Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

In the Foundation Phase, there are three Learning Programmes: Literacy, Numeracy and Life Skills. In the
Intermediate Phase, Languages and Mathematics are district Learning Programmes. Learning Programmes.
Learning Programmes must ensure that the prescribed outcomes for each learning area are covered
effectively and comprehensively. Schools may decide on the number and nature of other

Learning Programmes based on the organisational imperatives of the school, provided that the national
priorities and developmental needs of learners in a phase are taken into account. In the Senior Phase, there are
eight Learning programmes based on the Learning Area Statements.

Teachers will be responsible for the development of Learning Programmes. The Department of Education will
provide policy guidelines for the development of Learning Programmes in order to support this process.
Provinces will develop further guidelines where necessary in order to accommodate diversity. Teacher
education programmes will build the capacity of teachers, school management teams and departmental
support personnel to develop, implement, manage and support the development of learning programmes.

Learning Programme Guidelines

To ensure achievement of national standards set by the Revised National Curriculum Statement, policy
guidelines for relevant and appropriate Learning Programmes will be developed at national level in
collaboration with provinces. These guidelines will emphasise the principle of integrated learning and the
achievement of an optimal relationship between integration across learning areas and conceptual progression
from grade to grade. The National Education Policy Act (1996, section 3, paragraph 4) empowers the Minister of

Education to determine, among other things, such a national policy guideline for the development of Learning
Programmes These policy guidelines will provide information and guidance on:

 Integration within and across learning areas;
C  lustering of assessment standards;
R  elationships between learning outcomes;
T  ime allocation;
 Assessment;
B  arriers to learning;
 Designing a Learning Programme;
P  olicy and legislation;
T  raining, development and delivery;
R  esourcing and support;
 Planning and organisation.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

2.1 (ac1) – planning a Numeracy Learning
Programme for Grade R. 

The policy document, National policy pertaining to the programme and promotion requirements of the
National Curriculum Statement Grades R – 12, and the sections on the Curriculum and Assessment Policy as
contemplated in Chapters 2, 3 and 4 of this document constitute the norms and standards of the National
Curriculum Statement Grades R – 12. It will therefore, in terms of section 6A of the South African Schools Act,
1996 (Act No. 84 of 1996,) form the basis for the Minister of Basic Education to determine minimum outcomes
and standards, as well as the processes and procedures for the assessment of learner achievement to be
applicable to public and independent schools.

General aims of the South African Curriculum

The National Curriculum Statement Grades R - 12 gives expression to the knowledge, skills and values worth
learning in South African schools. This curriculum aims to ensure that children acquire and apply knowledge
and skills in ways that are meaningful to their own lives. In this regard, the curriculum promotes knowledge in
local contexts, while being sensitive to global imperatives.

The National Curriculum Statement Grades R - 12 serves the purposes of:

equipping learners, irrespective of their socio-economic background, race, gender, physical ability or
intellectual ability, with the knowledge, skills and values necessary for self-fulfilment, and meaningful
participation in society as citizens of a free country;

 Providing access to higher education;
 Facilitating the transition of learners from education institutions to the
workplace; and
P  roviding employers with a sufficient profile of a learner‘s competences.

The National Curriculum Statement Grades R - 12 is based on the following principles:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

S  ocial transformation: ensuring that the educational imbalances of the
past are redressed, and that equal educational opportunities are
provided for all sections of the population;
 Active and critical learning: encouraging an active and critical approach
to learning, rather than rote and uncritical learning of given truths;
H  igh knowledge and high skills: the minimum standards of knowledge
and skills to be achieved at each grade are specified and set high,
achievable standards in all subjects;
 Progression: content and context of each grade shows progression from
simple to complex;
 Human rights, inclusivity, environmental and social justice: infusing the
principles and practices of social and environmental justice and human
rights as defined in the Constitution of the Republic of South Africa. The
National Curriculum Statement Grades R – 12 is sensitive to issues of
diversity such as poverty, inequality, race, gender, language, age,
disability and other factors;
V  aluing indigenous knowledge systems: acknowledging the rich history
and heritage of this country as important contributors to nurturing the
values contained in the Constitution; and
C  redibility, quality and efficiency: providing an education that is
comparable in quality, breadth and depth to those of other countries.

The National Curriculum Statement Grades R - 12 aims to produce learners that are able to:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

I dentify and solve problems and make decisions using critical and
creative thinking;
 Work effectively as individuals and with others as members of a team;
 Organise and manage themselves and their activities responsibly and
effectively;
C  ollect, analyse, organise and critically evaluate information;
 Communicate effectively using visual, symbolic and/or language skills in
various modes;
U  se science and technology effectively and critically showing
responsibility towards the environment and the health of others; and
D  emonstrate an understanding of the world as a set of related systems
by recognising that problem solving contexts do not exist in isolation.

Inclusivity should become a central part of the organisation, planning and teaching at each school. This can
only happen if all teachers have a sound understanding of how to recognise and address barriers to learning,
and how to plan for diversity.

The key to managing inclusivity is ensuring that barriers are identified and addressed by all the relevant
support structures within the school community, including teachers, District-Based Support Teams,
Institutional-Level Support Teams, parents and Special Schools as Resource 6

Centres. To address barriers in the classroom, teachers should use various curriculum differentiation strategies
such as those included in the Department of Basic Education‘s

Time Allocation

Foundation Phase

  1.  The instructional time in the Foundation Phase is as follows:

SUBJECT

GRADE R (HOURS)

GRADES 1-2 (HOURS)

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

GRADE 3 (HOURS)
Home Language
10
7/8
7/8
First Additional Language
2/3
3/4
Mathematics
7
7
7
Life Skills

 Beginning Knowledge
C  reative Arts
 Physical Education
 Personal and Social Well-being

6
(1)
(2)

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

(2)
(1)
6
(1)
(2)
(2)
(1)
7
(2)
(2)
(2)
(1)
TOTAL
23
23
25
b. Instructional time for Grades R, 1 and 2 is 23 hours and for Grade 3 is 25 hours.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

(c) Ten hours are allocated for languages in Grades R-2 and 11 hours in Grade 3. A maximum of 8 hours and a
minimum of 7 hours are allocated for Home Language and a minimum of 2 hours and a maximum of 3 hours
for Additional Language in Grades R – 2. In Grade 3 a maximum of 8 hours and a minimum of 7 hours are
allocated for Home Language and a minimum of 3 hours and a maximum of 4 hours for First Additional
Language.
(d) In Life Skills Beginning Knowledge is allocated 1 hour in Grades R – 2 and 2 hours as indicated by the hours
in brackets for Grade 3.

Group Activity / Pair Activity 2.1:
1. Explain how the Learning programme for Grade R is unique compared to the other levels.
2. List and explain the advantages of the Grade R learning programme.

2.2 (ac2) - integration of mathematical
relationships across other learning areas  

Topics for Applying Mathematics to Everyday Situations
Students need help seeing how math applies to real life.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Mathematics students, particularly those in middle and high school, often question how or when they will use
their math skills in their everyday lives. While it can be hard for them to envision these abstract concepts
having a practical use, there are many ways teachers can cultivate students' understandings of real-life
mathematical applications. Making the connection between math and the real world will increase students'
understanding of and interest in the subject.

Finances: One straightforward way to help students see the practical uses of math skills is to connect math to
finances. There are many different lessons and activities to teach financial math, depending on the age level
and math topic. Students in elementary school can learn about the basics of adding and subtracting by using
money. Middle school students, likely beginning to study simple pre-algebra, can learn about saving money to
meet a certain goal and can use equations to find out how long the goal will take. Finally, high school students
studying higher math can learn about more complicated economic theories.

Statistics: Students often find it fun to study statistics, as it offers many everyday applications for ratio, fractions,
probability and data. One simple way to apply this kind of math to real life is to make predictions about different
aspects of classmates -- for instance, "How many of our classmates are likely to have brown hair if they have
brown eyes?" Activities like this can be applied to other situations, such as politics and weather, where students
can study data and make predictions. Students in higher level math classes can do this for more complicated
scenarios, such as the stock market.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Nutrition: An essential skill in everyday life, which directly relates to math skills, is nutrition. Elementary school
students can use a recipe to learn about basic measuring, adding and subtracting. Students in middle school
can create their own recipes, multiplying for large groups and manipulating recipes based on equations. Higher
level math students can do more complicated projects, where they learn about calories, body mass and how
to mathematically equate a healthy diet and lifestyle.

