UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Education – Department of Mathematics Education
⋄
ASSIGNMENT 3
Year Module – 2026
⋄
Module Code: TMN3704
Module Name: Teaching Mathematics in the Intermediate
Phase
Assignment No.: 3 (Compulsory)
Unique Number: 638428
Due Date: 8 July 2026
Year: 2026
Submitted in partial fulfilment of the requirements for Teaching Mathematics in the
Intermediate Phase
at the University of South Africa.
,UNISA | TMN3704 Teaching Mathematics – Assignment 3
Contents
1 Activity 1: Defining 2D Shapes and Curriculum Analysis 3
1.1 1.1 Definition of 2D Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 1.2 Two Key Concepts from the Definition of 2D Shapes . . . . . . . . . 3
1.2.1 Key Concept 1: Plane (Flat Surface) . . . . . . . . . . . . . . . . . . 3
1.2.2 Key Concept 2: Boundary (Sides and Angles) . . . . . . . . . . . . 4
1.3 1.3 CAPS Curriculum Requirements for Grade 5 . . . . . . . . . . . . . . 4
1.3.1 1.3.1 Term Placement of “Properties of 2D Shapes” in Grade 5 . 4
1.3.2 1.3.2 Time Allocation for “Properties of 2D Shapes” in Grade 5 . 5
2 Activity 2: Lesson Planning – Aim, Objectives, and Prior Knowledge 6
2.1 2.1 Aim of the Lesson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 2.2 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 2.3 Prior Knowledge Required for Angles Smaller than Right Angles . 7
3 Activity 3: Introduction of the Lesson on Angles Greater than Right Angles 8
4 Activity 4: Teaching Fractions Using a Fraction Wall 10
4.1 4.1 Two Key Concepts for Understanding Fractions . . . . . . . . . . . . . 10
4.1.1 Key Concept 1: Part-Whole Relationship . . . . . . . . . . . . . . . 10
4.1.2 Key Concept 2: Equivalent Fractions . . . . . . . . . . . . . . . . . . 10
4.2 4.2 Two Learning Approaches for Teaching Fractions . . . . . . . . . . . . 11
4.2.1 Learning Approach 1: Constructivist / Discovery Learning Approach 11
4.2.2 Learning Approach 2: Problem-Based Learning (PBL) . . . . . . 11
4.3 4.3 Assessment Questions for Each Key Concept . . . . . . . . . . . . . . 12
Page 1 of 20
,UNISA | TMN3704 Teaching Mathematics – Assignment 3
4.3.1 Assessment Questions for Key Concept 1: Part-Whole Relation-
ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3.2 Assessment Questions for Key Concept 2: Equivalent Fractions . 13
4.4 4.4 Analytical Rubric for Assessing Fractions Tasks . . . . . . . . . . . . . 13
5 Activity 5: Inquiry Investigation – Properties of a Rectangle (Grade 6) 14
5.1 Overview and Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2 Important Idea 1: Opposite Sides Are Equal in Length . . . . . . . . . . 15
5.3 Important Idea 2: All Four Angles Are Right Angles . . . . . . . . . . . . 16
5.4 Important Idea 3: Diagonals Are Equal in Length and Bisect Each Other 16
5.5 Important Idea 4: A Square Is a Special Rectangle . . . . . . . . . . . . . 17
5.6 Important Idea 5: Perimeter and Area Are Related but Distinct Prop-
erties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.7 Conclusion of Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Reference List 20
Page 2 of 20
,UNISA | TMN3704 Teaching Mathematics – Assignment 3
Activity 1: Defining 2D Shapes and Curriculum Analysis
The concept of two-dimensional (2D) shapes forms a foundational pillar within the Space and
Shape content area of Intermediate Phase mathematics. The Department of Basic Educa-
tion (2011) frames the study of space and shape as an area that moves learners from recog-
nition and simple description toward classification and more detailed description of charac-
teristics and properties. Each sub-activity below engages with the definition, key conceptual
components, and curriculum requirements prescribed in the Curriculum and Assessment Pol-
icy Statement (CAPS).
1.1 Definition of 2D Shapes
A two-dimensional (2D) shape is a flat, plane figure that exists in only two dimensions: length
and width. It has no depth or thickness. The boundaries of a 2D shape are defined by straight
or curved lines, and the interior of the shape occupies a measurable area within a flat plane. A
2D shape is fully described by the properties of its sides (number, length, and orientation), its
angles (the turns formed where sides meet), and its overall geometric classification. Examples
include squares, rectangles, triangles, circles, pentagons, and hexagons (Department of Basic
Education, 2011). Unlike three-dimensional (3D) objects, which have volume and can be held
in the hand, 2D shapes are representations on a flat surface and are perceptible only in terms
of their surface area and perimeter.
Key Distinction
2D Shapes vs. 3D Objects: A 2D shape such as a square occupies area on a flat
plane and has only length and width. A 3D object such as a cube has length, width,
and height, and therefore has volume. In classroom teaching, this distinction is cru-
cial because learners must not confuse the face of a 3D object with an independent 2D
shape (Department of Basic Education, 2011).
