Topicm8771db4afd27d085_1528449000663_0Topic

Floorings and tessellations

Levelm8771db4afd27d085_1528449084556_0Level

Second

Core curriculumm8771db4afd27d085_1528449076687_0Core curriculum

IX. Polygons, disks and circles. The student:

4) recognizes and names: a squaresquaresquare, a rectangle, a rhombus, parallelogram and a trapezium;

5) knows the most important properties of a squaresquaresquare, a rectangle, a rhombus, parallelogram and a trapezium, recognizes axially symmetric figures and indicates the axis of symmetry of figures.

Timingm8771db4afd27d085_1528449068082_0Timing

45 minutes

General objectivem8771db4afd27d085_1528449523725_0General objective

Matching a mathematical model to a simple situation and building it in various contexts, also in practical context.

Specific objectivesm8771db4afd27d085_1528449552113_0Specific objectives

1. Interpretation and the use of information presented both in a mathematical and popular science texts also using graphs, diagrams and tables.

2. Recognizing particular types of polygons.

3. Applying the properties of polygons in realistic context.

Learning outcomesm8771db4afd27d085_1528450430307_0Learning outcomes

The student:

- Recognizes particular types of polygons.

- Applies the properties of polygons in realistic contexts.

Methodsm8771db4afd27d085_1528449534267_0Methods

1. Brainstorming

2. Case study

Forms of workm8771db4afd27d085_1528449514617_0Forms of work

1. Individual.

2. Group work.

Lesson stages

Introductionm8771db4afd27d085_1528450127855_0Introduction

The students brainstorm the meaning of the ideas of flooringflooringflooring and tessellations, referring to their colloquial meanings. The teacher clarifies that the tessellationtessellationtessellation is the tiling of a plane using adjoining polygons, with no overlaps and no gaps. The flooring is the top covering of a floor, often decorative.

The teacher informs the students that the aim of the class is getting to know the possibility of using polygons to make tessellations and decorative floorings. Patterns on floorings are often made of regular polygons, which means the polygons whose all sides and angles are equal.

Procedurem8771db4afd27d085_1528446435040_0Procedure

The students observe the process of making tessellations, as repetitive elements, using the applet.

[Geogebra applet]

The students’ task is to observe how the shape of one polygonpolygonpolygon, a single element of the tessellationtessellationtessellation, changes when the position of its apex changes. Discussing the results of their work, the students use the terminology referring to polygons (a convex polygonpolygonpolygon, a concave polygonpolygonpolygon, a heptagon, etc.)

The students give examples of popular tessellations, that they know (e.g. ceramic tiles or woodblocks) They draw the patterns on the board.

Working in small groups, the students solve the tasks. They use the diagram TESSELLATIONS, where they can see a flooring patternpatternpattern commonly found in palaces.

[Illustration]

Task 1
1. How many different types of polygons do you need to make a patternpatternpattern similar to the one in the illustration? Give their names.

2. What do you think – can any type of polygonpolygonpolygon be used to make a tessellationtessellationtessellation? What does it depend on?

3. The point where the polygons used to make a tessellationtessellationtessellation “meet” is called the vertex of the tessellationtessellationtessellation. Find the measure of “touching” angles in one vertex of the tessellationtessellationtessellation. Find their sum. Have you noticed anything?

The conclusion the students should draw.

The sum of the angles with a mutual vertex in a tessellation measures 360 degrees.m8771db4afd27d085_1527752263647_0The sum of the angles with a mutual vertex in a tessellation measures 360 degrees.

The students use the information to solve the tasks individually.

Task 2
What is the maximum number of triangles “touching” at the vertex of the tessellationtessellationtessellation? And how many hexagons?

Task 3
Complete the sentences with appropriate number.

- … equilateral triangles and a regular hexagonhexagonhexagon,

- 3 triangles and … squares,

- A squaresquaresquare, a regular dodecagon and … triangles can “meet” at one vertex of a tessellationtessellationtessellation.

Task 4
What properties of polygons are used to design decorative floorings?

After discussing the results of the students’ work and explaining any doubts, the students work in small groups again. They design their own template to make tessellations. They cut the designed figure out of a cardboard and check the correctness of their patternpatternpattern by making drawings.

The students choose the best template. The winners get prizes, e.g. marks.

Lesson summarym8771db4afd27d085_1528450119332_0Lesson summary

The students do the consolidation tasks. They summarize the class and formulate the conclusions that they need to remember.

- The tessellation is the tiling of a plane using adjoining polygons, with no overlaps and no gaps. The flooring is the top covering of a floor, often decorative.m8771db4afd27d085_1527752256679_0The tessellation is the tiling of a plane using adjoining polygons, with no overlaps and no gaps. The flooring is the top covering of a floor, often decorative.

- The sum of the angles with a mutual vertex in a tessellationtessellationtessellation measures 360 degrees.

Selected words and expressions used in the lesson plan

patternpatternpattern

equilateral triangleequilateral triangleequilateral triangle

flooringflooringflooring

hexagonhexagonhexagon

pentagonpentagonpentagon

polygonpolygonpolygon

squaresquaresquare

tessellationtessellationtessellation