Current Events: An additional topic that offers math-based learning is studying current events. In many
situations students learn about, there is inherent math for them to study. When studying politics, there are
statistical and probability units to delve into. If students hear about a natural disaster, they can figure out the
particulars of the damage caused and the people affected and then project data into the future of the area.
There is math to be figured out when students learn about war, health care and even trends in popular culture.

The Use of Math in Everyday Life

Math doesn't have to be tedious or unrewarding. Simple math is useful in all kinds of everyday pursuits like
cooking, budgeting, shopping, building and traveling---to name a few. A few minutes each day of simple
addition and multiplication can help you get a handle on your resources, how they've been used in the past
and where you'd like to see them go.

Shop Smarter - Practice simple math on something everyone needs to do---grocery shopping. We all have to
shop, but some people save huge amounts on their grocery bills by using math to plan their shopping trips. A
woman featured in Southern Living magazine drastically lowered her shopping bill by planning meals around
which meats were on sale at the supermarket.

The most important mathematical concepts to use when shopping are ratios and percentages. If you are trying
to cut back on your bills, take a couple of hours to compare the costs of some of your favourite meals. Add up
the cost of the ingredients of a meal, then estimate how many servings you can get from the meal, and divide
by that number. If, for example, lentil soup costs $10 to make ten servings, you will spend $1 per serving.
Lasagna, on the other hand, might cost $13 to make eight servings. Thirteen divided by eight is 1.625, which
means that a serving of lasagna costs about $1.63. Using simple math, you can easily compare different foods
to determine how you can most economically serve your household meals. As you work on the best use of
your money, take time each week to compare your grocery bills. Calculate the percentage you saved on
groceries each week by using sales, coupons and strategic menu planning.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Budget your travel: Travel planning is another great use for mathematics in everyday life. Gasoline prices are a
constant variable in modern travel, making it essential to estimate your gas costs before taking a big trip. Say,
for example, that you plan to drive 1,000 miles over the weekend to visit family. If your car gets 27 miles per
gallon of gas and you plan to travel 1,000 miles, divide 1,000 by 27 to get the number of gallons of gas you will
need. In this case, you need 37 gallons. Multiply this by the price of gas to find out how much your trip will cost
in gasoline.
Streamline Your Work: Math also comes in handy when trying to maximize your productivity at work. If you can
easily measure the number of widgets or reports you produce per day, make a simple graph or chart to track
your improvement. If your job is more difficult to quantify, calculate the amount of time it takes you to do
certain tasks. Use percentages to chart your improvement as you streamline your processes.

Group Activity / Pair Activity 2.2:
1. Describe the application of Mathematics in daily activities of life.
2. List and explain any 5 instances that require mathematics literacy.
3. Demonstrate how mathematics is incorporated into planning for a Grade R curriculum.

2.3 (ac3) – plans that are child-centred and
relate to children's life world interests and
experiences. 

What Is a Child-Centered Constructivist Approach to Early Childhood Education?
In constructivist classroom children explore learning topics.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

The child-centered constructivist approach to early childhood education has its roots in the work of
psychologists Lev Vygotsky and Jean Piaget. Piaget's theories in child development, cognition and intelligence
worked as a framework to inspire the development of the constructivist approach to learning. The
constructivist approach views children as active participants in their own learning. Education is then much
more than rote memorization; instead, it is integrating and assimilating knowledge to be further used and
explored. Constructivist strategies seek to ignite a child's curiosity and love of learning.

The Principles of Constructivism

At the center of constructivist education is an environment in which children become active learners who make
choices and seek out experiences that foster their development. Teachers provide an integrated curriculum
that allows children to explore multiple themes and subjects within a topic. Children are empowered to
investigate and reorganize their knowledge bases. Children learn through developmentally appropriate
activities and learning exercises that challenge their academic, physical, social and emotional growth. Group
activities promote a sociomoral environment in which young children can learn about and practice respect for
one another. The daily schedule is flexible and loosely structured. Teachers allow students sufficient time to
fully explore topics.

The Teacher's Role

The role of the teacher in a constructivist approach to early childhood education is primarily one of guidance.
Teachers act as a guide to children's learning by facilitating activities and learning opportunities without
dictating learning objectives. They emphasize the whole child when designing curriculum and learning topics.
Teachers encourage young students to develop and investigate their own interests. Curiosity sparks effective
learning. Instead of the traditional concept of a teacher standing at the front of the classroom and dictating
information, educators become partners with their students. They encourage children to ask questions and get
involved. Teachers should consistently provide open-ended activities with multiple outcomes.

The Children's Role

In a constructivist classroom, children investigate their surroundings and learning topics. They act as young
scientists discovering the world around them. Because the teacher opens the classroom to imaginative
learning, children become important agents in their own education. Children are doing their own learning
rather than receiving learning given to them. They actively participate in projects and activities, choosing the
depth of learning in any given topic. Children assimilate what they have learned into what they already know,
creating new knowledge.

Practical Applications

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

A child-centered constructivist approach to early childhood education is applicable to various classroom
scenarios. Children benefit from group problem-solving. By working together to find solutions, students
experience cognitive growth. Teachers can then assist children in the reasoning process, encouraging them to
think and reason through problems. Science particularly lends itself to constructivism. Children are able to
satisfy their curiosity about the natural world through experiments. They can develop simple hypotheses, test
their theories and compare the results.

Child-centered Approach to Teaching

Allow preschoolers to discover knowledge through exploration.

In a child-centered approach to preschool, the learner, not the teacher, leads the way. When preschool
teachers adopt this practice, they allow young students to engage in exploration and make discoveries instead
of always presenting facts to the children. By allowing preschoolers to discover information through hands-on
exploration, teachers can show their students that learning is fun and help instill a love of the task.

Teacher as Facilitator

For child-centered learning to work, the teacher must act as a facilitator, not directly instructing the students
but instead providing them with tasks that promote learning. For example, a teacher might have students cut
out and glue down alphabet letters; this helps children develop eye-hand coordination, and they learn the
alphabet without a teacher standing in front of the class and laboriously discussing the skills.

Centered Learning

Many preschool teachers who adopt the child-centered approach rely on centers when directing students
through lessons. By setting up different centers around the room, the children can move through activities
more independently and at their own pace. A teacher might, for example, create a station where students
count items in boxes and another where they match upper- and lowercase letters. This set-up makes working
as a facilitator substantially easier, as it allows the teacher to move about the room and help students as they
complete the stations, instead of leading direct instruction.

Cooperative Tasks

Students can benefit from working with peers. Cooperative learning helps preschool students develop the
skills they will need later for education success. It also gives them a chance to benefit from the knowledge of
classmates. In the child-centered preschool classroom, educators should pair pupils as often as possible, as
doing so makes learning enjoyable and effective. When pairing learners, teachers should aim to create mixes in
which one student excels and other struggles. This allows students with differing skills to share their abilities
and help each other.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Observational Evaluations
In a child-centered class, observation is the most common method of evaluation. This is ideal for preschool
teachers, as their pupils often do not possess the skills necessary to complete any form of written assessment.
When evaluating students and their skills, teachers can monitor the children as they complete learning
activities and evaluate their degree of understanding based upon this observation.

Individual Activity 2.3:
1. What Is a Child-Centered Constructivist Approach to Early Childhood Education?
2. What are the advantages of having a child-centered programme against one that is not child centered?

