MATHEMATICAL LITERACY,
MATHEMATICS
AND MATHEMATICAL
SCIENCES
DEFINITION
Mathematics is the construction
of knowledge that deals with qualitative and quantitative relationships
of space and time. It is a human activity that deals with patterns, problem-solving,
logical thinking, etc., in an attempt to understand the world and make
use of that understanding. This understanding is expressed, developed and
contested through language, symbols and social interaction.
RATIONALE
Mathematical literacy, mathematics
and the mathematical sciences as domains of knowledge are significant cultural
achievements of humanity. They have both utilitarian and intrinsic value.
All people have a right of access to these domains and their benefits.
These domains provide powerful numeric, spatial, temporal, symbolic, communicative
and other conceptual tools, skills, knowledge, attitudes and values to:
- analyse;
- make and justify critical decisions;
and
- take transformative action,
thereby empowering people to:
- work towards the reconstruction
and development of South African society;
- develop equal opportunities and
choice;
- contribute towards the widest development
of the society’s cultures;
- participate in their communities
and in the South African society as a whole in a democratic, non-racist
and non-sexist manner;
- act responsibly in protecting the
total environment;
- interact in a rapidly-changing
technological global context;
- derive pleasure and satisfaction
through the pursuit of rigour, elegance and the analysis of patterns and
relationships;
- understand the contested nature
of mathematical knowledge; and
- engage with political organisational
systems and socio-economic relations.
SPECIFIC OUTCOMES
- Demonstrate understanding about
ways of working with numbers.
The development of the number concept
is an integral part of mathematics. All learners have an intuitive understanding
of the number concept. This outcome intends to extend that understanding.
Its aim is to enable students to know the history of the development of
numbers and number systems and to use numbers as part of their tool kits
when working with other outcomes. Solving problems and handling information,
attitudes and awareness may depend crucially on a confident understanding
and use of number.
- Manipulate number patterns in
different ways.
Mathematics involves observing,
representing and investigating patterns in social and physical phenomena
and within mathematical relationships. Learners have a natural interest
in investigating relationships and making connections between phenomena.
Mathematics offers a way of thinking, of structuring, organising and making
sense of the world.
- Demonstrate understanding of
the historical development of mathematics in various social and cultural
contexts.
Mathematics is a human activity.
All peoples of the world have contributed to the development of mathematics.
The view that mathematics is a European product must be challenged. Learners
must be able to understand the historical background of their communities’
use of mathematics.
- Critically analyse how mathematical
relationships are used in social, political and economic relations.
Mathematics is used as an instrument
to express ideas from a wide range of other fields. The use of mathematics
in these fields often creates problems. This outcome aims to foster a critical
outlook to enable learners to engage with issues that concern their lives
individually, in their communities and beyond. A critical mathematics curriculum
should develop critical thinking about how social inequalities, particularly
concerning race, gender and class, are created and perpetuated.
- Measure with competence and
confidence in a variety of contexts.
Measurement in mathematics is a
skill for universal communication. People measure physical attributes,
andestimate and develop familiarity with time. The aim is to familiarise
learners with appropriate skills of measurement, relevant units used, and
issues of accuracy.
- Use data from various contexts
to make informed judgements.
In this age of rapid information
expansion and technology, the ability to manage data and information is
an indispensable skill for every citizen. There is an ever-increasing need
to understand how information is processed and translated into useable
knowledge. Learners should acquire these skills for critical encounter
with information and to make informed decisions.
- Describe and represent experiences
with shape, space, time and motion, using all available senses.
Mathematics enhances and helps to
formalise the ability to grasp, visualise and represent the space in which
we live. In the real world, space and shape do not exist in isolation from
motion and time. Learners should be able to display an understanding of
spatial sense and motion in time.
- Analyse natural forms, cultural
products and processes as representations of shape, space, and time.
The mathematics forms, relationships
and processes embedded in the natural world and in aesthetic representations
are often unrecognised or suppressed. Learners should have access to that
mathematical knowledge which aims to unravel, critically analyse and make
sense of these forms, relationships and processes.
- Use mathematical language to
communicate mathematical ideas, concepts, generalisations and thought processes.
Mathematics is a language that uses
notations, symbols, terminology, conventions, models and expressions to
process and communicate information. Algebra is the branch of mathematics
where this language is mostly used. Learners' use of this language will
be developed.