1.2 Two Key Concepts from the Definition of 2D Shapes
Key Concept 1: Plane (Flat Surface)
The term plane refers to a flat, two-dimensional surface that extends infinitely in all directions
but has no depth. In the context of 2D shapes, the plane is the surface on which the shape re-
Page 3 of 20
, UNISA | TMN3704 Teaching Mathematics – Assignment 3
sides. For Grade 5 learners, the plane is most tangibly represented by the surface of a piece of
paper, a tabletop, or a drawn grid. The significance of this concept lies in the fact that it dis-
tinguishes 2D shapes from their 3D counterparts. A shape is “flat” because all of its points lie
within the same plane. Without an understanding of what a plane is, learners struggle to con-
ceptualise why a triangle drawn on paper differs from a triangular prism built from cardboard.
Van de Walle, Karp and Bay-Williams (2016) argue that spatial reasoning in young learners
develops through concrete engagement with flat and solid forms, and that the explicit com-
parison of planar figures with three-dimensional objects accelerates geometric understanding.
Teaching the concept of a plane through physical manipulation, for instance by having learn-
ers press shapes onto paper and observe that the resulting print is flat, gives the abstract idea
a tangible grounding.
Key Concept 2: Boundary (Sides and Angles)
The boundary of a 2D shape refers to the lines, whether straight or curved, that enclose the
shape and separate its interior from the space outside it. The boundary is composed of sides
(straight line segments) in polygons, or a single continuous curve in the case of a circle. Where
two sides of a polygon meet, they form an angle, which is the measure of the turn between the
two sides. In the CAPS document for Grade 5, learners are required to recognise and describe
right angles, angles smaller than right angles, and angles greater than right angles as specific
properties of 2D shapes (Department of Basic Education, 2011). An understanding of bound-
aries is therefore essential because it forms the entry point into angle recognition. Crowley
(1987), as cited by researchers applying the van Hiele model, notes that at Level 1 (Analysis),
learners begin to identify shapes by their properties rather than their overall appearance, and
properties are primarily communicated through the boundaries and the angles those bound-
aries create. A learner who cannot identify the boundary of a shape cannot begin to count its
sides or classify its angles.
1.3 CAPS Curriculum Requirements for Grade 5
1.3.1 Term Placement of “Properties of 2D Shapes” in Grade 5
According to the CAPS Intermediate Phase Mathematics document (Department of Basic Ed-
ucation, 2011), the topic “Properties of 2D Shapes” is taught in Terms 1 and 3 of Grade 5.
In Term 1, the focus is on recognising, visualising, and naming 2D shapes, including polygons
Page 4 of 20
College of Education – Department of Mathematics Education
⋄
ASSIGNMENT 3
Year Module – 2026
⋄
Module Code: TMN3704
Module Name: Teaching Mathematics in the Intermediate
Phase
Assignment No.: 3 (Compulsory)
Unique Number: 638428
Due Date: 8 July 2026
Year: 2026
Submitted in partial fulfilment of the requirements for Teaching Mathematics in the
Intermediate Phase
at the University of South Africa.
,UNISA | TMN3704 Teaching Mathematics – Assignment 3
Contents
1 Activity 1: Defining 2D Shapes and Curriculum Analysis 3
1.1 1.1 Definition of 2D Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 1.2 Two Key Concepts from the Definition of 2D Shapes . . . . . . . . . 3
1.2.1 Key Concept 1: Plane (Flat Surface) . . . . . . . . . . . . . . . . . . 3
1.2.2 Key Concept 2: Boundary (Sides and Angles) . . . . . . . . . . . . 4
1.3 1.3 CAPS Curriculum Requirements for Grade 5 . . . . . . . . . . . . . . 4
1.3.1 1.3.1 Term Placement of “Properties of 2D Shapes” in Grade 5 . 4
1.3.2 1.3.2 Time Allocation for “Properties of 2D Shapes” in Grade 5 . 5
2 Activity 2: Lesson Planning – Aim, Objectives, and Prior Knowledge 6
2.1 2.1 Aim of the Lesson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 2.2 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 2.3 Prior Knowledge Required for Angles Smaller than Right Angles . 7
3 Activity 3: Introduction of the Lesson on Angles Greater than Right Angles 8
4 Activity 4: Teaching Fractions Using a Fraction Wall 10
4.1 4.1 Two Key Concepts for Understanding Fractions . . . . . . . . . . . . . 10
4.1.1 Key Concept 1: Part-Whole Relationship . . . . . . . . . . . . . . . 10
4.1.2 Key Concept 2: Equivalent Fractions . . . . . . . . . . . . . . . . . . 10
4.2 4.2 Two Learning Approaches for Teaching Fractions . . . . . . . . . . . . 11
4.2.1 Learning Approach 1: Constructivist / Discovery Learning Approach 11
4.2.2 Learning Approach 2: Problem-Based Learning (PBL) . . . . . . 11
4.3 4.3 Assessment Questions for Each Key Concept . . . . . . . . . . . . . . 12
Page 1 of 20
,UNISA | TMN3704 Teaching Mathematics – Assignment 3
4.3.1 Assessment Questions for Key Concept 1: Part-Whole Relation-
ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3.2 Assessment Questions for Key Concept 2: Equivalent Fractions . 13
4.4 4.4 Analytical Rubric for Assessing Fractions Tasks . . . . . . . . . . . . . 13
5 Activity 5: Inquiry Investigation – Properties of a Rectangle (Grade 6) 14
5.1 Overview and Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2 Important Idea 1: Opposite Sides Are Equal in Length . . . . . . . . . . 15
5.3 Important Idea 2: All Four Angles Are Right Angles . . . . . . . . . . . . 16
5.4 Important Idea 3: Diagonals Are Equal in Length and Bisect Each Other 16
5.5 Important Idea 4: A Square Is a Special Rectangle . . . . . . . . . . . . . 17
5.6 Important Idea 5: Perimeter and Area Are Related but Distinct Prop-
erties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.7 Conclusion of Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Reference List 20
Page 2 of 20
,UNISA | TMN3704 Teaching Mathematics – Assignment 3
Activity 1: Defining 2D Shapes and Curriculum Analysis
The concept of two-dimensional (2D) shapes forms a foundational pillar within the Space and
Shape content area of Intermediate Phase mathematics. The Department of Basic Educa-
tion (2011) frames the study of space and shape as an area that moves learners from recog-
nition and simple description toward classification and more detailed description of charac-
teristics and properties. Each sub-activity below engages with the definition, key conceptual
components, and curriculum requirements prescribed in the Curriculum and Assessment Pol-
icy Statement (CAPS).
