Workshop 2

Teaching and Learning Plan the unit Circle.
 

Through investigation students will become familiar with the unit circle, and the use of the unit circle to evaluate the trigonometric functions sin, cos and tan for all angles. Students will then be able to use their knowledge of the unit circle to find all the solutions of equations.

To download this T&L plan, click here                                                                                    

T&L plan for trignometric functions (Higher Level Leaving Certificate)

Starting with examples from real life of the use of trigonometric functions, students will then use the unit circle to investigate the graph of the function y = sin x  by projecting the y coordinate onto an x-y plane. They will proceed to use tables of values to plot the graphs of sin x, cosx and tanx. Students then proceed to investigate and draw functions of the type "a sin bx", "a cos bx" where a, b are natural numbers and "tan x" leading to an understanding of the effect of changing the variable a and b. These investigations will also be carried out using dynamic geometry software.

To download this T&L plan, click here

To view interactive file on graphs of sine and cosine, click here

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T&L plan on Radians

For Leaving Certificate Higher Level students. Its purpose is to introduce radian measure from a “Teaching for Understanding” perspective. The plan takes an explorative approach to investigate the properties of radian measure. Students will be provided with a range of activities and teacher support to generate a deep understanding of radian measure so that students will be able to apply its use in problems.
 

To download T&L plan click here

To download student activity 1, click here | To download student activity 2, click here  

To view interactive file on radians, click here

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T&L plan on coordinate geometry of the circle

This Teaching and Learning plan is for both Leaving Certificate Ordinary level and Higher Level students. It takes the students through a series of activities which help them to construct the General equation of a circle with centre (h,k). The activities help students to visualise the loci of points on various curves and hence determine the locus of a point on a circle. For Higher level students the Teaching and Learning plan contains an activity by which they can arrive at the General equation of a circle of centre (h,k) by an alternative
method. The Higher level students, using an Activity Sheet, will also derive the general equation of a circle of centre (-g,-f).
 

To download T&L plan, click here

To download;
 

1. Student activity 1, click here

2. Student activity 2, click here

3. Student activity 3, click here

4. Student activity 4, click here                                                                                             

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T&L plan: An introduction to Geometry (Junior Certificate)

This lesson introduces first year students to plane geometry. The basic concepts which they meet are:
The plane, points, lines, line segments, rays (half-lines), collinear points, and length of line segments.
One of the major objectives of this lesson and of the following lessons is the development of instrumental understanding in the use of pencil, ruler and other instruments and the development of psychomotor skills (skills of physical coordination).

Learning Outcomes: All students will:

• Know about the origins of geometry
• Have an intuitive knowledge of the plane, points, lines, line segments, rays, length of line segments
• Have an interest in the subject and a desire to learn more.

To download this T&L plan, click here                                                                                     

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T&L plan: An introduction to Angles (Junior Certifcate)

The Objectives of this lesson are to introduce the concept of angle as a rotation and the various angle types: e.g. acute, obtuse, etc, in terms of how much rotation involved. Angle measure and naming of an angle is dealt with and the students are introduced to the concepts of parallel, perpendicular, vertical and horizontal lines.

Learning Outcomes: All students should be able to:

• Recognise angles in terms of rotation
• Recognise, classify and describe angles
• Recognise the various angle types in terms of degrees
• Relate angles to shape
• Know how to name an angle
• Understand and recognise parallel and perpendicular lines
• Understand and recognise vertical and horizontal lines

To download this T&L plan, click here                                                                                     

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T&L plan on Coordinate Geometry (Junior Certificate)

A basic introduction the the cartesian plane. The lesson begins with a brief discussion on how Renee Descartes developed the idea of the coordinate plane. It then moves on with numerous student activites, which enable students to discover how to plot and read points (ordered pairs) from the cartesian plane.

To download the T&L plan, click here

To download the student activity sheets, click here.                                                                 

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T&L plan on Vectors 

Leaving Certificate Higher level students are introduced to the topic of vectors. Through a discovery process students find out that vectors have both magnitude and direction. Then the concept of vector notation, the null vector, equal vectors and negative vectors are introduced. Everyday applications of vectors are used where possible. Accompanying this plan is an interactive file to demonstrate the concepts of a vector alternatively for those with access to the software package Autograph the appendix of the plan contains instructions on how to use this package to demonstrate the concepts of a vector.

To view T&L Plan, click here | To view student activity click here

To view interactive file on vectors, click here

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T&L Plan on the Triangle Law for the addition of Vectors

This is a continuation of the Vectors teaching and learning plan, it introduces the concept of the addition of two vectors by the Triangle Law. Examples of vectors from everyday situations are used where possible to enable students to gain both an understanding and appreciation of the topic, these include travelling to different locations, winds and currents. Accompanying this plan is an interactive file to demonstrate the concept and the appendix of the plan contains instructions on how to use the software package Autograph to do the same.

To view T&L Plan, click here  |  To view student activites, click here  

To view interactive file for Triangle Law of addition for vectors, click here

To view interactive file for parallelogram addition of vectors, click here

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Teaching & Learning Geometry: The Van Hiele Model

• The Van Hiele levels of geometric reasoning are sequential. Students must pass through all prior levels to arrive at any specific level.
• These levels are not age-dependent in the way Piaget described development.
• Geometric experiences have the greatest influence on advancement through the levels.
• Instruction and language at a level higher than the level of the student may inhibit learning

To view a presentation exploring the Van Hiele model, click here

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