Teaching and Learning Plans.

Difficulties in learning Probability and Statistics. (Strand 1)

This presentation offers a brief synopsis on the challenges and difficulties experienced by students when dealing with Probability and Statistics.

To view the presentation, click here

Teaching & Learning Geometry: The Van Hiele Model (Strand 2)

• 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

How to develop a T&L Plan

T&L Plans for probability.

• Distinguish certain from uncertain events
• Be able to describe events as being more or less likely from experience
• Order events from least likely to most likely and be able to justify their choice
• Use the scale from 0 to 1 informally placing everyday chance related events
• Represent and interpret probabilities as fractions, decimals and percentages

Lesson 3

• Understand and use the following terminology: trial, outcome, set of all possible outcomes, relative frequency, event, theoretical probability, equally likely outcomes
• Be able to list all the possible outcomes when rolling a die
• By experiment, be able to calculate the relative frequency for each outcome and note how it approaches the theoretical probability as the number of trials increases
• Be able to distinguish equally likely outcomes from those which are not.

Lesson 4 & 5        

Learning Outcomes: Students will,

• Investigate further what the concept of fairness means in a game with 2 dice.
• List all the possible outcomes for throwing 2 dice using a two way table.
• Relate the number of outcomes to the fundamental principle of counting
• Be able to come up with rules for a game which make it fair/unfair
• Construct a probability table
• Understand the relationship between an event and its complement
• Determine the probability of an event using the results of an experiment and can use this to predict the result of a repetition of the experiment, for equally likely outcomes. 
   

Lesson 6

• Learn about playing cards in a deck, colours, suits, number of cards etc
• Calculate the probability of drawing a particular card(s) from a deck

Lesson 7 & 8

• List the possible outcomes when tossing a coin and calculate the probability of getting a head or a tail.
• List all the possible outcomes when throwing 2 coins.
• Relate the number of outcomes to the fundamental principle of counting
• Determine the probability of an event using the results of an experiment and use this to predict the result of a repetition of the experiment, for equally likely outcomes.
• Use the term “independent events” 
   

T&L Plans for statistics.

How to register your school with Census at school.

Statistics and Data handling: A real data approach.

Census at school measurement worksheets.
 

Measurement worksheet for students to fill in before completing census at school survey

T&L Plans for Geometry

Click on the title to view T&L Plans available for Geometry

1. Introduction to Geometry:

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, length of line segments. One of the major objectives of this lesson 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

2. Introduction to Angles:

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

Designed for Junior Certificate students, this T&L plan iconsists of 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 view student activity, click here  | To view T&L Plan, click here

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

To view interactive radians, click here

5. Trigonometric Functions:

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 Sine & Cosine graph, click here

6. 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 view T&L Plan, click here   |  To view interactive file on unit circle, click here

7. Coordinate Geometry of the Circle:

For both Leaving Certificate Ordinary and Higher Level students. It takes the students through a series of activities 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. Higher level students, will also derive “the general equation of a circle of centre (-g,-f)”.

Click on any of the student activies listed below to view them

Student activity 1  |   Student activity 2   |   Student activity 3   |   Student activity 4  |
 

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 on vectors file, click here

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

An approach to problem solving.