P5 Parents’ Seminar Mathematics Strategies for …...P5 Parents’ Seminar Mathematics Strategies...

Springdale Primary School

P5 Parents’ Seminar MathematicsStrategies for Model Drawing II 18 Feb 2017

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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 upper primary problem sums using the

model approach• guide their child to solve problem 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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Why?(Introduction to model method)

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Curriculum Framework

0

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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 – 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 the primary school years.

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2018 PSLE Maths Format

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Changes to format of papers:• Paper 1 Booklet B

– Previously 10 (1m) and 5 (2m) questions– Now 5 (1m) and 10 (2m) questions

• Paper 2– Previously 13 long-structured questions– Now 12 long-structured questions

• Total Number of questions for both Papers– Previously 48 questions– Now 47 questions



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Changes to format of papers:• Distribution of marks

– Previously Paper 1 (40m) and Paper 2 (60m)– Now Paper 1 (45m) and Paper 2 (55m)

• Duration for Paper 1– Previously 50 min– Now 1 h

• Duration for Paper 2– Previously 1 h 40 min– Now 1 h 30 min


2018 PSLE F Maths Format

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Changes to format of papers:• Paper 2

– Previously 8 long-structured questions– Now 6 long-structured questions

• Total Number of questions for both Papers– Previously 48 questions– Now 46 questions

• Total Number of marks for both Papers– Previously 100 marks– Now 90 marks



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Changes to format of papers:• Duration for Paper 2

– Previously 1 h 15 min– Now 1 h

• Total Duration– Previously 2 h 15 min– Now 2 h


What? Explanation of different types of model

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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, i.e. equations

• Mainly 2 types – Part-Whole Models and Comparison Models.

• The rest are hybrids of these two types.

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Part-Whole Model

Part Part

Whole

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X Y


Part-Whole Model

Part

Part

Whole

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X

Y


Comparison Model

Comparison

X

Y

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Comparison Model

Comparison

X

Y

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Process of Model DrawingPhase 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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Example # 1

Fred is 3 years younger than Eunice. Dawn is 3 times as old as Eunice. Together, Eunice and Fred’s total age is 15 years less than Dawn’s age. How old is Dawn?

15Eunice

Fred

3

Dawn 3 3 3

?


Example #2ଷସ

of the sales from onions is as much as ଶଷ

of the sales from carrots. The sales from carrots is $240 more than the sales from onions. Find the total sales from the onions and carrots.

240

?

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O

C


Example #3

Abby had some sweets. She gave ଵ

of her sweets to Ben

and ଶହ

of the remainder to Cain. She had 12 sweets left. How many sweets did Abby have at first?

?

Ben

26

Cain 12


Example #4

Abby had some sweets. She gave ଵ

of her sweets to Ben

and ଷଵ

of the remainder to Cain. She had 49 sweets left. How many sweets did Abby have at first?

?

Ben

27

Cain 49


Example #5

Ray and Sean shared the cost of a present for their friend. Sean paid $73 and Ray paid $17 more than ଶ

ହof

the cost of the present. Find the cost of the present.

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73

Ray Sean

?

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Example #6

There are three boys in the Lee family. The ratio of the eldest boy’s age to that of the youngest is 4 : 1. The ratio of the middle boy’s age to that of the youngest is 2 : 1. The eldest boy is 4 years older than the middle boy. How old is the youngest boy?

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4Middle

Eldest

Youngest ?


Example #7

There are ଵଷ

as many P3 students as P4 students in a school. The ratio of the number of P5 students to that of P3 students is 4 : 1. There are 490 P4 and P5 students altogether. How many more P5 students than P3 students are there?

?

30

P4

P3

P5490


Example #8

The number of tourists who visited a town this year is 75% that of last year. There were 120 000 tourists last year. How many tourists visited the town this year?

This year

Last year

75 units

100 units

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120 000

?


Example #9

Alvin’s salary is 20% more than Barry’s salary.Álvin’s salary is $3600. Find Barry’s salary.

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Alvin

Barry

20 units

100 units

3600

?


Example #10

In February, the number of tourists who visited the zoo increased by 25% compared to January. In March, 60 000 tourists visited the zoo. This was a 40% decrease in the number of tourist compared to February. How many tourists visited the zoo in February?

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Jan

Feb

4 u 1 u

60 000

?

Mar 3 u


How?Hands-on practice with

drawing of models

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How?Home support for your child

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A Final Word

Common Model-drawing Pitfalls• Incorrect representation of the problem

sum• Incomplete representation of the

problem sum• Transfer error

• Missing equations• Missing units

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A Final Word

What Makes Model-drawing Difficult?• Knowledge Factors

– Linguistic 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

– Confidence– Perseverance– Motivation


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A Final Word

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A Final Word

Resources for Model-drawing• http://www.teach-kids-math-by-model-

method.com/• http://citeseerx.ist.psu.edu/viewdoc/download?

doi=10.1.1.555.5563&rep=rep1&type=pdf• Facebook group – “Maths Model Method –

Singapore”• iOS App - imath

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http://www.teach-kids-math-by-model-

http://citeseerx.ist.psu.edu/viewdoc/download?


Q & ATHANK YOU

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P5 Parents’ Seminar Mathematics Strategies for …...P5 Parents’ Seminar Mathematics Strategies...

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