# LESSON PLAN 3

- Construction of regular polygons

- Arts (includes music, architecture ...), ICT (includes technical education, computer science ...), Mathematics (includes geometry, proportionality, finances ...)

- ISCED 2 = Lower Secondary Education

## Duration

2 teaching hours (40 minutes each)

## Topic

To reconstruct – redraw a drawing consisting of regular polygons

## Synopsis

Solving problem tasks through the application of visual stories in the classroom. The goal is to apply the acquired knowledge to an everyday problem – to reproduce a given photo (scheme) of polygons.

## Contributors

Art or ICT teacher

## Framework

__Teacher’s coo____peration and division of work:__

Teacher (T1) – mathematics

A1: Creating an infographic to check students’ prior knowledge of quadrilaterals. Providing step-by-step online instructions for students to construct regular polygons and tracking and assisting students in their realization

A2: Creating a rubric and evaluating the students’ works according to a pre-set rubric for assessment.

A3: (for students with atypical development) The student does the same, but at a level that corresponds to his abilities. He works with the help of an educational assistant, and when learning, he uses photos and illustrations with instructions for drawing the polygons.

**Action plan formulation:**

One teaching unit is realised in two teaching hours. An art or technical education teacher can be consulted when evaluating the students’ works.

## Material / Equipment

Drawing tool, smart board

## Previous knowledge and skills

Definition of a regular polygon

## Learning Objectives

**Learning goals and objectives:**

- Know which polygons are regular
- Know how to construct a regular triangle, quadrilateral and hexagon

**Learning outcomes and expected outcomes:**

- Construct regular polygons, given a side and an interior angle.
- Solve simple geometry problems by using properties of sides and angles to identify equal lengths, calculate unknown angles, and explain reasoning.

## Methodology

Modern pedagogical and communication research emphasizes the importance of creative visual communication, first of all, due to the undoubtedly greater degree of engagement and involvement of students in the content, whereby they become motivated and inspired to participate in the class.

With the help of the infographic, polygons are classified in an easier way because it is given visually. Animated instructions for the construction of regular polygons in electronic form are repeatedly repeated on the smartboard, allowing all students to follow them, even if someone missed a step in the construction, the whole procedure will soon be repeated. That way, the teacher is free to follow the students’ work in the notebooks, instead of drawing on the board. The instructions are also posted on the website of the class zaharievasnezana.weebly.com , so they are available at any time, suitable for learning from home.

The second lesson begins with a discussion of how they drew the drawing – What skills and knowledge did you have to use? Which part was the most challenging for you? How did you decide where to start by drawing the drawing – center, periphery, arbitrary… solving this problem task enables the stimulation of lateral thinking among the students (that is why only one dimension is given for the whole drawing which, in turn, consists of several polygons)

## Preparation & Resources

Preparation, space setup, troubleshooting tips:

All necessary materials are in electronic form (available to students from home as well)

Resources, tools, materials, attachments, equipment

INFOGRAPHIC:

http://zaharievasnezana.weebly.com/uploads/1/1/1/4/11145769/4_orig.png

http://zaharievasnezana.weebly.com/uploads/1/1/1/4/11145769/35_orig.png

ANIMATION for:

- Regular polygons

https://www.mathopenref.com/polygonregular.html

- An equilateral triangle

https://www.mathopenref.com/constequilateral.html

- Square

https://www.mathopenref.com/constsquare.html

- Regular hexagon

https://www.mathopenref.com/consthexagon.html

PHOTOGRAPHY

## Implementation

The activity takes place in two hours of 40 minutes each. The drawing from the homework requires a little more time, because it is done at home, not in class. In the first lesson, the emphasis is placed on the correct construction of an equilateral triangle, a square and a regular hexagon, and most of the students are expected to see the construction of a regular pentagon or heptagon. In the second class, the drawings are presented and evaluated, and how the solution was arrived at when so many dimensions are missing is discussed. The goal is for them to experience the drawing as a puzzle in which they have to use the knowledge of mathematics about the properties of polygons, as well as the knowledge from technical education about dimensioning and determining missing dimensions.

## Outline of the Lesson

**A1:**

**WHAT IS MY NAME?**

K if an introductory activity, through questions and answers is repeated about the basic concepts related to regular polygons:

– What is a polygon? How do we name polygons by number of sides/angles/number of vertices?

-Which polygons do we say are regular?

– What is the name of a regular triangle?

-What is the name of a regular quadrilateral?

-How will you calculate the interior angle of a regular polygon?

Two infographics are open on the smart board in front of the students:

- Convex polygons
- Classification of quadrilaterals

Infographics are used for easier and more efficient determination of the properties of regular polygons that are needed further during the lesson for their construction.

Students follow animations that show step by step how to construct an equilateral triangle, a square and a regular hexagon.

They use their skills in drawing line segments of given length and angles to construct a regular pentagon with side length 3 cm and interior angle 108°. Students draw a side and an angle of the pentagon. Their partner checks the angle and side length measurements before they draw the next side. They repeat the same procedure for both an equilateral triangle and a regular hexagon and, if necessary, repeat the animations to facilitate the drawing process.

Discussion: What skills and knowledge did you need to use? Which part was the most challenging for you? Why do you think we used a set of triangles to draw a square and a rectangle, and an context for other regular polygons?

Homework is due – Polygon Art. Students should draw the same pattern in their notebooks with one dimension given – the central hexagon has a side of 1.5 cm. They need to show their creativity in finding solutions for how to draw the drawing, how to determine the missing dimensions, how to construct the polygons and how to ensure that the drawing is accurate and precise. Also, the coloring of the pattern is left to the students’ creativity.

A2: 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.

## Extension Activities

Students who progress faster can optionally try to draw a regular pentagon or heptagon by calculating an interior angle. For students with atypical development, a worksheet suitable to the student’s abilities has been prepared.

## Assessmement

Most of the students successfully completed the given task. Instead of drawing polygons in a notebook – which is sometimes boring, colorful illustration further encouraged them to succeed in their intention. Students who had no idea how to determine the dimensions went back to the beginning of the lesson and the animations, which contributed in a fun way to learn the facts about regular polygons.

The final conclusion is that this approach has a good effect on learning – the students showed more interest in completing the task, there was a final product – a drawing that can be easily evaluated and given feedback.

The students’ creativity came to the fore, as evidenced by the different techniques they used to make the drawings – there are simple drawings drawn only with a pencil, colored with wooden crayons or felt-tip pens, up to a collage of self-adhesive paper. *Students’ creations*

*See Annex 3 *