FMT3701 ASSIGNMENT 2 2026
DUE JUNE 2026
QUESTION 1
1.1 Explain the importance of recognizing patterns in early childhood education.
How do patterns serve as a foundation for developing algebraic concepts? (5)
Builds prediction skills - When children see patterns, they learn to predict what
comes next. This helps them think ahead and make good guesses.
Develops logical thinking - Patterns help children see how things are connected.
They learn to think in a logical way.
Builds mathematical foundations - Patterns are the basis for many math concepts.
As the study guide states, "mathematics is a science of pattern and order" (Study
Guide, Unit 1, p. 7; Van de Walle et al., 2014).
Helps make sense of the world – Children see patterns everywhere – in nature, in
music, in daily routines. Understanding patterns helps them make sense of their
world.
Develops problem-solving skills – When children work with patterns, they learn to
find solutions and think creatively.
Serve as a Foundation for Algebraic Concepts
Helps children see relationships – When children work with patterns, they learn
how things are connected. This is the first step to understanding algebra. For
, example, when they see that 2, 4, 6, 8 increases by 2 each time, they are learning
about relationships (Study Guide, Unit 3, p. 47).
Teaches generalization – Children learn to make general rules from specific
examples. The study guide says that "programmes that are organised around big
ideas and focus on problem solving provide cohesive learning opportunities that
allow learners to explore concepts in depth" (Study Guide, Unit 1, p. 9; Ontario
Ministry of Education, 2005:25). For example, when children see that 2+3=5 and
3+2=5, they learn the general rule about addition.
Develops logical reasoning – Patterns help children think in a logical way. They
learn to use "if...then" thinking, which is important for algebra. For example, "if the
pattern is red, blue, red, blue, then the next colour is red" (Study Guide, Unit 3, p.
49).
Builds understanding of functions – A function is a rule that connects two sets of
numbers. When children see patterns, they start to understand this connection. The
study guide explains that "a function is a rule that matches two sets of numbers in
such a way that for each first number there is one - and only one - possible second
number" (Study Guide, Unit 3, p. 51).
Moves from concrete to abstract thinking – Bruner's theory shows that children
learn first with real objects (enactive), then with pictures (iconic), and finally with
symbols (symbolic) (Study Guide, Unit 1, p. 12). Patterns help children move from
using real objects to using numbers and symbols, which is what algebra is all about.
,1.2 Define the concepts of space and shape in mathematical terms. Provide one
example of each that is relevant to foundation phase learners.
Space refers to position and movement. The study guide explains that "space can be
described as classifying objects in two categories: namely position and movement"
(Study Guide, Unit 4, p. 54).
Position describes where something is in relation to something else. We use words like
"on top of," "under," "behind," and "in front of" (Study Guide, Unit 4, p. 65).
Movement describes how something moves. There are three types: translating (sliding),
reflecting (flipping), and rotating (turning) (Study Guide, Unit 4, p. 54).
Example of Space for Foundation Phase Learners:
A teacher asks learners to place their pencil "on top of" their desk. Then the teacher
asks them to put their book "under" their chair. The learners are learning about position
in space. Another example is when learners describe where objects are, such as "the
ball is next to the box" or "the book is in front of the pencil" (Study Guide, Unit 4, p. 65).
Definition of Shape:
, Shape refers to the form or outline of an object. The study guide states that "in
geometry, a shape can be defined as the form of an object or its outline, outer boundary
or outer surface" (Study Guide, Unit 4, p. 55).
A 2-D (two-dimensional) shape is flat. It has length and breadth only. Examples include
squares, circles, and triangles (Study Guide, Unit 4, p. 55).
A 3-D (three-dimensional) object has length, breadth, and height. Examples include
boxes, balls, and cylinders (Study Guide, Unit 4, p. 56).
Example of Shape for Foundation Phase Learners:
Learners identify shapes in their classroom. They see a clock and say "that is a circle."
They look at a book and say "that is a rectangle." The teacher asks them to count the
sides and corners of each shape. This helps learners understand the properties of
shapes (Study Guide, Unit 4, p. 55).
QUESTION 2
2.1 Describe three key ideas in the content area of patterns, functions, and
algebra that are essential for foundation phase learners. Provide examples of how
these concepts can be introduced in the classroom.
Repeating Patterns
A repeating pattern has a core or basic unit that repeats over and over. The study guide
explains that "the core/basic unit is the smallest part of the pattern that repeats" (Study
Guide, Unit 3, p. 49). Learners need to be able to read a pattern, describe it, copy it,
and extend it.