2.4 (ac4) - Basic principles for selecting and
sequencing learning activities

A lesson plan is a teacher's detailed description of the course of instruction for one class. A daily lesson plan is
developed by a teacher to guide class instruction. Details will vary depending on the preference of the teacher,
subject being covered, and the need and/or curiosity of children. There may be requirements mandated by the
school system regarding the plan
Principles of Teaching Lesson Activities: Adhering to learning principles helps students build independent skills
that lead to successful classroom experiences.
Teaching students isn't just about the content and memorizing facts and material. It is also about the teaching
of thinking--the kind of thinking that leads to learning, independence and success. You can improve students'
academic performance by drawing from their background knowledge, setting learning objectives specific to
the tasks and student abilities and reflecting regularly on their learning.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Background Knowledge: By bringing in students' background knowledge about material related to new
learning, you can facilitate longer and deeper learning. Grant Wiggins, author of "Understanding by Design,"
writes about making learning interesting by relating it to students' background experiences and building in
plenty of hands-on opportunities as a way of engaging students. This guiding of instruction along a responsible
learning path leads to higher-order thinking and permanent learning.

Setting Learning Objectives: According to Anderson and Krothwahl in "Learning, Teaching and Assessing," by
setting learning objectives that connect directly to students' background, you will help build their ability to
think independently. Setting these objectives with student input makes them that much more meaningful and
effective. Both teaching and learning are more effective when objectives are clearly set, straightforward,
presented at the onset of each lesson, and directly connected to the task and all related assessments--tests,
quizzes and projects. Giving students plenty of opportunities to demonstrate their movement toward these
objectives, with feedback along the way, is also crucial to achievement.

Setting Expectations: Setting clear and straightforward expectations about behaviours and academic
performance helps students take responsibility for their own learning and leads to greater independent
success It is equally as important to make sure these expectations are in line with what students are capable
of, because if they're constantly failing they'll stop trying. There is a happy medium somewhere between what
they're capable of and what can challenge them. Finding this happy medium can be easily achieved by looking
at past academic performance such as grades on tests, quizzes and projects. Communicating these
expectations can and should be done both verbally and in writing through task-specific evaluation rubrics that
detail exactly what students should do, from the highest score possible to the lowest. This way, all
expectations are clear, and students know what constitutes exemplary work and what constitutes failure,
thereby taking responsibility for their own effort and results.

Reflection and Assessment: Author and educational researcher Eric Jensen says that in order for students to
really understand what they've been taught, they must have many opportunities along the learning path to
reflect. Reflection can be achieved by having students write about their learning experiences in writing
journals, or having discussions with peers prior to, during and after learning new material to discuss what they
learned. They might talk about what was new, what they learned that matched what they already knew and
what they liked or appreciated most about their learning. Assessment comes in after reflection, and with
reflection makes it more likely that students will be successful on any tests, quizzes or follow-up projects that
culminate in new learning.

Activities That Follow the Principles of Effective Teaching

Classroom activities using effective teaching principles helps students learn.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

While the principles of effective teaching might vary slightly depending on individual educators, they all
essentially share the same rules; create an active learning environment, focus attention, have high expectations
and balanced support, and help students connect the knowledge they have. All student activities should
reinforce these principles.

Write, write, and write: Inform students that they are constantly responsible for what they have learned in class,
or what they might not have learned and may have questions about. Have students write daily paragraphs in
response to this information. Lecture for 10 minutes about how you expect five questions based directly on that
day's presentation. This encourages note-taking. Give daily or weekly quizzes so that students know that they
are accountable for taking and reviewing notes.

Student Presentations: Student presentations are a good barometer for displaying how much students have
retained from a given lesson in addition to providing useful public speaking experience. Introduce the class to
the different learning styles, such as visual, aural or kinesthetic. Explain that teaching three different learners
how to bake a cake may require different techniques. A visual learner needs to see pictures and read
instructions; an aural learner requires hearing instructions and a kinesthetic learner must perform the steps
herself. Assign each student a mini-lesson that was taught in the past week, to be presented this time for
visual, aural, or kinesthetic learners.

Resources: Explain to your students that you do not expect them to know everything, just as they should not
expect you to know everything. Provide them with a list of online resources, such as online dictionaries, literary
critics, anthologies, problem-solving videos, etc., and have them use these resources on a regular basis.
Compiling a private vocabulary list and looking up the definitions should be part of their everyday work.

Principles of Effective Teaching: The principles of effective teaching encompass the ability to motivate
students. Likewise, they incorporate the essential elements of instruction put forth by Madeline Hunter in the
1960s.

Objective: The objective is what is to be taught. An objective is clear, concise and easy to understand. It's the
actionable part of teaching.

Correct Level of Difficulty: The correct level of difficulty regarding subject matter, desired objective and student
aptitude are assessed and adjusted according to the task and students at hand. Standards are taught at grade
level but adjusted according to assessment results.

Monitoring and Adjusting: Feedback is constantly gathered from students in order to make adjustments so all
students eventually understand the lesson. Testing and checking students, both overtly and covertly, is
constant.

Motivation: Motivation involves feeling tone, level of concern, student interest and connection, student success
rate and knowledge of results. Students are engaged and focused on the lesson or task.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Participation: Students are an active part of every lesson. Overt and covert techniques keep students involved.
Retention: Lessons are meaningful. Teachers model expectations. Students have ample time to demonstrate
mastery.

Group Activity / Pair Activity 2.4:
1. Define lesson plan.
2. Define learning activities.
3. List any 5 principles for planning Grade R children learning programmes and activities.

2.5 (ac5) - lessons learnt from previous
experiences of facilitating numeracy. 

A lesson plan is a teacher's detailed description of the course of instruction for one class. A daily lesson plan is
developed by a teacher to guide class instruction. Details will vary depending on the preference of the teacher,
subject being covered, and the need and/or curiosity of children. There may be requirements mandated by the
school system regarding the plan.
Developing a lesson plan
While there are many formats for a lesson plan, most lesson plans contain some or all of these elements,
typically in this order:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

 Title of the lesson
 Time required to complete the lesson
 List of required materials
L  ist of objectives, which may be behavioural objectives (what the student
can do at lesson completion) or knowledge objectives (what the student
knows at lesson completion)
 The set (or lead-in, or bridge-in) that focuses students on the lesson's
skills or concepts—these include showing pictures or models, asking
leading questions, or reviewing previous lessons
A  n instructional component that describes the sequence of events that
make up the lesson, including the teacher's instructional input and
guided practice the students use to try new skills or work with new ideas
 Independent practice that allows students to extend skills or knowledge
on their own
 A summary, where the teacher wraps up the discussion and answers
questions
A  n evaluation component, a test for mastery of the instructed skills or
concepts—such as a set of questions to answer or a set of instructions to
follow
A  risk assessment where the lesson's risks and the steps taken to
minimize them are documented.
A  nalysis component the teacher uses to reflect on the lesson itself —
such as what worked, what needs improving
 A continuity component reviews and reflects on content from the
previous lesson

A well-developed lesson plan

A well-developed lesson plan reflects the interests and needs of students. It incorporates best practices for the
educational field. The lesson plan correlates with the teacher's philosophy of education, which is what the
teacher feels is the purpose of educating the students.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Secondary English program lesson plans, for example, usually center around four topics. They are literary
theme, elements of language and composition, literary history, and literary genre. A broad, thematic lesson
plan is preferable, because it allows a teacher to create various research, writing, speaking, and reading
assignments. It helps an instructor teach different literature genres and incorporate videotapes, films, and
television programs. Also, it facilitates teaching literature and English together. Similarly, history lesson plans
focus on content (historical accuracy and background information), analytic thinking, scaffolding, and the
practicality of lesson structure and meeting of educational goals. School requirements and a teacher's
personal tastes, in that order; determine the exact requirements for a lesson plan.

Unit plans follow much the same format as a lesson plan, but cover an entire unit of work, which may span
several days or weeks. Modern constructivist teaching styles may not require individual lesson plans. The unit
plan may include specific objectives and timelines, but lesson plans can be more fluid as they adapt to student
needs and learning styles.

