p3 & p4 parents’ seminar mathematics strategies for model ......p3 & p4 parents’ seminar...
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Springdale Primary School
P3 & P4 Parents’ Seminar
Mathematics
Strategies for Model Drawing
27 Feb 2016
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Springdale Primary School
Objectives
At the end of this session, parents will be able
to:
• Understand the rationale of using the model
approach in solving problem sums
• solve middle primary story sums using the
model approach
• guide their child to solve story sums using the
model approach
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Outline
• Why? (Introduction to model method)
• What? (Explanation of different types
of model)
• How? (Hands-on practice with drawing
of model)
• How? (Home support for your child)
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Curriculum Framework
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Problem-solving Process
• Understanding the Problem– Look for given information– Visualize the information– Organize the information– Connect the information
• Devising a Plan (Strategy)• Carrying out the Plan (Strategy)
– Use computational skills– Use geometrical skills– Use logical reasoning
• Reflecting– Check reasonableness– Improve of the method used– Seek alternative solutions– Extend the solution to other problems
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Processes – Thinking Skills
• Thinking skills are skills that are used in a
thinking process, such as
– Classifying
– Comparing
– Analysing parts and whole
– Identifying patterns and relationships
– Induction
– Deduction
– Generalising
– Spatial visualisation
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Processes – Heuristics
• Heuristics are problem-solving strategies
when the solution to the problem is not
obvious. These include
– making a guess (e.g. trial and error/guess
and check, making a supposition)
– walking through the process (e.g. acting it
out, working backwards)
– using a representation (e.g. drawing a
diagram, tabulating)
– changing the problem (e.g. simplifying the
problem, considering special cases)
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Using a Representation
• Representations allow students to
– reflect on them;
– modify them; and
– link them to suitable problem-solving strategies
• Representations include
– Picture
– Model
– Diagram
– Table/List
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Mathematics Syllabus
Primary 1 and 2 Primary 3 and 4 Primary 5 and 6
• Whole Number
• Money, Measures
& Measuration
• Fractions
• Whole Number
• Money, Measures
& Measuration
• Fractions
• Decimals
• Whole Number
• Money, Measures
& Measuration
• Fractions
• Decimals
• Ratio & Proportion
• Percentage
• The model method is one of the most frequently
used problem-solving heuristics throughout
primary school.
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Mathematics Syllabus
• In secondary school, the
model is morphed to that
of the algebraic method.
http://www.math.harvard.edu/~engelw
ar/MathE305/Singapore%20Model%20M
ethod%20Text.pdf
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Mathematics Syllabus
• In the international scene,
the model method is
synonymous to that of
Singapore Mathematics.
http://math.nie.edu.sg/ame/matheduc
/tme/tmeV6_2/05-
Yan%20KC%20Final%20version.pdf
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Features of Model Drawing
• Simplify the problem.
• Visualize the problem from abstract to
concrete.
• Make sense of and manipulate the
information pictorially.
• Length of the rectangular bars is drawn
in relation to one another.
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Features of Model Drawing
• The available information is recorded
onto the models.
• Question marks are used to indicate the
unknown information.
• Translate the problem into mathematics
steps.
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Procedure of Model Drawing
Phase Action Questions
WHOLE Read the
whole problem
sum
� Have I read the whole
sum?
PART Read the sum
line by line
� What do I know?
� Can I draw a diagram to
show what I know?
� What do I not know?
� Can I draw a diagram to
show what I do not know?
LINK Read what
you have
written and
drawn
� How can I link up
whatever I have drawn?
� How can I solve the
problem?
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Types of Model
• Part-whole Model
• Comparison Model
• Before-after Model
…
• Modification of model
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Part-Whole Model
Part Part
Whole
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Part-Whole Model
Part
Part
Whole
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Examples
1. A container with 2 packets of milk has a mass of 1 200 g.
The same container with 4 packets of milk has a mass of
2 200 g. What is the mass of the empty container?
