UNIVERSITY OF SOUTH AFRICA
Department of Early Childhood Education and Development
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
EMA1501: Emergent Mathematics
Assessment 2 — Year Module, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
EMA1501
Module Code:
Emergent Mathematics
Module Name:
Assessment 2
Assessment:
2
Assignment Number:
June 2026
Due Date:
100
Total Marks:
Submitted in partial fulfilment of the require-
ments for Emergent Mathematics — UNISA 2026
,UNISA | EMA1501 Assessment 2 — 2026
Question 1: Mathematical Concepts in Playground Activities
1.1 Five Mathematical Concepts from the Playground Activity (5 marks)
Question: Analyse any five mathematical concepts that can be developed from the play-
ground activities described in the case study.
The playground scenario in the Dolphin class offers a rich context for emergent mathematical
learning. Mathematical knowledge starts during infancy and undergoes extensive development
over the first five years of life; it is just as natural for young children to think mathemati-
cally as it is for them to use language (Clements, Sarama and DiBiase, 2004, as cited in Geist,
2009). The five mathematical concepts evident in the case study are:
1. Counting and Number Sense – The children count 20 learners, 5 balls, 10 skipping
ropes, 5 tins, and 20 wooden blocks. They also count backwards while jumping back
to the starting point. These activities build one-to-one correspondence and cardinality
(Bezuidenhout, 2022).
2. Measurement and Size Comparison – The learners pick up five wooden blocks of
different sizes and place them inside a tin. Comparing the sizes of the blocks introduces
the concept of measurement through direct comparison, a foundational skill in the CAPS
Grade R curriculum (Department of Basic Education, 2011).
3. Sorting and Classification – By selecting five blocks of different sizes from a collection
of 20, the children implicitly sort and classify objects according to the attribute of size.
This is a core data-handling and patterning skill (Department of Basic Education, 2011).
4. Spatial Reasoning and Position – The children move over, around and back along a
path. They jump over the skipping ropes and navigate from one point to another, devel-
oping an understanding of positional language and direction (Gifford et al., 2022).
5. Pattern and Repetition – Each child rotates through the same sequence of actions:
pick up blocks, run, jump over ropes, place a block, return. This cyclical, repeated se-
quence forms a predictable pattern, which is central to algebraic thinking in emergent
mathematics (Geist, 2009).
1.2 Contribution of Each Concept to Logical Thinking (20 marks)
Question: Explain how each of the mathematical concepts you identified from the case study
will contribute towards logical thinking in emergent mathematics.
Page 2 of 16
,UNISA | EMA1501 Assessment 2 — 2026
Counting and Number Sense
When the Dolphin class children count objects in the basket and count backwards while jump-
ing, they are not simply reciting numbers. They are building the mental architecture for log-
ical sequencing. Counting demands that a child apply the logic of order: each number has a
specific place, and skipping one collapses the entire sequence. Selepe (2025) notes that young
children develop number sense through sensory and perceptual play by learning words and
interactively connecting meaning to those words, and by building hierarchically on previously
learnt concepts. This means that every time a child points to a ball and says “five,” they are
constructing a logical one-to-one relationship between a physical object and an abstract sym-
bol. Counting backwards, as required in the activity when returning to the starting point,
adds a further layer of logical reasoning because the child must reverse the sequence, which
requires mental flexibility and an understanding that number relationships work in both direc-
tions.
Measurement and Size Comparison
Selecting five blocks of different sizes requires that the children compare objects, make judge-
ments, and reason about what “bigger” and “smaller” mean in relation to one another. This
kind of direct comparison is the earliest form of measurement thinking, and it trains the brain
to evaluate relative quantities rather than absolute ones. According to the CAPS Foundation
Phase Mathematics document (Department of Basic Education, 2011), measurement in Grade
R centres on direct comparison using terms such as longer, shorter, heavier, and lighter. When
a child has to pick one large block and one small block and place them both in a tin, they
must reason about whether the objects will fit together, which introduces spatial logic. This
kind of comparative thinking is the seed from which more formal measurement skills grow.
Sorting and Classification
Sorting is an act of logical categorisation. When the children select blocks of different sizes,
they are making decisions based on an attribute, which is the defining move in logical classi-
fication. According to the CAPS Grade R document (Department of Basic Education, 2011),
learners should be able to sort objects according to attributes such as colour, shape, and size.