Setting an objective

The first thing a teacher does is create an objective, a statement of purpose for the whole lesson. An objective
statement itself should answer what students will be able to do by the end of the lesson. Harry Wong states
that, “Each [objective] must begin with a verb that states the action to be taken to show accomplishment. The
most important word to use in an assignment is a verb, because verbs state how to demonstrate if
accomplishment has taken place or not.” The objective drives the whole lesson, it is the reason the lesson
exists. Care is taken when creating the objective for each day’s lesson, as it will determine the activities the
students engage in. The teacher also ensures that lesson plan goals are compatible with the developmental
level of the students. The teacher ensures as well that their student achievement expectations are reasonable.

Selecting lesson plan material

A lesson plan must correlate with the text book the class uses. The school usually selects the text books or
provides teachers with a limited text book choice for a particular unit. The teacher must take great care and
select the most appropriate book for the students.

Types of Assignments

The instructor must decide whether class assignments are whole-class, small groups, workshops,
independent work, peer learning, or contractual:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

 Whole-class—the teacher lectures to the class as a whole and has the
class collectively participate in classroom discussions.
 Small groups—students work on assignments in groups of three or four.
 Workshops—students perform various tasks simultaneously. Workshop
activities must be tailored to the lesson plan.
 Independent work—students complete assignments individually.
 Peer learning—students work together, face to face, so they can learn
from one another.
 Contractual work—teacher and student establish an agreement that the
student must perform a certain amount of work by a deadline.

These assignment categories (e.g. peer learning, independent, small groups) can also be used to guide the
instructor’s choice of assessment measures that can provide information about student and class
comprehension of the material. As discussed by Biggs (1999), there are additional questions an instructor can
consider when choosing which type of assignment would provide the most benefit to students? These include:

W  hat level of learning do the students need to attain before choosing
assignments with varying difficulty levels?
W  hat is the amount of time the instructor wants the students to use to
complete the assignment?
 How much time and effort does the instructor have to provide student
grading and feedback?
W  hat is the purpose of the assignment? (e.g. to track student learning; to
provide students with time to practice concepts; to practice incidental
skills such as group process or independent research)
 How does the assignment fit with the rest of the lesson plan? Does the
assignment test content knowledge or does it require application in a
new context?

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Group Activity / Pair Activity 2.5:
1. Define lesson plan
2. Explain how a lesson plan is developed.
3. Design a lesson plan of your own using the guiding principles of lesson plan development.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

(ac6) - The application of lesson plans 

How to Apply Curiosity to Lesson Plans

Use curiosity to promote learning.

A deeper learning takes place when the learner has a desire to gain information. Curiosity is a key factor in
creating a student that yearns for learning. When students are curious about a topic, they will beg and plead
for information. Applying curiosity to lesson plans will increase student motivation.

Use an attention-getting opening to the lesson. Play a song that relates to your lesson; introduce a stuffed
animal or object to the class, dress like a character or make a thought-provoking statement.

Create a KWL (Know, Want to Know, Learned) chart before giving instruction. Students can give information
about what they already know about the topic and develop curiosity about what they want to learn.

Propose questions rather than telling answers. Allow the students to generate ideas about topics, and then
lead them into the correct thoughts instead of simply giving them the information.

Lead students in "what if" questioning. After students learn the concept, allow them to experiment by changing
factors. For example, what if we change the numbers in math; what if we add a different chemical in science
and what if the object had not been invented.

How to Use Manipulatives in Lesson Planning

Manipulatives are tangible objects teachers use in their instruction to illustrate various concepts. Most students
learn best when they are engaged in the learning process. Instruction that is visual and tactile is more effective
than lecture alone. When teachers let students handle manipulatives, they are giving their students
opportunities to see, touch and interact with objects that can help them to understand educational concepts
better. The first step to using manipulatives in your classroom is to prepare for these types of activities during
your lesson planning time.

Write down the standards you will be addressing during your lesson. Staying mindful of your standards will
help you to plan and use manipulatives effectively.

Gather supplies that will illustrate your lesson. For instance, you could use marbles, coins, dice and spinners as
math manipulatives. You might use a magnifying glass, a ruler or a dropper as a science manipulative. You
could use various types of instruments as manipulatives in a music class.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Write a plan that includes an introduction to a concept, instructions for using manipulatives, a demonstration
for using manipulatives and an evaluation and assessment of learning at the end of the lesson. Include a
review at the end of the lesson as well.

Practice using the manipulatives in activities you will demonstrate for the students. For instance, you might
design a lesson about probability in which you plan to have your students flip a quarter and make predictions
concerning the outcome of the coin flips. Do the activity yourself first to make sure you can explain and
demonstrate it well. Practicing with manipulatives also helps you to ensure an activity will work and will be
simple enough for students to understand.

Gather the supplies needed for the entire class at the end of your planning session. This is an important part of
being prepared before your students arrive.

How to Use Ice in Preschool Lesson Plans

Preschoolers love to play with ice. It's wet, cold and slippery. Thankfully, there are a lot of things that you can
do with it when it comes time to create lesson plans and activities. Keep reading to find out how you can use
ice in preschool lesson plans.

Create a sensory tub. Place a handful of ice cubes into a plastic tote filled with water and let the children play
with the ice cubes. You can experiment with different sizes of ice cubes for added stimuli.

Teach the children how to mix colours. Use ice in preschool lesson plans to show children what happens when
you mix colours together. Add a few drops of food colouring to each cube before freezing, and then put two or
three different coloured cubes together in a plastic bag. As the ice melts, the children can see how each colour
combination looks when mixed together.

Make ice cream. When the weather is warm, show your students how ice and a little salt can work together to
make their favourite summertime treat. You can use an ice cream maker, or simply make your own in plastic
bags.

Have a frozen treasure hunt. Before class, freeze several small trinkets in a paper cup full of water. Then pair up
your class into teams and have them race to see who can thaw out their treasure first. To make it more
complicated, have quiz questions ready. The team that gets the answer right is allowed to pour a glass of water
on their cube.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Group Activity / Pair Activity 2.6:
1. List and explain the advantages of using a lesson plan.
2. Explain how you can effectively apply a lesson plan to daily teaching.

So3 - numeracy learning activities.

Learner Tip:
Numeracy Activities

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Teach your kids numbers with fun activities.
The early stages of school are a huge step in a child's learning process. Math and English are skills which are
taught throughout a child's education. When taught in a fun-filled way, math will become an interesting subject
for your kids. Teaching math to kindergarten students is easy when you incorporate a few helpful activities in
your lesson plan. Math activities show children the various reasons why math is important and how it relates to
everyday life.
Play Hopscotch: Teach your kids how to play hopscotch. One of the many games children play in kindergarten
is hopscotch. Hopscotch not only gets your kids moving but it enables them to use their counting skills. Kids
learn how to recognize and count the numbers in the hopscotch squares.
Play with Bugs: Use bugs to get kindergartners interested in numeracy activities. Of course, you will use paper
bugs. Have your kids get creative by cutting out numbers 1 through 9. Show your kindergartners how to make
bugs like butterflies and ladybugs with the numbers. Your kids can draw on the numbers and play counting
games such as "one ladybug plus two ladybugs equals three."
Make a Clock: Make a clock for your class. Implementing numeracy activities includes telling time. Show your
students how to make a clock. Have your kids put each number on the clock. When the clock is finished teach
your kids how to say each number.
Count Beans: Get some beans and add them. Show your students how to add and subtract by using beans as a
substitute for numbers. Use different colour beans and mix them up in a cup. Dump out the cup and have your
kids separate and count like colours. Also have them count all the beans and subtract certain colours away
from the total group of beans.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Create a Book: Make a book with kindergartners. Show your kids how to make 1-2-3 book. On each page have a
different number and have your kids draw something to represent that number. For example, for the numeral 2
draw two suns. This activity is a fun way to teach numerals.

3.1 (ac3) - use mathematical language, concepts
and numeracy skills. 

Numeracy across the Curriculum

Numeracy is a proficiency that involves confidence and competence with numbers and measures. It requires
an understanding of the number system, a repertoire of computational skills and an inclination and ability to
solve number problems in a variety of contexts. Numeracy also demands practical understanding of the ways
in which information is gathered by counting and measuring, and is presented in graphs, diagrams, charts and
tables.

