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M1 Problem Solving

Heuristic approach (non-mechanical)

Understanding the problem statement

1. Define what is a heuristic approach

2. Identify and explain the problem statement

3. Explain ways to identify the problem statement

Discuss the following:

The meaning of heuristic approach

Polya’s 4-step heuristic to solve problems

The meaning of problem statement and ways to guide pupils to identify problem statement e.g. questioning

Develop understanding of heuristic approach in problem solving

In small groups, devise a problem-solving activity for primary school children. Then,

think of possible difficulties faced by primary school children when solving the problem, and

identify possible non –mechanical method to solve the problem

Group presentation

Write reflective log

Reading task:Burwood State College, Beginning To Tackle Real Problems – 2nd Pilot VersionPg 1-60

Deakin University, Problem Solving and Mathematical Modeling - Study Guidepg 1-2

Excellence and enjoyment : L&T in the primary years: Primary National Strategypg 8 -21

Give course pro forma, weekly outline & assessment guidelines to students

Suggested Readings:

Heinemann, Word Problems 4Pg 5-48

Kaye Stacey and Susie Groves: Strategies for Problem Solving, Objective Learning Materials pg.19 -26

Alfred S. Posamentier and Stephen Krulik: Problem-Solving Strategies for Efficient and Elegant Solutions: A Resource for the Mathematics Teacher

M2 Problem Solving

Discussion of possible analytical tools or strategies to solve problems

Assessment and reasonableness of solution

1. Use strategies and tools to solve problems

2. Assess the solution by reasoning

3. Assess the appropriateness of the solution

Solve Activity 1.1 (Deakin)


various strategies and tools to solve problems, and

justifications for choosing a desired strategy.

Do Tutorial 1.1 in groups (refer attached file)

Group presentation for Tutorial 1.1

Elicit students’ opinions on the reasonableness of their solutions


Reading task:Excellence enjoyment : L&T in primary years pg 30 -37

Heinemann, Word Problems 4Pg 5-48

Suggested Readings:

Deakin University, Problem Solving and Mathematical Modeling – Study Guide pg 1-44,73-95

Problem-Solving Toolkit Years 1 and 2/ P2 and P3

Burwood State College, Beginning To Tackle Real Problems – 2nd Pilot VersionPg 1-60

M3 Problem Solving

Further analysis

Real life examples: practical activities

1. Use the strategies to solve real life problems

Solve Activity 1.2 (Deakin)

Discuss the following: examples of real-life

problems, application of problem-

solving skills in real life, and




Reading task:Excellence and enjoyment : L&T in the primary years: Primary National Strategy pg 8 -21

Suggested Readings:

Stacey & Groves: Strategies for Problem Solving, Objective Learning Materials pg.19 -26

Alfred, Posamentier and Krulik: Problem-Solving Strategies for Efficient and Elegant Solutions: A Resource for the Mathematics

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RANCANGAN PENGAJARAN DAN PEMBELAJARAN MINGGUAN

PROGRAM: ____________________________________________________________________________ SEMESTER: ______ TAHUN: ______

Kursus: _____________________________________________________________________________________ Kod: ____________ Kredit: ____________

Program Ijazah Sarjana Muda Perguruan (PISMP) dengan Kepujian 2 1

WAJ3105 2 (2 + 0)Numerical Literacy

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creative problem solving in real life.

Teacher

M4 Operation and Computation

Means of performing calculationpencil and papercalculators and computersmental computationmanipulative materials

1. Discuss various methods of calculation

Discuss the standard of numerical literacy (numeracy)

Creative use of the following computational approaches to perform basic arithmetic operations: pencil-and-paper

algorithm. computational tools such

as abacus, electronic calculator and computer,

mental computation, physical manipulative

such as fingers, counters etc.

Do Tutorial 2.1 in groups(refer attached file)



Reading task:

The National Numeracy Strategy pg 4-8

Suggested Reading:Course reader pg 103 & 104

The National Numeracy Strategy pg 13


Appropriate and inappropriate uses of calculators and computers

1. Compare the usage of calculators and computers for calculation


the roles of calculators and computers in the teaching and learning of primary school subjects,

advantages and disadvantages of using calculator and computer in the teaching and learning of primary school subjects.




Surf the Internet to find ways of using calculators and computers in the teaching and learning of primary school mathematics

Suggested reading:The National Numeracy Strategypg. 8

The National Numeracy Strategypg. 9

Primary Mathematics : Teaching Theory and Practicepg. 56 & 57


Appropriateness :rough estimation or exact answers

1. Estimate numbers appropriately


The roles of estimation in computation.

Real-life situations that required exact answer for




Surf the Internet to look for information on application of estimation in real life.

Suggested Reading:Primary Mathematics : Teaching Theory and Practicepg. 39 & 40

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computation. Real-life situations that

only required rough estimate of answer for computation.

Group work:- show an example of the

mistakes in computation due to lack of understanding in the place value.

M7 Measurement

Intuitive notions of mathematical concepts:Practical activities with varied materialsDirect experience

Unconventional instruments and non standard-units e.g feet and hands

1. Carrying out practical activities to measure

2. Using instruments like hands and feet to measure


The concepts of measurement of basic physical quantities such as length, mass and volume of liquid.

The concept standard and non-standard units of measurement

The roles of estimation in measuring physical quantities

Carry out a practical activity using any non-standard units for length, mass, or volume of liquid e.g. Measure lengths based on body parts



Discuss Short Coursework 1


Surf the Internet to look for information on the history of measurement units for length, mass and volume of liquid.

Share information found from the Internet among course mates.