- Use various logical processes
to formulate, test and justify conjectures.
Reasoning is fundamental to mathematical
activity. Active learners question, examine, conjecture and experiment.
Mathematics programmes should provide opportunities for learners to develop
and employ their reasoning skills. Learners need varied experiences to
construct convincing arguments in problem settings and to evaluate the
arguments of others.
1. Demonstrate understanding about ways of
working with numbers
The development of number concept is an integral
part of mathematics. All learners have an intuitive understanding of the
number concept. This outcome intends to extend that understanding. Its
aim is to enable students to know the history of the development of numbers
and number systems and to use numbers as part of their tool kits when working
with other outcomes. Solving problems, handling information, attitudes
and awareness may depend crucially on a confident understanding and use
of number.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of use of
heuristics to understand number concept |
1.1 Use personal experiences
to show the significance of number
1.2 Express numbers in words and symbols |
| 2. Evidence of knowledge
of number history |
2.1 Understand counting
as an historical activity
2.2 Show knowledge of the history of counting in their own communities,
history of Roman numerals and the history of Arabic numerals
2.3 Understand importance of place value |
| 3. Estimation as a skill |
3.1 Estimate lengths,
heights, volume, mass and time
3.2 Use calculators to check |
| 4. Performance of basic
operations |
4.1 Add and subtract
positive whole numbers
4.2 Multiply and divide positive whole numbers
4.3 Do simple mental calculations |
| 5. Knowledge of fractions |
5.1 Share and divide
as an introduction to fractions
5.2 Use decimal fractions and place value
5.3 Do operations on money |
| 6. Solving of real life
and simulated problems |
6.1 Solve real life
or simulated problems |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of use of
heuristics to understand number concept |
1.1 Demonstrate the
use of a personal set of referents for large and small numbers |
| 2. Evidence of knowledge
of number history |
2.1 Understand counting
as an historical activity
2.2 Show knowledge of the history of counting in their own communities,
history of Roman numerals, history of Arabic numerals
2.3 Understand the importance of place value |
| 3. Evidence of estimation
approaches |
3.1 Estimate simple
multiplication
3.2 Estimate square roots of numbers up to a hundred |
| 4. Performance of basic
operations |
4.1 Add, subtract, multiply
and divide positive whole numbers
4.2 Add and subtract fractions
4.3 Perform operations on decimal fractions and money
4.4 Perform operations mentally
4.5 Use available technologies |
| 5. Solving of real life
and simulated problems |
5.1 Solve real life
or simulated problems |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of some