1.1 Definition of 2D Shapes
A two-dimensional (2D) shape is a flat, plane figure that exists in only two dimensions: length
and width. It has no depth or thickness. The boundaries of a 2D shape are defined by straight
or curved lines, and the interior of the shape occupies a measurable area within a flat plane. A
2D shape is fully described by the properties of its sides (number, length, and orientation), its
angles (the turns formed where sides meet), and its overall geometric classification. Examples
include squares, rectangles, triangles, circles, pentagons, and hexagons (Department of Basic
Education, 2011). Unlike three-dimensional (3D) objects, which have volume and can be held
in the hand, 2D shapes are representations on a flat surface and are perceptible only in terms
of their surface area and perimeter.
Key Distinction
2D Shapes vs. 3D Objects: A 2D shape such as a square occupies area on a flat
plane and has only length and width. A 3D object such as a cube has length, width,
and height, and therefore has volume. In classroom teaching, this distinction is cru-
cial because learners must not confuse the face of a 3D object with an independent 2D
shape (Department of Basic Education, 2011).
1.2 Two Key Concepts from the Definition of 2D Shapes
Key Concept 1: Plane (Flat Surface)
The term plane refers to a flat, two-dimensional surface that extends infinitely in all directions
but has no depth. In the context of 2D shapes, the plane is the surface on which the shape re-
Page 3 of 20
, UNISA | TMN3704 Teaching Mathematics – Assignment 3
sides. For Grade 5 learners, the plane is most tangibly represented by the surface of a piece of
paper, a tabletop, or a drawn grid. The significance of this concept lies in the fact that it dis-
tinguishes 2D shapes from their 3D counterparts. A shape is “flat” because all of its points lie
within the same plane. Without an understanding of what a plane is, learners struggle to con-
ceptualise why a triangle drawn on paper differs from a triangular prism built from cardboard.
Van de Walle, Karp and Bay-Williams (2016) argue that spatial reasoning in young learners
develops through concrete engagement with flat and solid forms, and that the explicit com-
parison of planar figures with three-dimensional objects accelerates geometric understanding.
Teaching the concept of a plane through physical manipulation, for instance by having learn-
ers press shapes onto paper and observe that the resulting print is flat, gives the abstract idea
a tangible grounding.
Key Concept 2: Boundary (Sides and Angles)
The boundary of a 2D shape refers to the lines, whether straight or curved, that enclose the
shape and separate its interior from the space outside it. The boundary is composed of sides
(straight line segments) in polygons, or a single continuous curve in the case of a circle. Where
two sides of a polygon meet, they form an angle, which is the measure of the turn between the
two sides. In the CAPS document for Grade 5, learners are required to recognise and describe
right angles, angles smaller than right angles, and angles greater than right angles as specific
properties of 2D shapes (Department of Basic Education, 2011). An understanding of bound-
aries is therefore essential because it forms the entry point into angle recognition. Crowley
(1987), as cited by researchers applying the van Hiele model, notes that at Level 1 (Analysis),
learners begin to identify shapes by their properties rather than their overall appearance, and
properties are primarily communicated through the boundaries and the angles those bound-
aries create. A learner who cannot identify the boundary of a shape cannot begin to count its
sides or classify its angles.
1.3 CAPS Curriculum Requirements for Grade 5
1.3.1 Term Placement of “Properties of 2D Shapes” in Grade 5
According to the CAPS Intermediate Phase Mathematics document (Department of Basic Ed-
ucation, 2011), the topic “Properties of 2D Shapes” is taught in Terms 1 and 3 of Grade 5.
In Term 1, the focus is on recognising, visualising, and naming 2D shapes, including polygons
Page 4 of 20
