# LESSON PLAN 8

- Composition of different types of symmetry

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

- ISCED 2 = Lower Secondary Education

## Duration

5 unites, 270 minute, 8 activities

## Topic

Construct geometric objects (line segment, triangles, quadrilaterals, …)

## Synopsis

Construct geometric objects (line segment, triangles, quadrilaterals, …) that are symmetric to given one using three different sorts of symmetry – radial symmetry, line symmetry and translation symmetry.

## Contributors

Math and other science teachers

## Framework

__Teacher’s cooperation and division of work:__

Teacher 1 – mathematics

Students will discover characteristics of symmetrical shapes, consecutively copy the given objects, find the shortest mapping procedure between two drawn objects, solve the problem task by applying mapping. Students will construct all kind of geometric objects that are symmetric to given ones using axial symmetry, radial symmetry and/or translation.

Teacher 2 – arts

Examine use of geometric objects and patterns in art history. Examine rhythm on paintings. Draw paintings using tempera based on examples they saw. Students work may be shown on an exhibition in school.

Teacher 3 – physics (science teacher)

In lesson of mirrors students will draw and describe the image created of an object created by reflection on a flat and spherical mirror, explain the creation of an image depending on the position of the object in front of the flat or spherical mirror, analyze the nature of the image depending on the position of the object in front of the mirror and apply the mirror equation.

## Material / Equipment

- paper triangles, board magnets
- geometric tools– triangles, ruler, compass
- computer and projector

## Previous knowledge and skills

Know how to construct geometrical object (point, line, triangle, quadrilateral, …) that is symmetric to given one using axial (line) symmetry, radial symmetry or translation.

## Learning Objectives

**Learning goals and objectives:**

Upon completion of the class students should know:

- explain the procedure and properties of the composition of different symmetries
- construct composition of different symmetries
- analyze composition of different symmetries
- find the shortest mapping procedure between two drawn objects
- solve the problem task by applying mapping.

**Learning outcomes and expected outcomes:**

- Apply gained information and knowledge to new situations
- Understand role of symmetry I everyday life, arts, architecture

Create new pattern using combinations of axial (line) symmetry, radial symmetry or translation.

## Methodology

Teacher should try to lead constructive debate, encourage each student to give their own opinion and examples. They should try to connect lesson with real life, art, architecture, application of symmetry and reflection in science.

Some materials can be published on platform even before so students can prepare. Assignment task and results (students work) should be published on platform so everybody involved in process can access them.

Also, assignments can be organized in pairs or smaller groups and platform can be used as way of communication and cooperation, and even tutoring. Groups or pairs can be formed in a way that each group contains at least one better student then rest of group so that he can be tutor to students in the group. In that case he is supposed to keep diary about instructions and directions he gave and how successful his “students” were.

The work on assignment is evaluated according to previously determined criteria and all students should know that criteria before they start their assignment. That can also be published on platform.

## Preparation & Resources

**Resources**** **

Resources, Tools, Material, Attachments, Equipment

Inspiration for assignment can be found here:

https://www.ikea.com/hr/hr/cat/rucno-izradeni-tepisi-39267/

https://www.tenstickers.hr/vinilni-tepisi/meksicke-plocice-s-uzorkom-suvremenih-tepiha-R1659

https://www.tenstickers.hr/vinilni-tepisi/elegantan-bijeli-ukras-suvremeni-vinil-tepih-R2249

https://www.tenstickers.hr/tapete-od/geometrijski/

for science lesson:

__https://edutorij.e-skole.hr/share/proxy/alfresco-noauth/edutorij/api/proxy-guest/a743968a-901e-4aa4-9117-d7d5dedac0d5/html/14441_Odbijanje_svjetlosti_-_sferna_zrcala.html__

## Implementation

This plan requires 5 units ( math 2 unites, 45 minutes each and assignment with due one week, art 1 unit, 90 min, science 2 unites, 45 min each). It can begin with either T1 or T2, but T3 must be after T1.

Art teacher (T2) explains symmetry in world of arts, encourages discussion, analyze work of arts on which symmetry can be found. Math teacher (T1) uses more theoretical approach, gives concrete constructional methods how objects are copied accurate and precisely. Teacher should insist on neatness and precision on constructions. Science teacher (T3) shows implementation and application of axial symmetry in science and real life.

## Outline of the Lesson

__Math__

This plan requires 2 units. First is in classroom (45 minutes) led by teacher, and second is students individual work. First unit contains three activities and second unit one activity.

__First unit__

First activity: In the beginning teacher try to recall from students what they remember. What kind of symmetries they learned in previous years of studying, what properties have each symmetry and how they construct. Teacher uses paper shapes and magnets and puts them on board. (http://bit.ly/3Y4AiM7)

Second activity: teacher gives first task to students, they discuss solutions and then simultaneously with them solves problem on board, helping students and guiding them step by step.

Third activity: teacher gives them another problem, again they discuss how to construct and they students draw solution in their notebook. Teacher project on screen powerpoint presentation (https://bit.ly/3WQKOpg) with solution step by step.

__Second unit__

Activity: Teacher shows students patterns in interior design which contains all sorts of symmetries. They discuss and reveals symmetry on pictures of wallpapers, carpets and tiles. After that teacher gives them assignment to design their own pattern of bathroom tiles which contains all symmetries they learn so far. This project assignment can be done at home in period of one week.

__Art __

This part of plan requires 90 min for two activities.

First activity: First 20 min teacher will show work of art on projector on which symmetry can be found. Teacher will lead debate and discussion.

Second activity: Rest of time of this unit students will create their own pictures based on pictures they were presented. Teacher will guide them and corrected if needed.

__Science (physics)__

This plan requires 2 units. 45 minutes each.

First unit: teacher explains and define flat and spherical mirrors, provides examples how image reflects, run debate how image reflect in different kind of mirrors. Give examples where mirrors are use (lenses, binoculars, periscope,..)

Second unit: gives mirror equation and perform calculations after which student calculate themselves different kind of tasks and applying formula on concave or convex mirrors.

## Extension Activities

Assignment adjustments for advanced students – they can do this assignment on PC

Assignment adjustments for students with some kind of disability – they can just sketch pictures this assignment, they don’t need to construct them with geometric accessories. They can use to paint marker pens, colors, tempera, collage, …whatever they feel comfortable with.

Or teacher can organize work on assignment so they can work in pairs like “student -tutor”, so students who need support can get help from better student, and successful student are motivated. They keep diaries about instructions and directions they give and progress of student they are trusted.