Mathematical skills can be consolidated and enhanced when pupils have opportunities to apply and develop
them across the curriculum. Poor numeracy skills, in particular, hold back pupils' progress and can lower their
self-esteem. To improve these skills is a whole-school matter. Each department should identify the
contribution it makes towards numeracy and other mathematical skills so that pupils become confident at
tackling mathematics in any context.  

Numeracy Policy

Numeracy is a key skill in students' learning and all students are entitled to quality experiences in this area and
that the teaching of numeracy is the responsibility of all staff and the school's approaches should be as
consistent as possible across the curriculum.
Curriculum areas will endeavour to ensure that materials presented to students will match their capability both
in subject content and in numerical demands. They will liaise with the Special Needs and Mathematics
departments when appropriate in order to support their teaching of numeracy.

All teachers should consider pupils' ability to cope with the numerical demands of everyday life and provide
opportunities for students to:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

H  andle number and measurement competently, mentally, orally and in
writing;
 Use calculators accurately and appropriately;
 Interpret and use numerical and statistical data represented in a variety
of forms.

Mathematics in other Subjects
You need to look for opportunities for drawing mathematical experience out of a wide range of children's
activities. Mathematics contributes to many subjects of the curriculum, often in practical ways. Activities such
as recording the growth of a plant or an animal, measuring temperature and rainfall, or investigating the cog
wheels in a bicycle can provide data or starting points for discussion in your mathematics lessons as well as
opportunities to apply and use mathematics in real contexts

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

English   Science  

Mathematics lessons can help to Almost every scientific
develop and support pupils' literacy
skills: for example, by teaching investigation or experiment is
mathematical vocabulary and
technical terms,  likely to require one or more of

the mathematical skills of

classifying, counting, measuring,

calculating, estimating, and

By asking children to read and Recording in tables and graphs. In
interpret problems to identify the
mathematical content, and by science pupils will, for example,
encouraging them to explain, argue
and present their conclusions to order numbers, including
others.  Equally, English lessons can
support your mathematics lesson. For decimals,  calculate means
example non-fiction texts can be
chosen in which mathematical and    percentages, use negative
vocabulary, graphs, charts and tables
have to be interpreted.   numbers when taking

temperatures, substitute into

formulae, re-arrange equations,

decide which graph is the most

appropriate to represent data, and

plot, interpret and predict from

graphs.   

Art, Design & Technology   Information & Communication
Technology

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Measurements are often needed Children will apply and use
in art and design and technology. mathematics in a variety of ways
Many patterns and constructions when they solve problems using
are based on spatial ideas and ICT. For example, they will collect
properties of shapes, including and classify data, enter it into data
symmetry.  handling software, produce

Designs may need enlarging or graphs and tables, and interpret and
reducing, introducing ideas of explain their results. Their work in
multiplication and ratio.  When food control includes the measurement of
is prepared a great deal of distance and angle, using uniform
measurement occurs, including non- standard then standard
working out times, adapting recipes, measures. When they use computer
and calculating cost; this may not models and simulations they will
be straightforward if only part of a draw on their abilities to manipulate
packet of ingredients has been numbers and identify patterns and
used.    relationships.

History, Geography and Religious Physical Education and Music
Education  

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

In history and geography children Athletic activities require
will collect data by counting and
measuring and make use of measurement of height, distance,
measurements of many kinds.
The study of maps includes the time and speed, while ideas of time,
use of co-ordinates and ideas of
angle, direction, position, scale symmetry, movement. position and
and ratio.   
direction are used extensively in

music. Dance, gymnastics and ball

games. The key to making the most

of these opportunities is

Historical ideas require To identify the mathematical
possibilities across the curriculum at
understanding of the passage of the planning stage. You should also
draw children's attention to the links
time. Which can be illustrated on a between subjects by talking
frequently about them, both in
time line? Similar to the number Mathematics and in other lessons.  

line that they already know.   

Numeracy Skills Count

Improved numeracy skills lead to better paid jobs, greater well-being and a less stressful life.

Numeracy skills are not just for scientists, accountants and the tax man, many professions require at least a
basic level of understanding when it comes to numeracy and mathematics.  Chris Humphries, Chairman of
National Numeracy, talking to the BBC said, “It is simply inexcusable for anyone to say ‘I can’t do maths.’” He
continued to suggest that many people cannot get jobs because they struggle to read graphs and interpret
documents, while plumbers may find it difficult to do the necessary calculations to install a boiler and as a
result lose income.  Careers New Zealand suggests that basic numeracy needed for the workforce includes:
counting quantities for a customer, the use of percentages and subtraction when giving a discount and using
division when calculating costs per head. CareersNZ continues to say that other desirable numeracy skills
include: measuring an area, calculating fuel consumption and understanding tables in reports and interpreting
graphs.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Group Activity / Pair Activity 3.1:
1. Discuss how important numeracy is to daily life
2. Apply numeracy to other learning areas and demonstrate the effects of not have literacy for learners.

3.2 (ac2) - principles and processes the of
mathematical concepts and numeracy
skills

What does it mean to be numerate?
Being numerate helps us to function responsibly in everyday life and contribute effectively to society. It
increases our opportunities within the world of work and establishes foundations which can be built upon
through lifelong learning. Numeracy is not only a subset of mathematics; it is also a life skill which permeates
and supports all areas of learning, allowing young people access to the wider curriculum.
We are numerate if we have developed:
the confidence and competence in using number which will allow individuals to solve problems, analyse
information and make informed decisions based on calculations.
A numerate person will have acquired and developed fundamental skills and be able to carry out number
processes but, beyond this, being numerate also allows us to access and interpret information, identify
possibilities, weigh up different options and decide on which option is most appropriate.
Numeracy is a skill for life, learning and work. Having well-developed numeracy skills allows young people to
be more confident in social settings and enhances enjoyment in a large number of leisure activities. For these
and many other reasons, all teachers have important parts to play in enhancing the numeracy skills of all
children and young people.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Numerate people rely on the accumulation of knowledge, concepts and skills they have developed, and
continually revisit and add to these. All practitioners, as they make use of the statements of experiences and
outcomes to plan learning, will ensure that the numeracy skills developed from early levels and beyond are
revisited and refreshed throughout schooling and into lifelong learning.

How are the numeracy experiences and outcomes structured?

The numeracy experiences and outcomes have been structured using eight organisers:

   Estimation and rounding
 Number and number processes
 Fractions, decimal fractions and percentages
M  oney
 Time
 Measurement
D  ata and analysis
 Ideas of chance and uncertainty.

All of these areas of numeracy will be familiar and all teachers will recognise how they impact on their own
lives. Reflecting on this will help teachers to identify where opportunities may exist to develop numeracy for
children and young people.

Mathematics is not my specialism. How will I contribute to the development of numeracy skills?

For individual teachers in secondary schools and other practitioners, it means asking the question, ‘How am I
meeting the numeracy needs of the learners in front of me?’. This does not mean that you will teach everything
that a mathematics teacher develops but that you think of the numeracy experiences you can provide for
young people. The greatest impact for learners will come where all practitioners, in all learning environments,
include rich numeracy experiences as part of their day-to-day learning and teaching programmes.

You might begin by asking to what extent you already provide numeracy experiences for learners. As a first
step, you may want to consider where numeracy plays a part in the aspects you contribute to the curriculum.
Does your programme involve estimating, measuring, using and managing time, carrying out money
calculations? Does it involve reading information from charts and tables or explaining consequences of
actions? If it does, and you highlight this and build upon it in the learning activities, you are making a valuable
contribution to developing numeracy in all learners.

What are the features of effective learning and teaching in numeracy?

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

The experiences and outcomes promote and support effective learning and teaching methodologies which
will stimulate the interest of children and young people and promote creativity and ingenuity.

A rich and supportive learning environment will support a skilful mix of a variety of approaches, including:

A  ctive learning and planned, purposeful play
 Development of problem-solving capabilities
D  eveloping mental agility
 Frequently asking children to explain their thinking
 Use of relevant contexts and experiences, familiar to children and young
people
 Using technology in appropriate and effective ways
 Building on the principles of assessment is for learning, including
understanding the purpose and relevance of the activities
 Both collaborative and independent learning
M  aking frequent links across the curriculum, so that concepts and skills
are developed further by being applied in different, relevant contexts
 Promoting an interest and enthusiasm for numeracy

Have we raised the bar in the expectations for numeracy?