knowledge of rational and irrational numbers, including the properties
of rational numbers |
1.1 Demonstrate knowledge
of the difference between rational and irrational numbers and the idea
of recurring decimals
1.2 Commit to memory the decimal equivalents of commonly used fractions
1.3 Use and understand negative numbers in context
1.4 Commit to memory the approximate decimal equivalents of 
and 
1.5 Illustrate properties of rational numbers |
| 2. Evidence of knowledge
of number history |
2.1 Show knowledge of
the history of counting in their own communities, history of Roman numerals,
history of Arabic numerals
2.2 Show knowledge of the activity of mathematics and mathematicians from
Africa, Asia, Middle East and South America |
| 3. Evidence of estimation
approaches |
3.1 Recognise the difference
between exact and approximate values
3.2 Estimate multiplication of rational numbers
3.3 Estimate square and cube roots of numbers
3.4 Estimation of heights and distances using a variety of approaches and
technologies
3.5 Use a variety of mental maths techniques and check the reasonableness
of results |
| 4. Performance of operations
accurately |
4.1 Use rules of order
of operations
4.2 Recognise significant digits
4.3 Show understanding of standard index form
4.4 Work with exponents, developing laws of exponents from numerical cases
4.5 Use a calculator to perform a sequence of numerical operations
4.6 Substitute numbers into formulae |
| 5. Evidence of knowledge
of percent, rate and ratio |
5.1 Use algebraic techniques
to solve problems involving percent, rate, and ratio
5.2 Solve problems involving proportions |
| 6. Solving of real life
and simulated problems |
6.1 Perform basic financial
computations
6.2 Perform general tax and sales tax computations
6.3 Pick and analyse authentic problems from newspapers and journals
6.4 Critically analyse at least two investment scenarios
6.5 Pick and analyse at least one local developmental problem |
| 7. Demonstration of
skills of investigative approaches within mathematics |
7.1 Investigate open-ended
questions
7.2 Ask and respond to questions like "what would happen if ...?"
7.3 Apply approaches that demonstrate reflective capabilities |
2. Manipulate number patterns in different
ways
Mathematics involves observing, representing and
investigating patterns in social and physical phenomena and within mathematical
relationships. Learners have a natural interest in investigating relationships
and making connections between phenomena. Mathematics offers ways of thinking,
structuring, organising and making sense of the world.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Identification of
the use of numbers for various purposes |
1.1 Give own understanding
of number manipulation from personal experiences
1.2 Show link between patterning and repetition
1.3 Identify, repeat and continue patterns of sounds, body movements, body
positions, art, music and stories |
| 2. Evidence that number
patterns and geometric patterns are recognised and identified using a variety
of media |
2.1 Identify and/or
copy simple number patterns in rows, columns and diagonals
2.2 Show a knowledge of skip counting starting at any number
2.3 Identify and/or copy linear patterns using two and three dimensional
shapes
2.4 Identify artistic patterns in South African cultures |
| 3. Completion and generation
of patterns |
3.1 Arrange numbers
in a logical sequence
3.2 Identify missing terms of number and geometric patterns
3.3 Extend or create linear patterns using 2D and/or 3D
3.4 Use concrete objects to extend, create and depict tiling or grid patterns
3.5 Generate step patterns |
| 4. Exploration of patterns
in abstract and natural contexts using mathematical processes |
4.1 Explore tessellation
4.2 Use plane shapes and solid objects to investigate step patterns and
symmetrically growing or shrinking patterns
4.3 Use inverses
4.4 Use available technology to generate patterns |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Identification of
the use of numbers for various purposes |
1.1 Demonstrate understanding
and biases in manipulating numbers from personal experiences, media and
other social groups.
1.2 Show an understanding of different beliefs about certain numbers |
| Evidence that number
patterns and geometric patterns are recognised and identified using a variety
of media |
2.1 Identify common
number patterns from experience, including skip counting
2.2 Recognise and work with arithmetic sequences
2.3 Recognise geometric patterns in 2D and 3D
2.4 Identify artistic patterns in South African cultures |
| 3. Completion and generation
of patterns |
3.1 Arrange numbers
in a logical sequence
3.2 Identify missing terms of number and geometric patterns
3.3 Create patterns growing concentrically or from a base
3.4 Show understanding of simple increase and decrease
3.5 Show understanding of and generate prime numbers |
| 4. Exploration of patterns
in abstract and natural contexts using mathematical processes |
4.1 Explore tessellation
and transformations
4.2 Express generalisations of patterns and develop formulae
4.3 Use inverses
4.4 Use available technologies to generate patterns
4.5 Identify patterns in nature |
| 5. Evidence of the use
of number patterns to address real and simulated problems |
5.1 Use sequences and
series to model real and simulated problems
5.2 Test consistency of solution
5.3 Identify equity issues of race, class and gender that arise from the
manipulation of numbers in a social context |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Identification of
the use of numbers for various purposes |
1.1 Demonstrate understanding
of and biases in manipulating numbers from personal experiences, media
and other social groups.
1.2 Show an understanding of different beliefs about certain numbers |
| 2. Evidence that number
patterns and geometric patterns are recognised and identified using a variety
of media |
2.1 Show common number
patterns from experience
2.2 Work with arithmetic sequence
2.3 Work with geometric progression
2.4 Generate geometric patterns in 2D and 3D
2.5 Identify artistic patterns in various cultures, at least two South
African, and two other |
| 3. Completion and generation
of patterns |
3.1 Arrange numbers
in a logical sequence
3.2 Complete number sequences and geometric patterns
3.3 Generate linear patterns, y = mx + c
3.4 Show understanding of simple increase and decrease
3.5 Work with compound increase and decrease |
| 4. Exploration of patterns
in abstract and natural contexts using mathematical processes |
4.1 Explore and understand
tessellations and transformations
4.2 Derive processes for a general rule
4.3 Show understanding of inverses
4.4 Use available technologies
4.5 Identify patterns in nature |
| 5. Representation of
number patterns using mathematical symbols |
5.1 Use terminology,
formulae and graphics to represent patterns, tables and sequences
|
| 6. Evidence of the use
of number patterns to address real and simulated problems |
6.1 Use of sequences
and series to model and interpret findings
6.2 Test consistency of solution
6.3 Identify equity issues of race, class and gender that arise from the
manipulation of numbers in a social context |
3. Demonstrate an understanding of the historical
development of mathematics in various social and cultural contexts
Mathematics is a human activity. All peoples of
the world have contributed to the development of mathematics. The view
that mathematics is a European product must be challenged. Learners must
be able to understand the historical background of their communities’ use
of mathematics.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence that mathematics
is understood as a human activity |
1.1 Demonstrate counting
and measurement in everyday life
1.2 Illustrate at least two mathematical activities at home
1.3 Show the link between mathematics and technology |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Understanding of
mathematics as a human activity |
1.1 Show knowledge of
counting styles in different cultures
1.2 Examine the history of measurement and the development of geometry
1.3 Show the link between mathematics and technology |
| 2. Knowledge of contestations
and Eurocentrism in the development of mathematics |
2.1 Analyse racial issues
and mathematics.
