P3 & P4 Parents’ Seminar Mathematics Strategies for Model Drawing 27 Feb 2016 Springdale Primary School 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 Springdale Primary School 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) Springdale Primary School 3 Curriculum Framework Springdale Primary School 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 – Springdale Primary School 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 Springdale Primary School 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) Springdale Primary School 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 Springdale Primary School 8
Mathematics Syllabus Primary 1 and 2 Primary 3 and 4 Primary 5 and 6 • Whole Number • Whole Number • Whole Number • Money, Measures • Money, Measures • Money, Measures & Measuration & Measuration & Measuration • Fractions • Fractions • Fractions • Decimals • Decimals • Ratio & Proportion • Percentage • The model method is one of the most frequently used problem-solving heuristics throughout primary school. Springdale Primary School 9 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 Springdale Primary School 10
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 Springdale Primary School 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. Springdale Primary School 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. Springdale Primary School 13 Procedure of Model Drawing Phase Action Questions WHOLE Read the � Have I read the whole whole problem sum? sum PART Read the sum � What do I know? line by line � 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 � How can I link up you have whatever I have drawn? written and � How can I solve the drawn problem? Springdale Primary School 14
Types of Model • Part-whole Model • Comparison Model • Before-after Model … • Modification of model Springdale Primary School 15 Part-Whole Model Part Part Whole Springdale Primary School 16
Part-Whole Model Part Whole Part Springdale Primary School 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 container milk milk container milk milk milk milk 2 200 ? Springdale Primary School 18
Examples 2. 3 shirts and 1 dress cost $84. 3 shirts and 3 dresses cost $132. Find the cost of a dress. 84 ? 132 Springdale Primary School 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? A B 49 64 A C B C 57 Springdale Primary School 20
Comparison Model X Y Comparison Springdale Primary School 21 Comparison Model X Y Comparison Springdale Primary School 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? ? 28 Aaron 4 84 Ben 4 Carl Springdale Primary School 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 60 Carl Springdale Primary School 24
Examples 6. The sum of 2 numbers is 1 568. The difference between them is 580. What is the greater number? ? Big 580 1 568 Small Springdale Primary School 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? 2 480 Big ? Small Springdale Primary School 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. 500 Potatoes ? Tomatoes Springdale Primary School 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 Springdale Primary School 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. Springdale Primary School 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? ? BEFORE Aaron Ben 72 AFTER Aaron Ben Springdale Primary School 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? BEFORE Aaron Ben ? AFTER 300 300 300 Aaron Ben 300 Springdale Primary School 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? BEFORE A ? B AFTER A 14 B Springdale Primary School 32
Hands-on Session Now it is your turn. :) Springdale Primary School 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 Springdale Primary School 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 Springdale Primary School 35 A Final Word Common Model-drawing Pitfalls • Incorrect representation of the story sum • Incomplete representation of the story sum • Transfer error Springdale Primary School 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 Springdale Primary School 37 Q & A THANK YOU Springdale Primary School 38
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