Our expectations for numeracy are indeed higher than previously. This is because of the increasing recognition
that we must raise levels of performance in numeracy and sustain them throughout lifelong learning. Many
other countries are raising the numeracy performance of their children, young people and wider population.
Scotland needs to perform at the highest level, so raising the bar in numeracy is important for each individual
and also for the prosperity of the nation.

To support this, experiences and outcomes without ceilings should ensure young people are challenged at an
appropriate level and are given the opportunity to progress at a suitably aspirational pace.

This paper and the experiences and outcomes in numeracy provide a clear statement of the expectations that
will support all practitioners in contributing confidently to the

What are broad features of assessment in numeracy?

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

As numeracy is the responsibility of all staff, and because of the importance of numeracy across all aspects of
a young person’s learning, all staff should be clear about their responsibilities and their roles in the assessment
of numeracy. Assessment will focus on how well children and young people can work with numbers and data
and how well they can use them in their learning and lives, including preparation for future work. From the
early years to the senior stages, and particularly at times of transition, it is vital to have a clear picture of the
progress each child and young person is making across all aspects of numeracy so that further learning can be
planned and action can be taken if any ground has been lost.

Teachers can gather evidence of progress as part of day-to-day learning both in mathematics classes and
across the curriculum. The use of specific assessment tasks will be important in assessing progress at key
points of learning. Children and young people’s progress will be seen in their skills in using number to solve
problems, in analysing information and in making informed decisions based on calculations. Approaches to
assessment should identify the extent to which children and young people can apply these skills in their
learning in and beyond the classroom, in their daily lives and in preparing for the world of work.

As children and young people gradually build up the concepts and skills contained in the experiences and
outcomes, they will demonstrate their competence and confidence in applying them in a number of ways. For
example:

C  an they explain their thinking to show their understanding of number
processes and concepts?
A  re they developing securely the full range of the skills and attributes set
out within the experiences and outcomes? As they apply these to
problems, can they draw on skills and concepts learned previously?
 As they tackle problems in unfamiliar contexts, can they confidently
identify which skills and concepts are relevant to the problem? Can they
then apply their skills accurately when working independently and with
others, and can they then evaluate their solutions?
A  re they developing their understanding of personal finance?
C  an they evaluate data to make informed decisions?
A  re they developing the capacity to engage with and complete tasks and
assignments?

Assessment of numeracy across learning, within and outside the classroom, offers children and young people
opportunities to practise and extend their skills, for example within enterprise activities, social studies,
technologies and science.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

What are broad features of assessment in numeracy?

As numeracy is the responsibility of all staff, and because of the importance of numeracy across all aspects of
a young person’s learning, all staff should be clear about their responsibilities and their roles in the assessment
of numeracy. Assessment will focus on how well children and young people can work with numbers and data
and how well they can use them in their learning and lives, including preparation for future work. From the
early years to the senior stages, and particularly at times of transition, it is vital to have a clear picture of the
progress each child and young person is making across all aspects of numeracy so that further learning can be
planned and action can be taken if any ground has been lost.

Teachers can gather evidence of progress as part of day-to-day learning both in mathematics classes and
across the curriculum. The use of specific assessment tasks will be important in assessing progress at key
points of learning. Children and young people’s progress will be seen in their skills in using number to solve
problems, in analysing information and in making informed decisions based on calculations. Approaches to
assessment should identify the extent to which children and young people can apply these skills in their
learning in and beyond the classroom, in their daily lives and in preparing for the world of work.

As children and young people gradually build up the concepts and skills contained in the experiences and
outcomes, they will demonstrate their competence and confidence in applying them in a number of ways. For
example:

C  an they explain their thinking to show their understanding of number
processes and concepts?
 Are they developing securely the full range of the skills and attributes set
out within the experiences and outcomes? As they apply these to
problems, can they draw on skills and concepts learned previously?
A  s they tackle problems in unfamiliar contexts, can they confidently
identify which skills and concepts are relevant to the problem? Can they
then apply their skills accurately when working independently and with
others, and can they then evaluate their solutions?
 Are they developing their understanding of personal finance?
 Can they evaluate data to make informed decisions?
A  re they developing the capacity to engage with and complete tasks and
assignments?

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Assessment of numeracy across learning, within and outside the classroom, offers children and young people
opportunities to practise and extend their skills, for example within enterprise activities, social studies,
technologies and science.

Group Activity / Pair Activity 3.2:
1. Compile a list of learning activities that are suited for a Grade R class. The activities must be guided by
principles and process of guiding the numeracy learning programme.

3.3 (ac3) - Activities enable children to
appreciate mathematical relationships, logic and
pattern in number and space. 

What can learning in mathematics enable children and young people to achieve?
Mathematics is important in our everyday life, allowing us to make sense of the world around us and to
manage our lives. Using mathematics enables us to model real-life situations and make connections and
informed predictions. It equips us with the skills we need to interpret and analyse information, simplify and
solve problems, assess risk and make informed decisions.
Mathematics plays an important role in areas such as science or technologies, and is vital to research and
development in fields such as engineering, computing science, medicine and finance. Learning mathematics
gives children and young people access to the wider curriculum and the opportunity to pursue further studies
and interests.
Because mathematics is rich and stimulating, it engages and fascinates learners of all ages, interests and
abilities. Learning mathematics develops logical reasoning, analysis, problem-solving skills, creativity and the
ability to think in abstract ways. It uses a universal language of numbers and symbols which allows us to
communicate ideas in a concise, unambiguous and rigorous way.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

To face the challenges of the 21st century, each young person needs to have confidence in using mathematical
skills, and Scotland needs both specialist mathematicians and a highly numerate population.

Mathematics equips us with many of the skills required for life, learning and work. Understanding the part that
mathematics plays in almost all aspects of life is crucial. This reinforces the need for mathematics to play an
integral part in lifelong learning and be appreciated for the richness it brings.

How is the mathematics framework structured?

Within the mathematics framework, some statements of experiences and outcomes are also identified as
statements of experiences and outcomes in numeracy. These form an important part of the mathematics
education of all children and young people as they include many of the numerical and analytical skills required
by each of us to function effectively and successfully in everyday life. All teachers with a responsibility for the
development of mathematics will be familiar with the role of numeracy within mathematics and with the
means by which numeracy is developed across the range of learning experiences. The numeracy subset of the
mathematics experiences and outcomes is also published separately; further information can be found in the
numeracy principles and practice paper.

The mathematics experiences and outcomes are structured within three main organisers, each of which
contains a number of subdivisions:

Number, money and measure

E  stimation and rounding
 Number and number processes
M  ultiples, factors and primes
 Powers and roots
 Fractions, decimal fractions and percentages
 Money
 Time
 Measurement
M  athematics – its impact on the world, past, present and future
 Patterns and relationships
 Expressions and equations.

Shape, position and movement

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

 Properties of 2D shapes and 3D objects
 Angle, symmetry and transformation.

Information handling

 Data and analysis
 Ideas of chance and uncertainty.

The mathematics framework as a whole includes a strong emphasis on the important part mathematics has
played, and will continue to play, in the advancement of society, and the relevance it has for daily life.

A key feature of the mathematics framework is the development of algebraic thinking from an early stage.
Research shows that the earlier algebraic thinking is introduced, the deeper the mathematical understanding
will be and the greater the confidence in using mathematics.

Teachers will use the statements of experiences and outcomes in information handling to emphasise the
interpretation of statistical information in the world around us and to emphasise the knowledge and skills
required to take account of chance and uncertainty when making decisions.

What are the features of effective learning and teaching in mathematics?