2.2 Demonstrate knowledge of ways of precolonial counting in Africa
2.3 Show development of mathematics in the middle east, Asia, Africa and
South America |
| 3. Knowledge of number
bases |
3.1 Work with other
number bases besides base ten |
| 4. Understanding of
the use of technology |
4.1 Show advantages
and disadvantages of technology
4.2 Use available technologies |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Understanding of
mathematics as a human activity |
1.1 Show knowledge of
counting styles in different cultures
1.2 Examine the history of measurement and the development of geometry
1.3 Show the link between mathematics and technology |
| 2.Knowledge of contestations
and Eurocentrism in the development of mathematics |
2.1 Critically analyse
the role of mathematics as a tool for differentiation
2.2 Critically analyse mathematics as a predominantly European activity
2.3 Analyse mathematical ideas from own culture
2.4 Show development of mathematics in the middle east, Asia, Africa and
South America |
| 3. Knowledge of number
bases |
3.1 Use number bases
other than base ten |
| 4. Understanding of
the use of technology |
4.1 Show advantages
and disadvantages of technology
4.2 Use available technologies |
4. Critically analyse how mathematical relationships
are used in social, political and economic relations
Mathematics is used as an instrument to express
ideas from a wide range of other fields. The use of mathematics in these
fields often creates problems. This outcome aims to foster a critical outlook
to enable learners to engage with issues that concern their lives individually,
in their communities and beyond. A critical mathematics curriculum should
develop critical thinking about how social inequalities, particularly concerning
race, gender and class, are created and perpetuated.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of knowledge
of the use of mathematics in the economy |
1.1 Demonstrate understanding
of the use of mathematics in shopping
1.2 Show understanding of price increases |
| 2. Evidence of the understanding
of budget |
2.1 Show understanding
of family budgeting
2.2 Show understanding of saving. |
| 3. Demonstrate knowledge
of the use of mathematics in determining location |
3.1 Mapping of immediate
locality
3.2 Word descriptions of directions and local transport |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of knowledge
of the use of mathematics in the economy |
1.1 Demonstrate understanding
of the use of mathematics in shopping
1.2 Show understanding of price increases |
| 2. Evidence of the understanding
of budget |
2.1 Manage family budgeting
2.2 Show importance of budget control |
| 3. Critical understanding
of mathematics use in the media |
3.1 Analyse graphical
representations used in newspapers and magazines |
| 4. Demonstrate knowledge
of the use of mathematics in determining location |
4.1 Draw a map of immediate
locality
4.2 Read maps and street finders |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of knowledge
of mathematical relationships in the workplace |
1.1 Understand critical
link between percentages and salary increases
1.2 Understand productivity as a ratio |
| 2. Evidence of knowledge
of mathematical relationships in the economy |
2.1 Demonstrate knowledge
of budgeting
2.2 Show understanding of taxes, rent and rates
2.3 Demonstrate the use and importance of finance charges and investments
2.4 Demonstrate importance of social service charges, pensions, medical
aid, insurance |
| 3. Evidence of the links
and concepts used in mathematics and fiscal policy |
3.1 Analyse income distribution
in South Africa
3.2 Analyse fluctuations of the value of a rand and purchase power |
| 4. Evidence of knowledge
of the use of mathematics in politics |
4.1 Compare the financing
of education under apartheid and after 1994
4.2 Compare population census under apartheid and after 1994 |
| 5. Critical understanding
of mathematics use in the media |
5.1 Recognise types
of graphs used in newspapers and journals
5.2 Critically analyse information from the media
5.3 Analyse the use and effect of advertisements in society |
| 6. Demonstration of
knowledge of the use of mathematics in determining location |
6.1 Work with mapping
scales
6.2 Read maps, from street finder to atlas maps |
5. Measure with competence and confidence in
a variety of contexts
Measurement in mathematics is a skill for universal
communication. People measure physical attributes, and estimate and develop
familiarity with time. The aim is to familiarise learners with appropriate
skills of measurement, relevant units used, and issues of accuracy.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of knowledge
