + 2 = 6 8 + 2 = 10
Multiples of 6
– 2 (Need)
6 12
6 – 2 = 4 12 – 2 = 10
Number of friends
Same Total
cupcakes
Outline
1. Mathematics Framework and Syllabus
2. Polya’s 4-steps to Problem Solving
3. Problem-solving Heuristics
4. Identify your child’s area of concern
5. Supporting your child in the learning of
Mathematics
P3/P4 Mathematics Workshop for Parents
Possible areas of concern
1. Factual Fluency
• Not counting with fingers
2. P3 to P4 Concepts
• Whole Numbers
• Mensuration (Length, Mass, Volume, Area and
Perimeter)
• Geometry (Angles, parallel & perpendicular lines)
3. Good habits
• Reading and understanding of questions
• Model drawing habit
• Checking their work
P3/P4 Mathematics Workshop for Parents
Outline
1. Mathematics Framework and Syllabus
2. Polya’s 4-steps to Problem Solving
3. Problem-solving Heuristics
4. Identify your child’s area of concern
5. Supporting your child in the learning of
Mathematics
P3/P4 Mathematics Workshop for Parents
Encourage critical thinking
Questioning techniques
• Let’s read again. What does this mean?
• What method can you use? Draw model?
• Can you solve part of it?
Which part can you solve first?
• Is your answer reasonable?
How do you know your answer is correct?
P3/P4 Mathematics Workshop for Parents
Importance of You (Parents)
P3/P4 Mathematics Workshop for Parents
You are IMPORTANT!
Role of Supportive Parent
• Create a home environment that
encourages learning
• Set expectations (but not unrealistic) with
your child on his/her achievement and
future aspiration
• Be involved in your child's education in
school and in the community
P3/P4 Mathematics Workshop for Parents
Praise & Mindsets
(Carol Dweck)
“praise wisely, not praising intelligence or
talent. That has failed. Don't do that
anymore.”
“praising the process that kids engage
in: their effort, their strategies, their focus,
their perseverance, their improvement.
This process praise creates kids who are
hardy and resilient.”
P3/P4 Mathematics Workshop for Parents
Confidence & Motivation
• Confidence is a self-belief in being able
to learn and make progress, and
motivation is an internal state that
arouses, directs and maintains behaviour.
• Confidence and motivation is a strong
impetus for learning. They influence
attitude towards Mathematics,
perceptions of its values and the
willingness to put in effort and employ
strategies to learn it well.
P3/P4 Mathematics Workshop for Parents
Effort-Based Ability Theory
Underlying principles
1) If I do, I understand.
2) After understanding, there should be practice.
3) Success breeds success.
Confidence
Ability
Effective Effort
Hard work
Strategies
Achievement
P3/P4 Mathematics Workshop for Parents
Thank you