From the early stages onwards, children and young people should experience success in mathematics and
develop the confidence to take risks, ask questions and explore alternative solutions without fear of being
wrong. They will enjoy exploring and applying mathematical concepts to understand and solve problems,
explaining their thinking and presenting their solutions to others in a variety of ways. At all stages, an emphasis
on collaborative learning will encourage children to reason logically and creatively through discussion of
mathematical ideas and concepts.

Through their use of effective questioning and discussion, teachers will use misconceptions and wrong
answers as opportunities to improve and deepen children’s understanding of mathematical concepts.

The experiences and outcomes encourage learning and teaching approaches that challenge and stimulate
children and young people and promote their enjoyment of mathematics. To achieve this, teachers will use a
skilful mix of approaches, including:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

P  lanned active learning which provides opportunities to observe, explore,
investigate, experiment, play, discuss and reflect
M  odelling and scaffolding the development of mathematical thinking
skills
L  earning collaboratively and independently
O  pportunities for discussion, communication and explanation of thinking
 Developing mental agility
U  sing relevant contexts and experiences, familiar to young people
M  aking links across the curriculum to show how mathematical concepts
are applied in a wide range of contexts, such as those provided by
science and social studies
 Using technology in appropriate and effective ways
 Building on the principles of assessment is for learning, ensuring that
young people understand the purpose and relevance of what they are
learning
D  eveloping problem-solving capabilities and critical thinking skills.

Mathematics is at its most powerful when the knowledge and understanding that have been developed are
used to solve problems. Problem solving will be at the heart of all our learning and teaching. We should
regularly encourage children and young people to explore different options: ‘what would happen if...?’ is the
fundamental question for teachers and learners to ask as mathematical thinking develops.

Examples of logic games that kids can engage in Alphabet Numbers Puzzle

The Puzzle:

Given only one of each letter in the alphabet, what are
the smallest and largest numbers that you could write down?

12 Days of Christmas Puzzle

The Puzzle:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

According to the traditional song, on the first day of Christmas (25th December), my true love sent to me:
A partridge in a pair tree
On the second day of Christmas (26th December), my true love sent to me THREE presents:
Two turtle doves
A partridge in a pear tree
On the third day of Christmas (27th December and so on) my true love sent to me SIX presents:
Three French hens
Two turtle doves
A partridge in a pear tree
This carries on until the twelfth day of Christmas, when my true love sends me:
Twelve drummers drumming
Eleven pipers piping
Ten lords a-leaping
Nine ladies dancing
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five gold rings
Four calling birds
Three French hens
Two turtle doves
A partridge in a pear tree
After the twelve days of Christmas are over, how many presents has my true love sent me altogether?

Group Activity / Pair Activity 3.3:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

1. Design a list of fun question and activities that are involving for kids such as puzzles, quiz, etc and make
them useful in mathematics or numeracy context.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

3.4 (ac4) - Activities enable children to develop
an appreciation of simple economic principles
and technological processes based on their
everyday experience. 

Principles of Economics

Clarification and Proposal In the beginning there is Econ 101 that introduces students to the "Principles of
Economics". Many introductory textbooks use this term in their title (see e.g. the widely used books by Gregory
Mankiw and by Frank & Bernake). There appear to exists several dozens of books with this title. .

Not surprisingly, the meaning of the term "Principles of Economics" varies. There are two main concepts of
"Principles":

 Economic Principles*, referring to the idea of "principles of economic life".
Mankiw's list of 10 principles (below) is a good example of this notion.
These are principles of how the economy works (or should work), hence,
they refer to the economy or economic actors. They are thought to
parallel the principles or laws in natural science.
P  rinciples of Economics, referring to the basic methods and concepts
economists use when doing economics, hence to economic analysis. In
this view the term "economics" refers to the discipline, not to the
economy. This type of principles is often interwoven with the first type in
the textbooks. Lists of principles of doing economics are harder to find. I
propose such a list below in order to clarify the basic concepts that make
up and shape the analysis and the thinking of economists.

*) Taken literally, the principles are not thought to be "economic" themselves --- though, of course, the
employment of "economic principles" can often be economical.

. Mankiw's "Ten Principles of Economics" -

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

.
How People Make Decisions

P  eople Face Tradeoffs. To get one thing, you have to give up something
else. Making decisions requires trading off one goal against another. 
T  he Cost of Something is What You Give Up to Get It. Decision-makers
have to consider both the obvious and implicit costs of their actions. 
 Rational People Think at the Margin. A rational decision-maker takes
action if and only if the marginal benefit of the action exceeds the
marginal cost. 
P  eople Respond to Incentives. Behaviour changes when costs or benefits
change. 

How the Economy Works as A Whole

 Trade Can Make Everyone Better Off. Trade allows each person to
specialize in the activities he or she does best. By trading with others,
people can buy a greater variety of goods or services. 
 Markets Are Usually a Good Way to Organize Economic Activity.
Households and firms that interact in market economies act as if they are
guided by an "invisible hand" that leads the market to allocate resources
efficiently. The opposite of this is economic activity that is organized by a
central planner within the government. 
G  overnments Can Sometimes Improve Market Outcomes. When a
market fails to allocate resources efficiently, the government can change
the outcome through public policy. Examples are regulations against
monopolies and pollution. 

How People Interact

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

 A Country's Standard of Living Depends on Its Ability to Produce Goods
and Services. Countries whose workers produce a large quantity of
goods and services per unit of time enjoy a high standard of living.
Similarly, as a nation's productivity grows, so does its average income.
P  rices Rise When the Government Prints Too Much Money. When a
government creates large quantities of the nation's money, the value of
the money falls. As a result, prices increase, requiring more of the same
money to buy goods and services. 
 Society Faces a Short-Run Tradeoff Between Inflation and
Unemployment. Reducing inflation often causes a temporary rise in
unemployment. This tradeoff is crucial for understanding the short-run
effects of changes in taxes, government spending and monetary policy.  

. Slembeck's "Ten Principles of Economics (as a Discipline)" . .

S  carcity: Economists study situations where needs or wants exceed
means. Therefore, people have to make choices.
R  ationality is assumed to guide people's choices or decisions. They
systematically gauge all pros (benefit or "utility") and cons ("cost") of all
alternatives or options they are facing when deciding. 
P  references: People are equipped with fixed and given preferences that
allow them to assign utilities to all options, and to choose the option that
maximizes (net) utility.
 Restrictions: People faces constrain that they cannot change themselves,
and thus have to take as given (such as budgets, input cost etc.).
Maximization is always constraint by restrictions.

Combining the first four points makes up for the "rational choice approach" of neoclassical economics.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

 Opportunity Cost is induced by scarcity, and by the need to make
choices. All choices always involve opportunity cost because deciding in
favor of one option always means deciding against some other option(s).
There are two main aspects of opportunity cost: 1) Utility maximizing
choices induce opportunity cost to be minimal (static aspect). 2) Choices
may be revised when opportunity cost rises (dynamic aspect).
T  he Economic Principle is the application of rationality to situations of
scarcity: Minimize cost with regard to a given goal (e.g., level of utility) OR
maximize utility for a given level of cost or input. Hence the "economic
principle" frames situations as a minimizing or a maximizing problem, and
allows assessing efficiency. Do not mix the two formulations! Applying
the principle avoids wasting valuable resources.
 Efficiency of activities, rules, transactions or distributions is a basic theme
in economic analysis. Efficiency is most often assessed either in terms of
the economic principle (minimize cost or maximize utility) or the Pareto
criterion (with regard to transactions and distributions).
M  arginal Analysis is a typical way for economists to look at problems.
They analyze decisions in terms of marginal benefits and marginal costs.
Marginal thinking is rather uncommon among non-economists, however.
 Equilibrium is a fundamental notion in economic analysis. Basic
economic models deal with the comparison of two (or possibly more)
equilibria (comparative statics). Economist think in terms of equilibria,
which are situations where no one has an incentive to change his or her
behaviour. The Nash equilibrium is the most fundamental formulation of
the concept of equilibrium as used in economics.
G  ame Theory is an approach to study situations of interdependence
where people have incentives to think and behave strategically.