of the importance of measurements |
1.1 Show knowledge of
measurements from experience |
| 2. Evidence of knowledge
of standards |
2.1 Show some knowledge
of non-standard forms of measurement
2.2 Demonstrate understanding of reasons for standardisation
2.3 Demonstrate knowledge of SI Units |
| 3. Evidence of knowledge
of the concepts used in measurement |
3.1 Understand concepts
used in the measurement of space in 2D and 3D
3.2 Comparison of masses of objects.
3.3 Measure personal mass
3.4 Understand money as a unit of measurement |
| 4. Evidence of knowledge
of the concept of time |
4.1 Use language to
express times of the day
4.2 Show knowledge of how to read time |
| 5. Evidence of the knowledge
of the concept of temperature |
5.1 Explain difference
between hot and cold
5.2 Explain dangers of very high or very low temperatures
5.3 Give examples of temperature related equipment at home, their dangers
and uses |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of knowledge
of the importance of measurements |
1.1 Demonstrate knowledge
of measurements from experience
1.2 Measure lengths using simple instruments
1.3 Use measurements in various contexts, including sizes of clothes and
shoes |
| 2. Evidence of knowledge
of standards |
2.1 Understand and use
of units of measurement
2.2 Define relationship between millimetres, centimetres, metres and kilometres
2.3 Convert between units of length |
| 3. Evidence of knowledge
of working with concepts and units of measurement |
3.1 Estimate distances
using scale diagrams and maps
3.2 Develop and use formulae in measurements in 2D and 3D |
| 4. Evidence of knowledge
of working with mass |
4.1 Compare masses of
objects.
4.2 Demonstrate that objects of same size can have different masses
4.3 Use standard units of measurement |
| 5. Evidence of knowledge
of working with time |
5.1 Read and understand
time to tenths of a second
5.2 Understand and use the twenty-four hour clock
5.3 Describe and convert between seconds, minutes, hours, days, weeks,
months and years
5.4 Describe a leap year |
| 6. Evidence of knowledge
of working with temperature |
6.1 Use different thermometers
6.2 Work with different units of measurement |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of understanding
of error |
1.1 State at least two
situations that result in error in measurement |
| 2. Evidence of knowledge
of working with concepts and units of measurement |
2.1 Apply formulae use
in measurements of regular polygons and polyhedra
2.2 Calculation of areas of regular and irregular figures using decomposition
and estimation
2.3 Identification, measurement of and use of  ,
including the circumference and area of circles.
