The abilities by end of Grade 5:
(Calculator is allowed unless otherwise stated.)
1 WHOLE NUMBERS
Numbers up to 10
million Include: • reading and writing numbers in numerals and in words,
• rounding off numbers to the nearest 1000.
Four operations
Include:
• multiplication and division by tens, hundreds and thousands
without using calculators,
• solving word problems involving the 4 operations,
• estimation of answers in calculations,
• checking reasonableness of answers.
Order of operations
Include: • combined operations involving the 4 operations,
• use of brackets.
2 FRACTIONS
Concept of fraction
as division Include: • association of a fraction with division,
• conversion between fractions and decimals.
Four operations
Include
• addition and subtraction of proper fractions without using
calculators,
• addition and subtraction of mixed numbers,
• multiplication of two proper fractions without using
calculators,
• multiplication of an improper fraction and a proper/improper
fraction,
• multiplication of a mixed number and a whole number,
• division of a proper fraction by a whole number without using
calculators,
• solving word problems involving the 4 operations.
Exclude:
• calculations involving more than 2 different denominators,
• multiplication of a mixed number by a proper fraction/improper
fraction/mixed number,
• division of an improper fraction/mixed number by a whole
number.
(Denominators of given fractions should not exceed 12, for
calculations without using calculators.)
3 DECIMALS
Four operations
Include:
• multiplication and division of decimals (up to 3 decimal places)
by tens, hundreds and thousands without using calculators,
• solving word problems involving the 4 operations,
• rounding off answers to a specified degree of accuracy,
• estimation of answers in calculations,
• checking reasonableness of answers.
Exclude multiplication and division by a decimal.
4 PERCENTAGE
Percentage
Include: • expressing a part of a whole as a percentage,
• use of the percentage symbol (%),
• writing fractions and decimals as percentages, and vice versa,
• finding a percentage part of a whole,
• solving up to 2-step word problems involving percentage,
• discount, GST and annual interest.
Exclude:
• expressing one quantity as a percentage of another, e.g. “A is
60% of B”.
• comparison of two quantities by percentage, e.g. “ A is 20%
more than B.”
5 RATIO
Ratio Include:
• interpretation of a : b and a : b : c, where a, b and c are whole
numbers,
• writing equivalent ratios,
• expressing a ratio in its simplest form,
• finding the ratio of two or three given quantities,
• finding the missing term in a pair of equivalent ratios,
• finding one quantity given the other quantity and their ratio,
• solving up to 2-step word problems involving ratio.
Exclude ratios involving fractions and decimals.
6 MEASUREMENT
Length, mass and
volume
Include:
• conversion of a measurement from a smaller unit to a larger
unit in decimal form, and vice versa,
∗ kilometres and metres
∗ metres and centimetres
∗ kilograms and grams
∗ litres and millilitres
Area of triangle
Include: • identifying the base of a triangle and its corresponding height,
• use of formula to calculate the area of a triangle.
Exclude finding the base/ height of a triangle given its area.
Volume of cube and
cuboid
Include:
• building solids with unit cubes,
• measurement of volume in cubic units,
• drawing cubes and cuboids on an isometric grid,
• measurement of volume in cubic centimetres (cm3)/ cubic
metres (m3),
• use of formula to calculate the volume of a cube/ cuboid,
• finding the volume of liquid in a rectangular tank,
• conversion between , ml and cm3,
• solving up to 3-step word problems involving the volume of a
cube/ cuboid.
Exclude conversion between cm3 and m3.
7 GEOMETRY
Angles Include use of the following properties to find unknown angles:
∗ angles on a straight line,
∗ angles at a point,
∗ vertically opposite angles.
Triangle
Include:
• identifying and naming the following types of triangles
∗ isosceles triangle,
∗ equilateral triangle,
∗ right-angled triangle,
• use of the property that the angle sum of a triangle is 180o,
• finding unknown angles,
• drawing a triangle from given dimensions using ruler, protractor
and set squares.