How to Teach Economics to Kids

A solid grasp of the basic economic concepts can be of great help to kids.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Teaching economics to children can be challenging, but it is an important undertaking. It is essential for every
child to learn the basics of economics, such as the spending, earning and saving of money. A good way to
teach economic lessons to kids is to start with the bare fundamentals and add on to their knowledge as they
get older. So, while they can move on to the more complicated topics at a later stage, it can be of great help to
give them a solid grasp of the basic concepts earlier.
Explain the concept of money to children. They should know what each piece of money is called and what it is
worth. Learning how to count money is also an important part of the lesson. Giving each child either real
money or fake money to count is a good way to teach them the basics of money and its worth.
Earning money is something every child should learn. By teaching them the concept of getting a job or getting
an allowance, they will be able to understand how important earning money is. Give the children opportunities
throughout each week to earn fake money in the classroom for doing good deeds.
Saving money is as important as earning money. Give children the basic concept of saving money by
demonstrating the use of a piggy bank. The fake money children earn throughout the week can be saved in a
"piggy bank" that each child has.
Spending money is the fun part of having money. It is important, however, to teach the children how to spend
wisely. At the end of each week, the classroom can have a store to redeem their fake money for tangible items.
This can also be combined with saving money, such as when a child wants a certain item, they need to save
their money up until they can afford it.
How to Teach Students Basic Economics

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Focus on teaching your students the practical application of the concepts of economics.
Economics is not just about equations and manipulation of numbers. It is important for students to learn
economics as a practical application of certain basic laws that govern the various aspects of daily life. Through
the use of activities such as role play and group projects, you can teach students the fundamental concepts of
economics such as trade, savings and other financial transactions. Although specific activities will need to be
modified to match requirements of different age groups, making these interesting is key to promote
understanding.
Teach about trade through the concept of the value of an item. Divide children into groups of five and give
each group an object, preferably different ones. Ask groups to trade by persuading another group to exchange
their objects. Have a group try to force another group to part with their article. Discuss observations on how a
group decided which group to trade with and what sentiments the forced trading evoked. Explain how trade
implies giving up something to get something in return.
Explain about prices and demands by holding an auction in the classroom. Describe what an auction means
and how the process works. Bring some knick knacks to the class and put those up for bidding. Hand out
different amounts of plastic money to each group. Start off with a small price and ask groups to bid depending
on the amounts they have. Remind them to plan correctly so that they have enough money to get more than
one object. Give groups the option of not bidding on items they don't wish to have. Discuss the results of this
auction and point out how items sell for greater price when there are more people wanting them -- that is,
when demand is high.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Teach about money management by mapping income and expense. Ask them to list their allowances and any
wages they receive from running errands and calculate their total income. Have children prepare a list of items
they spend on and calculate their total expenses. Use this activity to conduct a discussion about the difference
between needs and wants. Explain how distinguishing between the two will help them save money for
something more valuable.
Use the resources available on websites of the Council for Economic Education, California State University
Northridge and James Madison University to develop lesson plans that teach a practical application of
economic concepts.
Encourage an interest in economics by carrying out classroom economic projects that involve actual planning
and execution of a business. For example, with lower classes, have the children set up a lemonade stand. With
older kids, try ideas such as a food outlet.
How to Teach Basic Economics

Teaching basic economic theory may help students make wise financial decisions in the future.
Understanding economic theory is becoming increasingly important for preparing students to make wise
financial decisions for the future. Many states, such as Virginia, have added economic standards for education
in recent years. These standards provide a framework for understanding which economic theories are
necessary for students to learn before they graduate. Teachers can use these guides to determine which basic
economic theories are essential to understand the overall concepts and find ways to introduce them to
students that are engaging and memorable.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Consult your curriculum guide to see if your state or district has already laid out basic economic concepts for
you to teach. For example, teachers in Virginia are asked to teach students about scarcity, resources, choice,
opportunity cost, price, incentives, supply and demand, production and consumption. If your state or district
has not laid out standards for economics, consult the standards from other states or districts for ideas for how
to group your instruction.

Break up the concepts into instructional units so that students acquire similar ideas on similar days. For
example, a teacher in Virginia might break up the above concepts into three classes. On day one, she could
teach students about scarcity, resources, production and consumption. On day two, she could teach about
choice and opportunity cost, and on day three she could teach about supply and demand, price and
incentives.

Start with basic vocabulary and give students’ examples for how these concepts are applied in real life. For
example, LD Online suggests having students draw pictures or write sentences to summarize the meaning of
new vocabulary words. The website suggests finding multiple ways to teach the words in context and ask
students to come up with real world examples to make new vocabulary stick. This is important for economics
so that students can see how theories apply in real life.

Use simulations to help students experience economic theories. For example, you might play musical chairs to
help students understand the concept of scarcity. The Foundation for Teaching Economics includes many
resources for incorporating economic simulations into classroom instruction, as well as ideas for introducing
and debriefing the simulations

Assess student learning throughout classroom activities and after classroom instruction to ensure that
students have acquired the basic theories and are ready to move on to more advanced material. For example,
after conducting the game of musical chairs, the teacher might ask students to make a list of ways that scarcity
affects them at home or at school. She might then come back to the concept of scarcity when discussing how
governments make decisions about what to buy as part of her lesson on opportunity cost.

How to Use Technology in Teaching Preschool

Young children should have technology experience.

In today's world, it is imperative that educators keep students engaged and incorporate opportunities for
exposure and proficiency with technology. This exposure should begin as early as preschool so that students
are prepared for Smart classrooms and individual computer activities that may be encountered during the
course of their education.

Join the preschooler at the computer and use it as a time to share the functions of the keyboard, mouse,
monitor and tower, as well as how to click and drag. Also, allow the child to watch while you are active at the
computer, allowing him to become more comfortable with using the computer on his own.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Use a word processing program to allow the child to familiarize her with the keyboard, while learning the
letters of the alphabet and the numbers. This activity also helps the student become aware of concepts of
print, since the typed font will go across the screen from left to right just as the words in a storybook.
Locate online storybook websites that read the words of the stories to the students and only require a click of
an arrow to advance the pages. Sit with the child while going through the story and ask meaningful questions
that provide the opportunity for critical thinking, building comprehension skills, and characterization skills.
Acquire old cell phones and teach the preschooler how to use the keypad to dial 911 and their home phone
number during a unit on safety. Allow the students’ time to practice dialling the numbers on the phone.
Locate websites that contain age-appropriate math and reading games that the child can play independently.
Allow the students to work in pairs to play the games, so that they are able to have assistance with the
technology, if needed.

Group Activity / Pair Activity 3.4:
1. Define economic principles
2. List and explain any 5 economic principles.
3. Demonstrate how you can apply economic principles to children daily lives through a learning
programme.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

3.5 (ac5) - Activities and materials to are culture-
fair and promote an anti-bias approach. 

Culture Fair Intelligence Test
Eine Beispielaufgabe aus den Coloured Progressive Matrices von John C. Raven

Culture Fair Intelligence Test (CFIT) (zu Deutsch: „Kulturell fairer Intelligenztest“) ist eine Bezeichnung für eine
Form von Intelligenztests, bei denen Menschen aus unterschiedlichen Kulturen (z. B. Amazonas-Bewohner und
Mitteleuropäer) bzw. sozialen Schichten innerhalb von Gesellschaften (z.  B. Akademiker und Handwerker)
Chancengleichheit besitzen sollen (d.  h. bei gleichen Fähigkeiten gleiche Ergebnisse zu erzielen). Dies wird
dadurch versucht, dass Sprache an sich und Kulturtechniken wie Lesen oder Mathematik keine Rolle spielen
sollen bei der Bearbeitung des Tests.
In der Regel handelt es sich bei Culture-Fair-Tests einfach um sprach- und zahlenfreie Intelligenztests zum
logischen Denken. Die bekanntesten Culture Fair Intelligence Tests sind

d  er „Culture Fair Test I“ von Raymond Bernard Cattell
d  ie sog. „Ravens progressive Matrizentests“: („Standard Progressive
Matrices“ bzw. „Coloured Progressive Matrices“) von John C. Raven

ECD NQF 4 - Student Guide Knowledge Module 2