2.4 Understanding and calculation of surface area
2.5 Calculation of volume and mass of an object
2.6 Express volumes in millilitres and litres
2.7 Comparison of masses of objects.
2.8 Explain the difference between mass and weight |
| 3. Evidence of knowledge
of working with time |
3.1 Read and understand
time zones |
| 4. Evidence of knowledge
of working with temperature |
4.1 Use different thermometers
4.2 Convert between Celsius, Fahrenheit and Kelvin scales |
| 5. Evidence of knowledge
of relationships between various units used commonly in science |
5.1 Understand difference
between distance and displacement
5.2 Understand difference between speed and velocity
5.3 Understand relationship between volume and density |
6. Use data from various contexts to
make informed judgements
In this technological age of rapid information
expansion, the ability to manage data and information is an indispensable
skill for every citizen. There is an ever-increasing need to understand
how information is processed and translated into usable knowledge. Learners
should acquire these skills for critical encounter with information and
to make informed decisions.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Identification of
situations for investigation |
1.1 Identify situations
for data collection |
| 2. Collection of data |
2.1 Choose methods of
data collection
2.2 Use interviews and sampling
2.3 Use technology |
| 3. Organisation of data |
3.1 List and arrange
data in a logical order
3.2 Sort relevant data
3.3 Group data |
| 4. Application of statistical
tools |
4.1 Choose relevant
method
4.2 Show understanding of averages, variance, frequency |
| 5. Display of data |
5.1 Draw summary
5.2 Represent data using graphs, charts, tables, text
5.3 Use available technologies |
| 6. Communication of
findings |
6.1 Show understanding
of use of simple and statistical language |
| 7. Critical evaluation
of findings |
7.1 Explain meanings
of information
7.2 Analyse validity
7.3 Analyse the impact of results
7.4 Make projections over time |
| 8. Evidence of knowledge
of ways of counting |
8.1 Show strategies
for choosing
8.2 Demonstrate knowledge of the idea of chance. |
| 9. Understanding of
the concept of probability |
9.1 Make predictions
9.2 Use to address real or simulated problems |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Identification situations
for investigation |
1.1 Identify situations
for data collection |
| 2. Collection of data |
2.1 Choose an appropriate
method
2.2 Demonstrate various methods for interviewing and sampling
2.3 Use available technologies in collecting data |
| 3. Organisation of data |
3.1 Arrange in a logical
order, listing
3.2 Sort, sequence and classify data |
| 4. Application of statistical
tools |
4.1 Use and understand
averages, variance and frequency |
| 5. Display of data |
5.1 Summarise and display
data using graphs, charts, tables and text
5.2 Use available technologies to display data |
| 6. Communication of
findings |
6.1 Use ordinary and
statistical language |
| 7. Critical evaluation |
7.1 Explain meanings
of information
7.2 Analyse validity of information
7.3 Analyse the impact of results
7.4 Give projections over time |
| 8. Evidence of knowledge
of ways of counting |
8.1 Show strategies
for choosing
8.2 Demonstrate knowledge of the idea of chance |
| 9. Understanding of
the concept of probability |
9.1 Make predictions
9.2 Use probability to address real or simulated problems |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Identification situations
for investigation |
1.1 Identify situations
for data collection |
| 2. Collection of data |
2.1 Choose an appropriate
method
2.2 Demonstrate various methods for interviewing and sampling
2.3 Use available technologies in collecting data |
| 3. Organisation of data |
3.1 Arrange in a logical
order, listing
3.2 Sort, sequence and classify data |
| 4. Application of statistical
tools |
4.1 Use and understand
averages, variance and frequency |
| Display of data |
5.1 Summarise and display
data using graphs, charts, tables and text
5.2 Use available technologies to display data. |
| 6. Communication of
findings |
6.1 Use ordinary and
statistical language |
| 7. Critical evaluation |
7.1 Explain meanings
of information
7.2 Analyse validity of information
7.3 Analyse the impact of results
7.4 Give projections over time |
| 8. Evidence of knowledge
of ways of counting |
8.1 Show strategies
for choosing
8.2 Demonstrate knowledge of the idea of chance |
| 9. Understanding of
the concept of probability |
9.1 Make predictions
9.2 Use probability to address real or simulated problems |
7. Describe and represent experiences with
shape, space, time and motion,using all available senses
Mathematics enhances and helps to formalise the
ability to grasp, visualise and represent the space in which we live. In
the real world, space and shape do not exist in isolation from motion and
time. Learners should be able to display an understanding of spatial sense
and motion in time.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Description of the
position of an object in space |
1.1 Represent objects
in various forms of Geometry
1.2 Show links between Algebra and Geometry |
| 2. Descriptions of changes
in shape of an object |
2.1 Demonstrate movement
of points with time an irrelevant variable
2.2 Transform and tessellate shapes |
| 3. Descriptions of orientation
of an object |
3.1 Show understanding
of the concept of point of reference in 2D and 3D
3.2 Show understanding of perceptions by an observer from different reference
points
3.3 Work with projections
3.4 Use available technologies in simulations |
| 4. Demonstrate an understanding
of the interconnectedness between shape, space and time. |
4.1 Show the effect
of movement and shape
4.2 Demonstrate an understanding of changes of perceptions of space and
shape though different media.