DUE JUNE 2026
QUESTION 1
1.1 Explain the importance of recognizing patterns in early childhood education.
How do patterns serve as a foundation for developing algebraic concepts? (5)
Builds prediction skills - When children see patterns, they learn to predict what
comes next. This helps them think ahead and make good guesses.
Develops logical thinking - Patterns help children see how things are connected.
They learn to think in a logical way.
Builds mathematical foundations - Patterns are the basis for many math concepts.
As the study guide states, "mathematics is a science of pattern and order" (Study
Guide, Unit 1, p. 7; Van de Walle et al., 2014).
Helps make sense of the world – Children see patterns everywhere – in nature, in
music, in daily routines. Understanding patterns helps them make sense of their
world.
Develops problem-solving skills – When children work with patterns, they learn to
find solutions and think creatively.
Serve as a Foundation for Algebraic Concepts
Helps children see relationships – When children work with patterns, they learn
how things are connected. This is the first step to understanding algebra. For
, example, when they see that 2, 4, 6, 8 increases by 2 each time, they are learning
about relationships (Study Guide, Unit 3, p. 47).
Teaches generalization – Children learn to make general rules from specific
examples. The study guide says that "programmes that are organised around big
ideas and focus on problem solving provide cohesive learning opportunities that
allow learners to explore concepts in depth" (Study Guide, Unit 1, p. 9; Ontario
Ministry of Education, 2005:25). For example, when children see that 2+3=5 and
3+2=5, they learn the general rule about addition.
Develops logical reasoning – Patterns help children think in a logical way. They
learn to use "if...then" thinking, which is important for algebra. For example, "if the
pattern is red, blue, red, blue, then the next colour is red" (Study Guide, Unit 3, p.
49).
Builds understanding of functions – A function is a rule that connects two sets of
numbers. When children see patterns, they start to understand this connection. The
study guide explains that "a function is a rule that matches two sets of numbers in
such a way that for each first number there is one - and only one - possible second
number" (Study Guide, Unit 3, p. 51).
Moves from concrete to abstract thinking – Bruner's theory shows that children
learn first with real objects (enactive), then with pictures (iconic), and finally with
symbols (symbolic) (Study Guide, Unit 1, p. 12). Patterns help children move from
using real objects to using numbers and symbols, which is what algebra is all about.
,1.2 Define the concepts of space and shape in mathematical terms. Provide one
example of each that is relevant to foundation phase learners.
Space refers to position and movement. The study guide explains that "space can be
described as classifying objects in two categories: namely position and movement"
(Study Guide, Unit 4, p. 54).
Position describes where something is in relation to something else. We use words like
"on top of," "under," "behind," and "in front of" (Study Guide, Unit 4, p. 65).
Movement describes how something moves. There are three types: translating (sliding),
reflecting (flipping), and rotating (turning) (Study Guide, Unit 4, p. 54).
Example of Space for Foundation Phase Learners:
A teacher asks learners to place their pencil "on top of" their desk. Then the teacher
asks them to put their book "under" their chair. The learners are learning about position
in space. Another example is when learners describe where objects are, such as "the
ball is next to the box" or "the book is in front of the pencil" (Study Guide, Unit 4, p. 65).
Definition of Shape:
, Shape refers to the form or outline of an object. The study guide states that "in
geometry, a shape can be defined as the form of an object or its outline, outer boundary
or outer surface" (Study Guide, Unit 4, p. 55).
A 2-D (two-dimensional) shape is flat. It has length and breadth only. Examples include
squares, circles, and triangles (Study Guide, Unit 4, p. 55).
A 3-D (three-dimensional) object has length, breadth, and height. Examples include
boxes, balls, and cylinders (Study Guide, Unit 4, p. 56).
Example of Shape for Foundation Phase Learners:
Learners identify shapes in their classroom. They see a clock and say "that is a circle."
They look at a book and say "that is a rectangle." The teacher asks them to count the
sides and corners of each shape. This helps learners understand the properties of
shapes (Study Guide, Unit 4, p. 55).
QUESTION 2
2.1 Describe three key ideas in the content area of patterns, functions, and
algebra that are essential for foundation phase learners. Provide examples of how
these concepts can be introduced in the classroom.
Repeating Patterns
A repeating pattern has a core or basic unit that repeats over and over. The study guide
explains that "the core/basic unit is the smallest part of the pattern that repeats" (Study
Guide, Unit 3, p. 49). Learners need to be able to read a pattern, describe it, copy it,
and extend it.
