# LESSON PLAN 10

- Counting Principles and Properties of Events

- Arts (includes music, architecture ...), Mathematics (includes geometry, proportionality, finances ...)

- ISCED 2 = Lower Secondary Education

## Duration

Learning duration: 3 hours / 4 periods / 45 mins each

## Topic

Facilitate pupils of ages 10-13 to be able to count more formally numbers, quantities etc. Definition of an “event” in mathematics, its “elements” and how we can develop other approaches to count these numbers (other than the elementary school simplistic approaches, like the abacus or the fingers of our hands).

Pupils will explore the key concepts for counting and how to deal with “independent events”. They will practice in class how they can deal with events that cannot occur simultaneously and also be able to deal with repeating elements up to a certain point.

## Synopsis

This learning plan deals with the need for handling data, as the 21st century is characterized by a huge increase in data handling.

**Learning Objective**: The pupils will learn and develop skills that will help them in understanding and using some elementary counting principles.

**Learning Outcome**: This learning plan aims to provide pupils (of ages of 10-13) with the basic knowledge that will help them in realizing real-world situations where there is a need for using and understanding these principles of counting.

Relevant activities and examples will be given. As the classes of students are inclusive, the whole approach will provide activities that range over a broad spectrum of difficulties.

## Contributors

- Mathematics (T1) -Main Role-
- Art (T2)
- Economics (T3)

(T2 and T3 will support the activities through their special areas and provide the context for understanding and applying the counting principles in the context of their topics).

## Framework

Teacher’s cooperation and division of work: in the present lesson plan, 3 teachers are expected to be involved:

- Teacher T1 – Mathematics: (with main responsibility of identifying and delivering the topic, promoting/ helping/ organising the whole learning procedure).
- Activity 1 (A1): Development of activities related to the principles of counting, in the context of the driving questions
- Activity 2 (A2): Monitoring exercises in the spirit of the aims and objectives of this topic.

- Teacher T2 – Art:
- Activity 3 (A3) Supporting students in illustrating/presenting some of the ideas in the activities. Helping students visualise how our topic connects with the real world.

- Teacher T3 – Economics:
- Activity 4 (A4) Supporting students in the calculating part of our topic, implementing data in real life problems. Help them connect our topic with the real world.

**Action plan formulation:**

**STAGE 1**: Activities A1 and A2 (by T1) are the main activities of the lesson (taking place on the first two periods of 45 mins). Communication between T1 with T2 and T3 for designing and developing their A3 and A4 relevant to the topic.

**STAGE 2**: Activity A3 (by T2) will take place during the third period (duration: 45 mins)

**STAGE 3**: Activity A4 (by T3) will take place during the fourth period. A3 will be the last step of the process and will be used as a short evaluation exercise as well. (duration: 45 mins)

## Material / Equipment

For S1: Computers/ Tablets

For S2: Material for designing

Virtual Reality (VR) program on painting

For S3: Scientific calculator

## Previous knowledge and skills

The pupils must have the basic skills for counting from primary school as well as to be able to perform simple mental arithmetical operations (add, subtract, multiply, divide). Having simple-problem solving techniques, will also be helpful.

## Learning Objectives

**Number 1**: Pupils will understand the various types of data and learn how to organize

and represent data in forms that will facilitate counting.

**Number 2**: Pupils will learn and apply the multiplication principle for counting in the

case of independent events.

**Number 3**: Pupils will learn and apply the addition principle for counting in the case of

mutually exclusive events.

**Number 4**: Pupils will discuss and learn to use the principle of inclusion-exclusion for

counting.

**Learning Outcomes and expected results:**

At conclusion of the activity students should:

**Number 1**: Construct the set of outcomes of an event

**Number 2**: Identify if two or more events are related or independent.

**Number 3**: Solve counting problems by either applying elementary counting techniques, or by using the sum and product rules, or the principle of inclusion-exclusion.

**Number 4**: Become proficient on counting techniques and possess the foundations for basic permutations, combinations, and generally basic probability principles.

## Methodology

The students should be able to work by the adoption of the flipped classroom method for work that has to be done at home as well as by investigation and the adoption of the Socratic method.

