, PLEASE USE THIS DOCUMENT AS A GUIDE ONLY
QUESTION 1
1.1 You are teaching a Grade 11 mathematics class on Euclidean geometry. Learners are
exploring the properties of circles, specifically the theorem that the angle subtended at the centre
of a circle is twice the angle subtended at the circumference on the same arc. Some learners
attempt to memorize the theorem without understanding why it works, while others try to
reason it out by drawing diagrams and testing examples.
1.1.1 Design a classroom activity that enables learners to construct their own understanding of
this circle theorem.
Title of Activity: Discovering the Central Angle Theorem
Grade: 11
Topic: Euclidean Geometry - Circle Geometry
Theorem to be Discovered: The angle subtended by an arc at the centre of a circle is twice the size of
the angle subtended by the same arc at the circumference.
Activity Structure (Three-Part Lesson Format based on Van de Walle, 2016, as cited in TMS3725,
Study Guide, p. 71-72):
Step 1: The 'Before' Phase (Introduction - 10 minutes)
Prior Knowledge Activation: Start by asking learners to draw a circle with a centre point 'O'.
They must draw two points, A and B, anywhere on the circumference. Then, they need to draw
the radii OA and OB. Ask: "What is the name of the angle at the centre, ∠AOB?" (Answer: A
central angle). "Can you estimate its size?" This reviews the concept of a central angle.
Posing the Problem: Draw a new circle with centre O. Place points A and B on the
circumference. Now, place a third point, C, on the circumference (on the same arc as either A
or B, but not between them). Draw the chords AC and BC to form ∠ACB.
Articulate Learner Responsibilities (TMS3725, Study Guide, p. 72): "Today, you will become
mathematical detectives. Your task is to investigate the relationship between the angle at the
centre (∠AOB) and the angle at the circumference (∠ACB) on the same arc (AB). You will
not be told the answer. Instead, you will discover it by drawing, measuring, and discussing with
your group. You will need to record your findings and be ready to explain your conclusion,
justifying why you think it is true."
QUESTION 1
1.1 You are teaching a Grade 11 mathematics class on Euclidean geometry. Learners are
exploring the properties of circles, specifically the theorem that the angle subtended at the centre
of a circle is twice the angle subtended at the circumference on the same arc. Some learners
attempt to memorize the theorem without understanding why it works, while others try to
reason it out by drawing diagrams and testing examples.
1.1.1 Design a classroom activity that enables learners to construct their own understanding of
this circle theorem.
Title of Activity: Discovering the Central Angle Theorem
Grade: 11
Topic: Euclidean Geometry - Circle Geometry
Theorem to be Discovered: The angle subtended by an arc at the centre of a circle is twice the size of
the angle subtended by the same arc at the circumference.
Activity Structure (Three-Part Lesson Format based on Van de Walle, 2016, as cited in TMS3725,
Study Guide, p. 71-72):
Step 1: The 'Before' Phase (Introduction - 10 minutes)
Prior Knowledge Activation: Start by asking learners to draw a circle with a centre point 'O'.
They must draw two points, A and B, anywhere on the circumference. Then, they need to draw
the radii OA and OB. Ask: "What is the name of the angle at the centre, ∠AOB?" (Answer: A
central angle). "Can you estimate its size?" This reviews the concept of a central angle.
Posing the Problem: Draw a new circle with centre O. Place points A and B on the
circumference. Now, place a third point, C, on the circumference (on the same arc as either A
or B, but not between them). Draw the chords AC and BC to form ∠ACB.
Articulate Learner Responsibilities (TMS3725, Study Guide, p. 72): "Today, you will become
mathematical detectives. Your task is to investigate the relationship between the angle at the
centre (∠AOB) and the angle at the circumference (∠ACB) on the same arc (AB). You will
not be told the answer. Instead, you will discover it by drawing, measuring, and discussing with
your group. You will need to record your findings and be ready to explain your conclusion,
justifying why you think it is true."