Suggested Reading:The National Numeracy StrategySupplement of examples :Year 1,2 &3 (vol 5) pg 90 -93Focus on measurement of length

Primary Mathematics QTS pg 52-53

M8 Measurement

Metric units and conversion

1. Convert measurements into metric units


Imperial and metric units The relationship between

the commonly used metric units

Basic measurement units for length, mass and volume of liquid and the use of prefixes in metric units

Wrong use of abbreviations for some common measuring units such as: M instead of m;

Do Tutorial 3.2 in groups(refer attached file)



Surf the Internet to find information on the historical development of metric units for length, mass and volume of liquid.

Share information found from the Internet among course mates.

Short Coursework 1: (30%)

Create a brochure/ posterWeek : 7, 8, 9Submission date: End of week 9

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KG instead of kg, L instead of l etc.

M9 Measurement

Contextual teaching: Taking measurement to gather data needed to solve problem in daily life

1. Gather data to help them solve problems in daily life

In small groups, students are required to:

identify a problem in real life that might be solved using certain measurement data

discuss ways of collecting the measurement data required to solve the problem

develop a plan to collect the measurement data

Group presentation for problem-solving task.


Problem-Solving Task:Implement the plan for collection of measurement dataUse the measurement data to develop a solution for the real-life problem.

M10 Spatial Sense

2-D and 3-D: Plane and solid objects

To construct 3-D solids

1. Identify 2D shapes of plane geometry like polygon, triangles quadrilaterals, etc

2. List properties of objects in 3D solids

3. Use the vocabulary associated with 3D solids

4. Use manipulative materials to investigate the properties of 3D solids

5. Relate shapes and solids in the environment

Discuss the following: Existence of various 3-D

solids and 3-D shapes in the environment.

Practical activity: Examine models of

various 3-D solids such as cube, cuboids, prisms, pyramid, cylinders, cone, hemi-sphere, sphere)

List properties of various 3-D solids

Identify various 2-D shapes from 3-D solids

Construct various 3-D solids from nets or build skeleton of 3-D shapes from match sticks and plasticine.

Group presentation of ISL practical task (W11) Do Tutorial 4.1 in groups (refer attached file)



Practical Task:In small groups, identify and collect examples of 2-D shapes and 3-D solids that exist in the environment.

Short Coursework 2 (Part I) : 2D Tessellation

Short Coursework 2 (Part I)(15 % = 15 marks)Create tessellation using 2D shapesWeek : 11Submission date : W12

M11 Spatial Sense

1. Construct 2D and 3D objects

Discussion the following: Do Tutorial 4.2 in groups (refer attached file)

Write reflective log Encourage the use of software such as GSP to construct 2-D

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Availability to handle, measure and use in the construction of 3D solids

To construct 2-D shapes from simple materials or with conventional instruments

from simple materials

Basic measurable properties of polygons such as side, perimeter, area and angle.

Basic measurable properties of 3-D solids such as side, surface area, volume and angle.

Practical activity: Construction of 2-D shapes using conventional instruments such as ruler, set squares and compass. Construction of 2-D

shapes using simple materials such as a string and a thumb tack to construct a circle; a string and two thumb tacks to construct an ellipse


Short Coursework 2 (Part II) : Construction of polyhedral

shapes

Short Coursework 2 (Part II):(15 % = 15 marks)Create polyhedral Week : 12Submission date : W13

M12 Spatial Sense

Draw spatial concepts and relationships from activities

1. Use geometry in daily life

2. Use the language and vocabulary related to geometry


Definition of Spatial Sense

Why children should learn geometry?

The importance of spatial sense in everyday life

Van Hiele Model of Learning Geometry- Visualization- Analysis- Informal Deduction- Deductive- Rigor

(Focussing on the first 3 levels of Van Hiele’s Model)



Write reflective logReaders :

Reading task:Guiding children learn Mathematic pg 353-397

Suggested reading:Curriculum Specification for Primary School Mathematics – 3-D and 2-D shapes

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M13 Data Analysis and Interpretation

Read and interpret quantitative information in tables, charts or graphs

Instructions on reading/ Interpretation of data

1. Collect data 2. Tabulate data

3. Use charts and graphs to present data


The process of collecting quantitative data

Tabulation of data Representation of data

using appropriate graphs such as pictograph, pie chart, bar graph and line graph.

Interpretation of data- Deceptions in visual displays of data

Group presentation for practical task in ISL (W14)


Practical task:In groups, students collect one type of data from two different groups of students and represent the data using appropriate graph.Justify the choice of graph used.

Suggested reading:The National Numeracy Strategypg 114 – 115


Statistics: collection, analysis and interpretation of numerical data

Critically examine statistics given

1. Using statistics and ICT to analyse and interprete data.


The use of central-tendency measures such as mean, median and mod to describe and compare data.

The use of dispersion measures such as standard deviation to describe and compare data.

The use of frequency polygon to study trend in data.

Based on data from practical task in ISL (W14), find the mean, mod, median and standard deviation for the two sets of data.

Describe and compare the two sets of data based on mean, mod, median and standard deviation.


Reading task:The National Numeracy Strategy-Department for Education and Employment.UKpg 117

Encourage the use of graphing calculator and computer software such as MsExcel and SPSS in finding the statistics.


Exploration of events related to chances (intuitive idea of probability)

1. explore events using probabillity

Practical activity:In groups, students perform probability experiments such as (a) flipping a coin, (b) tossing a die, (c) throwing a thumb tack etc

Discuss the following: experimental probability theoretical probability the use of ratio in




Reading task:The National Numeracy Strategy-Department for Education and Employment.UKpg 113

Suggested reading:Middle Grades Math Tools For Success (Practice Hall Needham) Page 480 - 488

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theoretical probability

M16 Revision

M17 Revision

M18 Examination

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