In this context, the first activity aims at creating motivation and connection to real-world activities.

Discussion and reflection are essential in understanding the concepts and processes involved.

## Preparation & Resources

- Print worksheets/handouts.
- Prepare projector.
- Prepare for small group work (if the group consists of varying levels of self-directed learning experience and skill pupils).
- Prepare cards for “Quizizz’ Paper Mode” form of quiz and results’ discussion

**Material needs**

Textbook on relevant chapter (ages 10-13)

The presentation on the Counting Principles by the Khan Academy

**Extra resources:**

(relevant quizzes from www.quizizz.com)

## Implementation

**Activity 1 (A1) in Mathematics**

Topic: Introduction to counting and basic combinatorics

Taks/Activities:

- Simple math real-life problem solving – warming up
- Give Annexes 1 and 2 as a worksheet.
- Give students a few minutes to practise (15 mins).
- Discuss their results (20 mins).
- Conclude (10mins).

**Activity 2 (A2) in Mathematics**

Topic: Problem solving – Integrating and connecting, analysis and interpretation

Taks/Activities:

- Instructing students to organise teams of 3 or 4. Ice-breaking
- Give Annexes 4 up to 9 (depending on time) [see document Lesson Plan 10 annex] on whiteboard/interactive board or as a PPT
- Teamwork, use Quizizz paper mode to answer as a team.
- Conclude.

**Activity 3 (A3) in Arts**

Topic: Illustrations for the Counting Principles

Tasks/Activities:

- Research on the subject to present it to classmates in an attractive way
- Give Annex 10
- Give students 20 minutes to practise.
- Discuss their results (15 mins).
- Conclude (10mins).

**Activity 4 (A4) in Economics**

Topic: Using simple Econometrics to calculate the dietary value of lunches.

Taks/Activities:

- Simple economic real-life problem solving – warming up
- Give Annex 11 as a worksheet.
- Give students a few minutes to practise (20 mins)
- Discuss their results (15 mins).
- Conclude (10 mins)

## Outline of the Lesson

**A1 and A2 in Mathematics**

This plan consists of two parts/activities (A1 and A2). First (45 minutes) led by teacher and pupils work alone on worksheets and discussion follows. In the second part (another 45 mins), pupils work in teams of 3 or 4 and produce results after teamwork and discussions among them. The remaining annexes (out of 11 designed) will be set as extra work/ homework.

**A3 in Art**

This part of plan requires 45 mins for one activity (A3). Pupils, facilitated by their Art teacher to produce illustrations on the counting principles. Creativity and imagination used are two key-skills for STEAM education.

**A4 in Economics**

This part of plan requires 45 mins for one activity (A4). Pupils use simple econometric techniques to calculate the dietary value of lunches

## Extension Activities

- Extend or reduce the amount of difficulty for every pupil separately.
- Teacher T2 could also propose inclusions of simpler or more advanced artistic elements to be included in the project, depending on the ability of each student.
- Teacher T3 could stage a small theatrical act of the actual serving in a restaurant. Make it easier for pupils to visualise the problem. Mathematical Theatre is a growing activity of STEAM education in Europe.
- Assignment adjustments for advanced students – they can do this assignment on PC or tablet (Bring.Your.Own.Device. – BYOD program)
- Assignment adjustments for students with some kind of disability – they can just sketch pictures of the combinations they make on A1 and A2. They don’t need to use any complex formulae.
- In S2, they can use to paint marker pens, colours, tempera, collage, whatever they feel comfortable with.
- Easier/harder quizzes from our library on www.quizziz.com will be used.Extend or reduce the amount of difficulty for every pupil separately.

## Assessmement

There is a rubrics available (see annex 12) that can help the teacher assess pupils’ success.

There is also teaching material (annexes 1 to 11) that can be used in class, problems relevant to the Activities planned by this lesson plan. Annexes not used in class can be given as homework. Easier tasks to the slower learning students and harder tasks to the faster learning ones.

Assessment should be based on the following:

- Continuous debate and feedback as students are involved in the activities
- Short quiz (www.quizizz.com) after each activity (that aims to identify the understanding of the principles and their use in problem-solving)