4.3 Visualise and represent objects from various spatial orientations |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Description of the
position of an object in space |
1.1 Represent objects
in various forms of Geometry
1.2 Show links between Algebra and Geometry |
| 2. Descriptions of changes
in shape of an object |
2.1 Demonstrate movement
of points with time an irrelevant variable
2.2 Transform and tessellate shapes |
| 3. Descriptions of orientation
of an object |
3.1 Show understanding
of the concept of point of reference in 2D and 3D
3.2 Show understanding of perceptions by an observer from different reference
points
3.3 Work with projections
3.4 Use available technologies in simulations |
| 4. Demonstrate an understanding
of the interconnectedness between shape, space and time |
4.1 Show the effect
of movement and shape
4.2 Demonstrate an understanding of changes of perceptions of space and
shape though different media
4.3 Visualise and represent objects from various spatial orientations |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Description of the
position of an object in space |
1.1 Represent objects
in various forms of Geometry
1.2 Show links between Algebra and Geometry |
| 2. Descriptions of changes
in shape of an object |
2.1 Demonstrate movement
of points with time an irrelevant variable
2.2 Transform and tessellate shapes |
| 3. Descriptions of orientation
of an object |
3.1 Show understanding
of the concept of point of reference in 2D and 3D
3.2 Show understanding of perceptions by an observer from different reference
points
3.3 Work with projections
3.4 Use available technologies in simulations |
| 4. Demonstrate an understanding
of the interconnectedness between shape, space and time |
4.1 Show the effect
of movement and shape
4.2 Demonstrate an understanding of changes of perceptions of space and
shape though different media
4.3 Visualise and represent objects from various spatial orientations |
8. Analyse natural forms, cultural products
and processes as representations of shape, space, and time
Mathematical forms, relationships and processes
embedded in the natural world and in cultural representations are often
unrecognised or suppressed. Learners should be able to unravel, critically
analyse and make sense of these forms, relationships and processes.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Recognition of natural
forms, cultural products and processes and their value |
1.1 Observe nature,
cultural products and processes
1.2 Explain use and value of cultural products and processes
1.3 Analyse different cultural products and processes at different epochs |
| 2. Representation of
natural forms, cultural products and processes in a mathematical form |
2.1 Represent cultural
products and processes in various mathematical forms - 2D and 3D
2.2 Represent nature in mathematical form |
| 3. Generation of ideas
through natural forms, cultural products and processes |
3.1 Use representations
to generate new ideas |
| 4. Extensions of natural
forms, cultural products and processes in the economy |
4.1 Critically analyse
the misuse of nature and cultural products and processes |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Recognition of natural
forms, cultural products and processes and their value |
1.1 Observe nature,
cultural products and processes
1.2 Explain use and value of cultural products and processes
1.3 Analyse different cultural products and processes at different epochs |
| 2. Representation of
natural forms, cultural products and processes in a mathematical form |
2.1 Represent cultural
products and processes in various mathematical forms - 2D and 3D
2.2 Represent nature in mathematical form |
| 3. Generation of ideas
through natural forms, cultural products and processes |
3.1 Use representations
to generate new ideas |
| 4. Extensions of natural
forms, cultural products and processes in the economy |
4.1 Critically analyse
the misuse of nature and cultural products and processes |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Recognition of natural
forms, cultural products and processes and their value |
1.1 Observe nature,
cultural products and processes
1.2 Explain use and value of cultural products and processes
1.3 Analyse different cultural products and processes at different epochs |
| 2. Representation of
natural forms, cultural products and processes in a mathematical form |
2.1 Represent cultural
products and processes in various mathematical forms - 2D and 3D
2.2 Represent nature in mathematical form |
| 3. Generation of ideas
through natural forms, cultural products and processes |
3.1 Use representations
to generate new ideas |
| 4. Extensions of natural
forms, cultural products and processes in the economy |
4.1 Critically analyse
the misuse of nature and cultural products and processes |
9. Use mathematical language to communicate
mathematical ideas, concepts, generalisations, and thought processes
Mathematics is a language that uses notations,
symbols, terminology, conventions, models and expressions to process and
communicate information. The branch of mathematics where this language
is mostly used is Algebra. Learners' use of this language will be developed.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Use of language to