The logical thinking required here is a form of if-then reasoning: “if this block is the same size
as one I already picked, then I must put it back and choose another.” This kind of decision-
Page 3 of 16
,UNISA | EMA1501 Assessment 2 — 2026
making builds systematic, rule-based thinking that underpins later mathematical reasoning
in areas like algebra and set theory. Geist (2009, as cited in Clements, Sarama and DiBi-
ase, 2004) notes that activities integrating decision-making and the making of relationships
throughout the child’s day are the core goal of emergent mathematics.
Spatial Reasoning and Position
The physical movement through the obstacle of skipping ropes directly trains spatial reason-
ing. Children must track their own position relative to the ropes and other learners, decide
where to jump, and plan a path back to the starting point. Gifford et al. (2022) note that the
outdoor environment is well-suited to physical play and offers rich opportunities for children
to build mental maps of their surroundings. This mental mapping is logical thinking applied
to space. When a child knows they are “in front of” the tin and then moves “behind” the rope,
they are applying spatial logic, the same cognitive skill that later supports understanding of
geometry, coordinates, and even data graphs. Studies confirm that young children’s spatial
reasoning is a critical predictor of later mathematics performance, because thinking about the
positions of objects in space and their distance from one another lays foundations for measure-
ment concepts (Gifford et al., 2022).
Pattern and Repetition
The rotational structure of the activity is a repeating pattern. Each child completes the same
sequence: select five blocks, run to the tin, jump over the ropes, place a block by a group
member, return jumping. This repetition introduces the logical concept of regularity, the idea
that a rule governs what happens next. Logical thinking depends on the ability to predict
outcomes based on patterns, and this is precisely what children develop when they follow and
internalise a repeated sequence. Geist (2009) explains that rhythm and music allow children
to recognise mathematical patterns, and the same principle applies to physical movement
sequences. A child who can anticipate and follow a movement pattern is training the same
brain circuit that will later allow them to identify number patterns such as skip counting and
multiplication tables.
Page 4 of 16
, UNISA | EMA1501 Assessment 2 — 2026
Implementation Insight
In a South African Grade R classroom, outdoor play like the Dolphin class scenario
is not simply recreational. According to the CAPS Foundation Phase Mathematics
document (Department of Basic Education, 2011), mathematics content areas – includ-
ing numbers, patterns, shape, measurement, and data handling – must be introduced
through play-based activities. Every jump over a rope, every block placed by a friend,
and every backwards count is a structured mathematical experience.
Page 5 of 16
Department of Early Childhood Education and Development
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
EMA1501: Emergent Mathematics
Assessment 2 — Year Module, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
EMA1501
Module Code:
Emergent Mathematics
Module Name:
Assessment 2
Assessment:
2
Assignment Number:
June 2026
Due Date:
100
Total Marks:
Submitted in partial fulfilment of the require-
ments for Emergent Mathematics — UNISA 2026
,UNISA | EMA1501 Assessment 2 — 2026
Question 1: Mathematical Concepts in Playground Activities
1.1 Five Mathematical Concepts from the Playground Activity (5 marks)
Question: Analyse any five mathematical concepts that can be developed from the play-
ground activities described in the case study.
The playground scenario in the Dolphin class offers a rich context for emergent mathematical
learning. Mathematical knowledge starts during infancy and undergoes extensive development
over the first five years of life; it is just as natural for young children to think mathemati-
cally as it is for them to use language (Clements, Sarama and DiBiase, 2004, as cited in Geist,
2009). The five mathematical concepts evident in the case study are:
1. Counting and Number Sense – The children count 20 learners, 5 balls, 10 skipping
ropes, 5 tins, and 20 wooden blocks. They also count backwards while jumping back
to the starting point. These activities build one-to-one correspondence and cardinality
(Bezuidenhout, 2022).
2. Measurement and Size Comparison – The learners pick up five wooden blocks of
different sizes and place them inside a tin. Comparing the sizes of the blocks introduces
the concept of measurement through direct comparison, a foundational skill in the CAPS
Grade R curriculum (Department of Basic Education, 2011).
3. Sorting and Classification – By selecting five blocks of different sizes from a collection
of 20, the children implicitly sort and classify objects according to the attribute of size.
This is a core data-handling and patterning skill (Department of Basic Education, 2011).
4. Spatial Reasoning and Position – The children move over, around and back along a
path. They jump over the skipping ropes and navigate from one point to another, devel-
oping an understanding of positional language and direction (Gifford et al., 2022).
5. Pattern and Repetition – Each child rotates through the same sequence of actions:
pick up blocks, run, jump over ropes, place a block, return. This cyclical, repeated se-
quence forms a predictable pattern, which is central to algebraic thinking in emergent
mathematics (Geist, 2009).
