,TMS3725 EXAM OCT/NOVEMBER2023
Question 1
1.1 Explain what it means to do mathematics. (4)
To do mathematics means to engage in the study, exploration, and
application of patterns, relationships, and structures using logic and
problem-solving skills. It involves the identification and
manipulation of mathematical objects such as numbers, shapes,
equations, and functions, in order to understand and explain
various phenomena in the world. Doing mathematics often
requires logical reasoning, critical thinking, and creativity to solve
problems, prove theorems, make predictions, and make
connections between different mathematical concepts. It allows us
to describe, model, and quantify real-world phenomena, as well as
to develop abstract ideas and theories. Doing mathematics is a
continuous process of learning and discovery that helps us develop
our mathematical thinking skills and expand our understanding of
the principles and applications of mathematics.
1.2 The quality of mathematics that learners learn depends on the
mathematical tasks/activities they are exposed to. Routine and
non-routine problems are often used in mathematics classrooms.
These tasks play a role in teaching mathematics for understanding.
In your classroom, you intend using the following tasks:
Task 1: Find the equation of the line through the origin and point
(4; 2)
Task 2: Find the equations of lines through (4; 2)
1.2.1 To which topic do these tasks belong? (2)
These tasks belong to the topic of linear equations and lines.
, 1.2.2 What prior knowledge is required for learners to complete
these tasks? (3)
Prior knowledge required for learners to complete these tasks
includes understanding the concept of a line, knowing how to find
the equation of a line given two points or a point and slope, and
being familiar with basic algebraic operations.
1.2.3 Which task is an example of a routine problem? Justify your
answer. (5)
Task 2 is an example of a routine problem. This is because it asks
for the equations of lines through a given point, which is a
straightforward and standard process that can be solved using the
point-slope formula or slope-intercept form.
1.2.4 Which of these tasks could be used to promote relational
understanding?
Justify your answer.(4)
Task 1 could be used to promote relational understanding. This is
because it requires learners to find the equation of a line through
the origin and a specific point. By understanding the relationship
between the origin and the given point, learners can gain a deeper
understanding of how the equation of a line is determined and how
it can be manipulated based on specific points.
Question 2
2.1 A parallelogram is defined as a quadrilateral in which both pairs
of opposite sides are parallel. What pre-knowledge concepts would
Grade 10 learners need to know before learning parallelogram
theorems? (2)
Question 1
1.1 Explain what it means to do mathematics. (4)
To do mathematics means to engage in the study, exploration, and
application of patterns, relationships, and structures using logic and
problem-solving skills. It involves the identification and
manipulation of mathematical objects such as numbers, shapes,
equations, and functions, in order to understand and explain
various phenomena in the world. Doing mathematics often
requires logical reasoning, critical thinking, and creativity to solve
problems, prove theorems, make predictions, and make
connections between different mathematical concepts. It allows us
to describe, model, and quantify real-world phenomena, as well as
to develop abstract ideas and theories. Doing mathematics is a
continuous process of learning and discovery that helps us develop
our mathematical thinking skills and expand our understanding of
the principles and applications of mathematics.
1.2 The quality of mathematics that learners learn depends on the
mathematical tasks/activities they are exposed to. Routine and
non-routine problems are often used in mathematics classrooms.
These tasks play a role in teaching mathematics for understanding.
In your classroom, you intend using the following tasks:
Task 1: Find the equation of the line through the origin and point
(4; 2)
Task 2: Find the equations of lines through (4; 2)
1.2.1 To which topic do these tasks belong? (2)
These tasks belong to the topic of linear equations and lines.
, 1.2.2 What prior knowledge is required for learners to complete
these tasks? (3)
Prior knowledge required for learners to complete these tasks
includes understanding the concept of a line, knowing how to find
the equation of a line given two points or a point and slope, and
being familiar with basic algebraic operations.
1.2.3 Which task is an example of a routine problem? Justify your
answer. (5)
Task 2 is an example of a routine problem. This is because it asks
for the equations of lines through a given point, which is a
straightforward and standard process that can be solved using the
point-slope formula or slope-intercept form.
1.2.4 Which of these tasks could be used to promote relational
understanding?
Justify your answer.(4)
Task 1 could be used to promote relational understanding. This is
because it requires learners to find the equation of a line through
the origin and a specific point. By understanding the relationship
between the origin and the given point, learners can gain a deeper
understanding of how the equation of a line is determined and how
it can be manipulated based on specific points.
Question 2
2.1 A parallelogram is defined as a quadrilateral in which both pairs
of opposite sides are parallel. What pre-knowledge concepts would
Grade 10 learners need to know before learning parallelogram
theorems? (2)