Exclude:
• geometrical construction where the use of compasses is
required,
• finding angles involving additional construction of lines,
• exterior angles.
Parallelogram,
rhombus and
trapezium
Include:
• identifying and naming parallelogram, rhombus and trapezium,
• properties of parallelogram, rhombus and trapezium,
• finding unknown angles,
• drawing a square/rectangle/parallelogram/rhombus/trapezium
from given dimensions using ruler, protractor and set squares.
Exclude:
• the term ‘diagonal’ and its related properties,
• geometrical construction where the use of compasses is
required,
• finding angles involving additional construction of lines.
8 DATA ANALYSIS
Average of a set of
data
Include:
• interpretation of average as "total amount ÷ number of items",
• calculation of the average number/quantity,
• finding the total amount given the average and the number of
items,
• solving word problems involving average.
Enriching your metacognitive experience
To develop the metacognitive awareness of students and to enrich the metacognitive experience:
• Expose students to general problem solving skills, thinking skills and
heuristics, and how these skills can be applied to solve problems.
• Encourage students to think aloud the strategies and methods they
use to solve particular problems.
• Provide students with problems that require planning (before solving)
and evaluation (after solving).
• Encourage students to seek alternative ways of solving the same
problem and to check the appropriateness and reasonableness of the
answer.
• Allow students to discuss how to solve a particular problem and to
explain the different methods that they use for solving the problem.
• Expose students to general problem solving skills, thinking skills and
heuristics, and how these skills can be applied to solve problems.
• Encourage students to think aloud the strategies and methods they
use to solve particular problems.
• Provide students with problems that require planning (before solving)
and evaluation (after solving).
• Encourage students to seek alternative ways of solving the same
problem and to check the appropriateness and reasonableness of the
answer.
• Allow students to discuss how to solve a particular problem and to
explain the different methods that they use for solving the problem.
Why Attitude is important in learning Math?
Attitudes refer to the affective aspects of mathematics learning such as:
• Beliefs about mathematics and its usefulness
• Interest and enjoyment in learning mathematics
• Appreciation of the beauty and power of mathematics
• Confidence in using mathematics
• Perseverance in solving a problem
• Beliefs about mathematics and its usefulness
• Interest and enjoyment in learning mathematics
• Appreciation of the beauty and power of mathematics
• Confidence in using mathematics
• Perseverance in solving a problem
Modelling
Mathematical modelling is the process of formulating and improving a mathematical model to represent and solve real-world problems.
Through mathematical modelling, students learn to use a variety of representations
of data, and to select and apply appropriate mathematical methods and tools in solving real-world problems.
Through mathematical modelling, students learn to use a variety of representations
of data, and to select and apply appropriate mathematical methods and tools in solving real-world problems.
Heuristics
. To give a representation,
e.g. draw a diagram, make a list, use equations
• To make a calculated guess,
e.g. guess and check, look for patterns, make suppositions
• To go through the process,
e.g. act it out, work backwards, before-after
• To change the problem,
e.g. restate the problem, simplify the problem, solve part of the
problem
e.g. draw a diagram, make a list, use equations
• To make a calculated guess,
e.g. guess and check, look for patterns, make suppositions
• To go through the process,
e.g. act it out, work backwards, before-after
• To change the problem,
e.g. restate the problem, simplify the problem, solve part of the
problem
Skills
Numerical calculation
Algebraic manipulation
Spatial visualisation
Data analysis
Measurement
Use of mathematical tools
Estimation
Algebraic manipulation
Spatial visualisation
Data analysis
Measurement
Use of mathematical tools
Estimation
Processes
Reasoning, communication and connections
Thinking skills and heuristics
Application and modelling
Thinking skills and heuristics
Application and modelling
Why Math is important?
In our real world, we can use the 5 inter-related components:-
concepts
attitudes
metacognition
processes
skills
CAMPS
in solving a wide range of situations that could be non-routine and open-ended.
concepts
attitudes
metacognition
processes
skills
CAMPS
in solving a wide range of situations that could be non-routine and open-ended.
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