Find my Centre - Authentic Task

ACTIVITY 3

Objective:  

This is a collaborative activity to consolidate the learning of angles in a circle viz a viz APPLIED LEARNING MODE.

ICT tools:  

your choice (Geogebra, Geometer Sketch Pad etc)

 mould making process

TASK:
You are a mechanical engineer that is supervising a mould making process. You have just been tasked to replicate a circular object in your production line. The products must be precise (congruent of the highest degree) and must be mass produced efficiently at the shortest possible time with minuscule margin of error. 

The first task is to produce a mould by which all the objects will be replicated from. 

To facilitate the process, you are required to first determine how you would determine the following

1. centre of the circle
2. radius of the circle / sphere

For the above activity, you are required to use the angles properties discovered in the topic. 
Do provide the logical reasoning in your answer.
Post your solution in blog page assigned to you.
Remember time is a factor so you have to plan your time very well.

Assessment 2013

Dear SSTudents,

1. Performance Task 2 (in lieu of Elementary Mathematics)

As mentioned earlier the deadline of the PT2 is 16 September 2013 @ 2359. To date many students have submitted their products with high quality questions and 'proof's.  Effective use of ICT tools (google, Blog, Geogebra, Keynote, Powerpoint, Pretzi etc) have further enhanced the final product.

2. Paper 3 (in lieu of Additional Mathematics)

The assessment information will be as follows:
Date:    23  September  2013 (Monday)
            (Please be punctual and ensure you have a heavier meal in the morning)
Time:   3.00 pm to 4.00 pm
Venue: Auditorium
Note that you are required to sit according to your classes and index numbers. The teachers will supervise you on this.

Logistic:
TI84 Graphic Calculator (or other approved GC model)
(no other calculator will be allowed)
Stationery - pen and ruler

3. Information on EOY
Please refer to your class math blog or google site earlier entries on this.


All the best - you can do it because we have faith in you but do you!

Angles in a Circle - SELF DIRECTED

ACTIVITY 1

Objective:  

This is a self directed activity to consolidate the learning of angles in a circle. 

ICT tools:  

Math Blog for activity specifications

TI-Nspire CAS

tns file will be given at the beginning of session

ACTIVITY 2

Objective:  

This is a collaborative activity to consolidate the learning of angles in a circle viz a viz formative assessment. 

Error analysis will follow the assessment.

ICT tools:  

TI-Nspire CAS

tns -based poll will be used to assess learning.

ACTIVITY 3

Objective:  

This is a collaborative activity to consolidate the learning of angles in a circle viz a viz APPLIED LEARNING MODE.

ICT tools:  

TI-Nspire CAS

TASK:
Given the object, determine how you would determine the following

1. centre of the circle
2. radius of the circle / sphere

For the above activity, you are required to use the angles properties discovered in the topic. Do provide the logical reasoning in your answer.

Circle - Alternate Segment Theorem

source: http://www.onlinemathlearning.com

The Alternate Segment theorem states

An angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

link to activity

Recall that a chord is any straight line drawn across a circle, beginning and ending on the curve of the circle.

In the following diagram, the chord CE divides the circle into 2 segments. Angle CEAand angle CDE are angles in alternate segments because they are in opposite segments.

  

The alternate segment theorem states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment

In terms of the above diagram, the alternate segment theorem tells us that angleCEA and angle CDE are equal.

Example:

In the following diagram, MN is a tangent to the circle at the point of contact A.Identify the angle that is equal to x

  

Solution:

We need to find the angle that is in alternate segment to x.

x is the angle between the tangent MN and the chord AB.

We look at the chord AB and find that it subtends angle ACB in the opposite segment.

  

So, angle ACB is equal to x.

Circle - Cyclic Quadrilateral

source: http://www.artofproblemsolving.com/

A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. They have a number of interesting properties.

Properties

In cyclic quadrilateral :

• 
• 
• 
• 
• 

Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

• Ptolemy's Theorem
• Brahmagupta's formula

the link

Circle - angles @ centre & angles in same segment

Class based activity:

Objectives: 

to proof the validity of the following theorems through geometrical manipulations using Geogebra.

Theorem 1: Angle at the centre theorem

Theorem 2: Angle in a semi circle theorem

Theorem 3: Angles in the same segment

Activity 1:

Using the attached links explore the following:

a. the various permutations of Angle at the centre theorem

b. the relationship between Angle at the centre theorem and Angle in a semi circle theorem

Activity 2:

Using the attached links explore the limitations of Angles in the same segment theorem.

link to activity1

link to activity2

Circle - angle properties

source: http://www.onlinemathlearning.com/angles-circle.html

source: http://www.bbc.co.uk

Circle - Chord

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Angles in a Circle

Angles properties