P3 & P4 Parents’ Seminar Mathematics Strategies for Model ......P3 & P4 Parents’ Seminar Mathematics Strategies for Model Drawing 27 Feb 2016 1 Springdale Primary School Objectives

Springdale Primary School

P3 & P4 Parents’ Seminar

Mathematics

Strategies for Model Drawing

27 Feb 2016

1


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

2


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)

3


Curriculum Framework

4


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

5


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

6


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)

7


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

8


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.

9



• 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

10



• 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

11


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.

12


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.

13


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?

14


Types of Model

• Part-whole Model

• Comparison Model

• Before-after Model

…

• Modification of model

15


Part-Whole Model

Part Part

Whole

16


Part-Whole Model

Part

Part

Whole

17


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

?

18


Examples

2. 3 shirts and 1 dress cost $84.

3 shirts and 3 dresses cost $132.

Find the cost of a dress.

132

84

?

19


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

20


Comparison Model

Comparison

X

Y

21


Comparison Model

Comparison

X

Y

22


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

23


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

24


Examples

6. The sum of 2 numbers is 1 568.

The difference between them is 580.

What is the greater number?

580Big

Small1 568

?

25


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

26


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

27


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

?

28


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.

29


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

30


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

31


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

32


Hands-on Session

Now it is your turn. :)

33


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

34


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

35


A Final Word

Common Model-drawing Pitfalls

• Incorrect representation of the story sum

• Incomplete representation of the story

sum

• Transfer error

36


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

37


Q & A

THANK YOU

38

Documents

P3 & P4 Parents’ Seminar Mathematics Strategies for Model ......P3 & P4 Parents’ Seminar Mathematics Strategies for Model Drawing 27 Feb 2016 1 Springdale Primary School Objectives