# LESSON PLAN 4

- String. A general array member

- Arts (includes music, architecture ...), ICT (includes technical education, computer science ...), Other (social studies, geography,,,), Science (includes physics, biology ...)

- ISCED 2 = Lower Secondary Education

## Duration

1 teaching unit, 2 hours, 3 activities

## Topic

Discovering patterns in everyday life

## Synopsis

The aim of the activity is to enable students to perceive patterns in everyday life. Connecting mathematical concepts with everyday situations allows easier and more permanent adoption of the same.

## Contributors

art education teacher

## Framework

**Teacher’s coo****peration and division of work:**

Teacher 1 (T1) – mathematics

A1: Preparation of materials to review what was learned about Fibonacci (biography and story of rabbits) and Fibonacci sequence, as well as placing materials in electronic form on an Internet platform to be available to students.

A2: Explaining through everyday examples how to distinguish whether a sequence is algebraic, geometric, Fibonacci sequence or neither. Creating online quizzes to check your understanding of these concepts.Composing tasks at three difficulty levels for practice

A3: Creating a rubric and evaluating the students’ works according to a pre-set rubric for assessment.

**Action plan formulation:**

3 activities are included, the third activity can be carried out in collaboration with an Art Education teacher.

## Material / Equipment

## Previous knowledge and skills

Knowledge of the Fibonacci rule and how to generate sequences using it is required. This is done with activity A1 – before the start of the lesson, at home, they read the text Let me tell you a story… which is assigned to the link on genil.ly

## Learning Objectives

**Learning goals and objectives:**

- Generating terms of a linear sequence using the rule for determining the next term and determining any term of the sequence using the general term.
- Finding rules for determining the next term and the general term of an array, including a visual display.

**Learning outcomes and expected outcomes:**

- Students can recognize whether a sequence is arithmetic, geometric, Fibonacci, or neither.
- Students know how to determine the next term in a numerical or algebraic sequence.
- Students develop an understanding of the world based on experiential learning.

## Methodology

The initial activity is designed as a flipped classroom. Thus, there is more time in class for perceiving this concept in nature and everyday life, as well as an opportunity to raise the cognitive level of the tasks that will be solved.

The class activity is conducted according to the AIDA method. Through examples from everyday life, students are encouraged to perceive patterns in the environment. The quizzes are worked together as a class. Students have to explain their answer to move on to the next question, which encourages discussion among them

In the main part, chain exercises are carried out – the first student to solve a task is chosen by the teacher, after solving the task, he forces the students to think about the tasks, because they do not know who will be called. Thus, instead of relying on the students who answer the questions the fastest (mostly several of the same students answer), the students themselves choose the order of answers, thus everyone takes part in the teaching process. And the role of the teacher turns into an observer of the learning process, which is organized, coordinated and implemented by the students. The teacher intervenes if necessary (none of the students know how to solve the task or the solution is wrong). They are given tasks at three difficulty levels that are printed on colored paper – the easiest on green, the middle level on yellow and the hardest on red paper. The student who solves pulls a card according to his own abilities (knowledge), which includes all students – everyone can solve a task.

Evaluation of the homework is done according to the given rubric – the evaluation is between students. When the criteria are pre-set, students achieve higher results. Inter-student assessment, in turn, allows for the development of discussion between students and a deeper understanding of the assessment criteria.

## Preparation & Resources

Preparation, space setup, troubleshooting tips:

Before class begins, students should have the free PhiShot mobile app downloaded . For the introductory part of the lesson, everyday objects are needed – plant branches, eggs, etc.

Resources, tools, materials, attachments, equipment

https://mathigon.org/ – the main part of the lesson when students are introduced to arithmetic and geometric progression, as well as the Fibonacci sequence (the story of the rabbits and the spiral)

https://app.genial.ly/?from=login-true – the entire activity is collected in one interactive image on Genially, with links to other activities https://view.genial.ly/6355705024cb410010b87032/interactive-content-nizi

https://wordwall.net/myactivities – knowledge test quiz

PhiShot a Play Store application that allows students to take photos of everyday objects where they notice the Fibonacci sequence (spiral)

## Implementation

Instead of a dry enumeration of facts, the interactive Mathigon app introduces the basic concepts of sequences through examples from everyday life. Connecting mathematical problems to everyday life allowed understanding how things and objects function in the environment (mostly through the photographs they took). The quizzes and assignments provided confirmation of the degree of mastery of the terms rule of sequence, next and general member of sequence. The productions reflect the level of understanding of the concept taught in this course content

## Outline of the Lesson

A1 (10-15 minutes): The initial activity is designed as a flipped classroom. Students are already familiar with Fibonacci and the Fibonacci sequence from the previous year. Repetition of what has been learned is required (this is done before class, at home, on materials offered by the teacher). Thus, there is more time in class for perceiving this concept in nature and everyday life, as well as an opportunity to raise the cognitive level of the tasks that will be solved.

A2 (40 minutes): The lesson activity is carried out according to the AIDA method

block 1 ( attention) – With the help of material in electronic form, the need to analyze mathematical data in everyday life (predictions of volcanic activity or finances) is explained . https://mathigon.org/course/sequences/introduction

Through appropriately chosen examples (the appearance of Halley’s comet and the decrease in the height of a ball’s bounce), the difference between arithmetic and geometric progression is explained, and then what was learned about the Fibonacci sequence is repeated. https://mathigon.org/timeline/fibonacci

https://mathigon.org/course/sequences/arithmetic-geometric

The teacher shows examples on the computer or from everyday life where the Fibonacci spiral is found (architecture, art, design, flora and fauna, man, natural phenomena, space…).

https://view.genial.ly/6355a2c6bc04130018479fec/interactive-content-galerija

Students use the PhiShot mobile app to discover patterns in the offered examples, but also in examples that they will discover on their own (in plants, human body, egg, logo, etc…). Each student should take at least one photo.

in the environment

block 2 ( interest) – Students’ interest in this topic is encouraged through dosed information. Two quizzes are done, jointly as a class. Students should explain their answer to move on to the next question

block 3 (desire) – Chain exercises are performed (tasks at three weight levels)

block 4 (action) – Students receive instructions for homework – to draw the Fibonacci spiral, but as a work of art. Instructions are given as to what the drawing should contain in the form of a rubric

A3 (40 minutes): Evaluation is carried out according to a given rubric – the evaluation is among students – each student presents his drawing to the others and explains why he thinks it should be evaluated with a certain number of points. The other students discuss and give their opinion whether they agree or not.

See images in Annex 4.

## Extension Activities

The very choice of tasks in the main part of the lesson meets the needs of both the students who are progressing faster and those who are lagging behind.

Regarding the homework, a video was assigned with instructions on how to draw the spiral. For students who, despite the instructions, cannot draw the spiral, the teacher provides an already printed spiral in which they should place their drawing

## Assessmement

Discussion – the material being worked with is interactive, students say their answers before you can go further in the presentation.

Quiz on classifying strings according to the rule

Quiz for determining the common term and next term in a sequence

Photography by PhiShot (whether or not they see a Fibonacci sequence in everyday life)

Checklist and rubric for evaluating the works