express mathematical observations |
1.1 Share observations
using all available forms of expression, verbal and non-verbal |
| 2. Use of mathematical
notation, symbols. |
2.1 Represent ideas
using mathematical symbols
2.2 Use mathematical notation |
| 3. Use of mathematical
conventions and terminology |
3.1 Formulate expressions,
relationships and sentences |
| 4. Interpretation and
analysis of models |
4.1 Read and explain
models
4.2 Analyse models and give meaning
4.3 Use models to solve problems |
| 5. Representation of
real life and simulated situations |
5.1 Use abstraction
to simulate word problems
5.2 Represent real life or simulated situations in a mathematical format
5.3 Use technology to represent and process observations |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Use of language to
express mathematical observations |
1.1 Share observations
using all available forms of expression, verbal and non-verbal |
| 2. Use of mathematical
notation, symbols |
2.1 Represent ideas
using mathematical symbols
2.2 Use mathematical notation efficiently |
| 3. Use of mathematical
conventions and terminology |
3.1 Combine notation
logically
3.2 Formulate expressions, relationships and sentences
3.3 Use conventional mathematical language |
| 4. Interpretation and
analysis of models |
4.1 Read and explain
models
4.2 Analyse models and give meaning
4.3 Use models to solve problems |
| 5. Construction of models |
5.1 Use mathematical
language to construct models |
| 6. Representation of
real life and simulated situations |
6.1 Use abstraction
to simulate word problems
6.2 Represent real life or simulated situations in a mathematical format
6.3 Use technology to represent and process observations |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Use of language to
express mathematical observations |
1.1 Share observations
using all available forms of expression, verbal and non-verbal |
| 2. Use of mathematical
notation, symbols |
2.1 Represent ideas
using mathematical symbols
2.2 Use mathematical notation efficiently |
| 3. Use of mathematical
conventions and terminology |
3.1 Combine notation
logically
3.2 Formulate expressions, relationships and sentences
3.3 Use conventional mathematical language |
| 4. Interpretation and
analysis of models |
4.1 Read and explain
models
4.2 Analyse models and give meaning
4.3 Use models to solve problems |
| 5. Construction of models |
5.1 Use mathematical
language to construct models |
| 6. Representation of
real life and simulated situations |
6.1 Use abstraction
to simulate word problems
6.2 Represent real life or simulated situations in a mathematical format
6.3 Use technology to represent and process observations |
10. Use various logical processes to formulate,
test and justify conjectures
Reasoning is fundamental to mathematical activity.
Active learners question, examine, conjecture and experiment. Mathematics
programmes should provide opportunities for learners to develop and employ
their reasoning skills. Learners need varied experiences to construct convincing
arguments in problem settings and to evaluate the arguments of others.
FOUNDATION PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of logical
reasoning in addressing problems |
1.1 Demonstrate reasoning
processes of association, comparison, classification and categorisation
1.2 Report mathematical reasoning processes verbally and visually |
| 2. Ability to justify
familiar and unfamiliar hypotheses |
2.1 Recognise familiar
or unfamiliar situations
2.2 Infer from known experiences
2.3 Demonstrate respect for different reasoning approaches |
| 3. Evidence of use of
empirical or theoretical rationale in justifying conjectures |
3.1 Choose relevant
data as a basis for prediction
3.2 Construct logical steps in an understandable order
3.3 Test validity of judgement |
INTERMEDIATE PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of logical
reasoning in the solution of problems |
1.1 Use various reasoning
approaches
1.2 Report mathematical reasoning processes clearly |
| 2. Ability to justify
familiar and unfamiliar hypotheses |
2.1 Recognise familiar
or unfamiliar situations
2.2 Infer from known paradigms
2.3 Demonstrate respect for different reasoning approaches |
| 3. Evidence of use of
empirical or theoretical rationale in justifying conjectures |
3.1 Choose relevant
data as a basis for prediction
3.2 Construct logical steps in an understandable order
3.3 Test validity of judgement |
SENIOR PHASE
| ASSESSMENT CRITERIA |
RANGE STATEMENT |
| 1. Evidence of logical
reasoning in the solution of problems |
1.1 Use various reasoning
approaches
1.2 Express reasoning processes clearly |
| 2. Ability to prove
familiar and unfamiliar hypotheses |
2.1 Recognise familiar
or unfamiliar situations
2.2 Design a sequence of inferences
2.3 Extract from known paradigms
2.4 Demonstrate respect for different reasoning approaches |
| 3. Evidence of use of
empirical or theoretical rationale in justifying conjectures |
3.1 Choose relevant
data as a basis for prediction
3.2 Construct logical steps in an understandable order
3.3 Test validity of judgement |
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