1.2 Contribution of Each Concept to Logical Thinking (20 marks)
Question: Explain how each of the mathematical concepts you identified from the case study
will contribute towards logical thinking in emergent mathematics.
Page 2 of 16
,UNISA | EMA1501 Assessment 2 — 2026
Counting and Number Sense
When the Dolphin class children count objects in the basket and count backwards while jump-
ing, they are not simply reciting numbers. They are building the mental architecture for log-
ical sequencing. Counting demands that a child apply the logic of order: each number has a
specific place, and skipping one collapses the entire sequence. Selepe (2025) notes that young
children develop number sense through sensory and perceptual play by learning words and
interactively connecting meaning to those words, and by building hierarchically on previously
learnt concepts. This means that every time a child points to a ball and says “five,” they are
constructing a logical one-to-one relationship between a physical object and an abstract sym-
bol. Counting backwards, as required in the activity when returning to the starting point,
adds a further layer of logical reasoning because the child must reverse the sequence, which
requires mental flexibility and an understanding that number relationships work in both direc-
tions.
Measurement and Size Comparison
Selecting five blocks of different sizes requires that the children compare objects, make judge-
ments, and reason about what “bigger” and “smaller” mean in relation to one another. This
kind of direct comparison is the earliest form of measurement thinking, and it trains the brain
to evaluate relative quantities rather than absolute ones. According to the CAPS Foundation
Phase Mathematics document (Department of Basic Education, 2011), measurement in Grade
R centres on direct comparison using terms such as longer, shorter, heavier, and lighter. When
a child has to pick one large block and one small block and place them both in a tin, they
must reason about whether the objects will fit together, which introduces spatial logic. This
kind of comparative thinking is the seed from which more formal measurement skills grow.
Sorting and Classification
Sorting is an act of logical categorisation. When the children select blocks of different sizes,
they are making decisions based on an attribute, which is the defining move in logical classi-
fication. According to the CAPS Grade R document (Department of Basic Education, 2011),
learners should be able to sort objects according to attributes such as colour, shape, and size.
The logical thinking required here is a form of if-then reasoning: “if this block is the same size
as one I already picked, then I must put it back and choose another.” This kind of decision-
Page 3 of 16
,UNISA | EMA1501 Assessment 2 — 2026
making builds systematic, rule-based thinking that underpins later mathematical reasoning
in areas like algebra and set theory. Geist (2009, as cited in Clements, Sarama and DiBi-
ase, 2004) notes that activities integrating decision-making and the making of relationships
throughout the child’s day are the core goal of emergent mathematics.
Spatial Reasoning and Position
The physical movement through the obstacle of skipping ropes directly trains spatial reason-
ing. Children must track their own position relative to the ropes and other learners, decide
where to jump, and plan a path back to the starting point. Gifford et al. (2022) note that the
outdoor environment is well-suited to physical play and offers rich opportunities for children
to build mental maps of their surroundings. This mental mapping is logical thinking applied
to space. When a child knows they are “in front of” the tin and then moves “behind” the rope,
they are applying spatial logic, the same cognitive skill that later supports understanding of
geometry, coordinates, and even data graphs. Studies confirm that young children’s spatial
reasoning is a critical predictor of later mathematics performance, because thinking about the
positions of objects in space and their distance from one another lays foundations for measure-
ment concepts (Gifford et al., 2022).
Pattern and Repetition
The rotational structure of the activity is a repeating pattern. Each child completes the same
sequence: select five blocks, run to the tin, jump over the ropes, place a block by a group
member, return jumping. This repetition introduces the logical concept of regularity, the idea
that a rule governs what happens next. Logical thinking depends on the ability to predict
outcomes based on patterns, and this is precisely what children develop when they follow and
internalise a repeated sequence. Geist (2009) explains that rhythm and music allow children
to recognise mathematical patterns, and the same principle applies to physical movement
sequences. A child who can anticipate and follow a movement pattern is training the same
brain circuit that will later allow them to identify number patterns such as skip counting and
multiplication tables.
Page 4 of 16
, UNISA | EMA1501 Assessment 2 — 2026
Implementation Insight
In a South African Grade R classroom, outdoor play like the Dolphin class scenario
is not simply recreational. According to the CAPS Foundation Phase Mathematics
document (Department of Basic Education, 2011), mathematics content areas – includ-
ing numbers, patterns, shape, measurement, and data handling – must be introduced
through play-based activities. Every jump over a rope, every block placed by a friend,
and every backwards count is a structured mathematical experience.
Page 5 of 16