1 200
2 200
milkcontainer milk
milkcontainer milk milk milk
?
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Examples
2. 3 shirts and 1 dress cost $84.
3 shirts and 3 dresses cost $132.
Find the cost of a dress.
132
84
?
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Examples
3. I am thinking of 3 numbers.
Number A and Number B adds up to 49.
Number B and Number C adds up to 57.
Number A and Number C adds up to 64.
What are the 3 numbers?
49 BA
C
A64
B
C
57
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Comparison Model
Comparison
X
Y
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Comparison Model
Comparison
X
Y
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Examples
4. Aaron is 28 years older than Ben.
Ben is 4 years older than Carl.
If their total age is 84 years, what is Aaron’s age?
28Aaron
Ben
Carl
84
?
4
4
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Examples
5. Aaron has thrice the number of marbles Ben has.
Carl has twice the number of marbles Aaron has.
If Carl has 60 more marbles than Ben, how many
marbles does Aaron have?
Aaron
Ben
Carl
?
60
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Examples
6. The sum of 2 numbers is 1 568.
The difference between them is 580.
What is the greater number?
580Big
Small1 568
?
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Examples
7. The difference between 2 numbers is 2 480.
The greater number is 5 times as big as the smaller number.
What is the sum of the 2 numbers?
Big
Small?
2 480
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Examples
8.�
�of the sales from potatoes is as much as
�
�of the sales
from tomatoes. The sales from the potatoes is $500
less than the sales from tomatoes. Find the total sales
from the potatoes and tomatoes.
Potatoes
Tomatoes
?
500
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Examples
9. At a concert, there were twice as many girls as boys.
The number of adults is �
�of the number of girls. There
are 360 fewer adults than girls. How many people were
at the concert?
Girls
Boys
Adults
360
?
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Before-After Model
• A basic change situation involves
3 elements
– the initial value of a quantity
– the change, which can be an increase or
decrease, and
– The final value of the quantity
• 2 models are drawn for comparison.
• It is not always the case when the
before model is drawn first.
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Examples
10. Aaron had 5 times as many marbles as Ben. After Aaron
gave 72 marbles to Ben, they each had the same number
of marbles. How many marbles did Aaron had at first?
Aaron
Ben
?
72
Aaron
Ben
BEFORE
AFTER
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Examples
11. Aaron had 6 times as much money as Ben at first. When
their mother gave them $300 each, Aaron has 3 times as
much money as Ben now. How much money did they
have at first?
Aaron
Ben
?
?
Aaron
Ben
BEFORE
AFTER
300
300 300 300
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Examples
12. Class A had �
�the number of pupils in Class B. After 14 pupils
were transferred out from Class A, Class A had �
�the number
of pupils in Class B. How many pupils were there in both
classes altogether in the beginning?
A
B
?
BEFORE
AFTER A
B
14
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Hands-on Session
Now it is your turn. :)
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A Final Word
What Makes Model-drawing Difficult?
• Knowledge Factors
– Linguistic knowledge
– Algorithmic knowledge
– Conceptual knowledge
– Schematic knowledge
http://repository.nie.edu.sg/jspui/bitstream/10497/132/1/ME-2-1-93.pdf
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A Final Word
What Makes Model-drawing Difficult?
• Affective factors
– Interest and motivation
– Confidence
– Perseverance
http://repository.nie.edu.sg/jspui/bitstream/10497/132/1/ME-2-1-93.pdf
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A Final Word
Common Model-drawing Pitfalls
• Incorrect representation of the story sum
• Incomplete representation of the story
sum
• Transfer error
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A Final Word
Resources for Model-drawing
• Facebook group – “Maths Model Method
– Singapore”
• http://www.teach-kids-math-by-model-
method.com/
• http://citeseerx.ist.psu.edu/viewdoc/dow
nload?doi=10.1.1.555.5563&rep=rep1&ty
pe=pdf
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Q & A
THANK YOU
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