By the end of this unit, the students will be able to:

• Apply the formula to calculate the perimeter and the area of a rectangle
• Identify the main characteristics of the mosaic art

• Video
• Worksheet with pictures of ancient and contemporary art pieces
• “Make a mosaic” online tool
• Evaluation activity

In order to deliver this lesson, the teacher will need to have a basic knowledge about the characteristics of the mosaic art. He/she also knows how to work under the umbrella of Problem based learning and should have experimented ahead of time with the online tool “Make a mosaic” to support students accordingly. Lastly, the teacher is suggested to prepare a refreshing activity for students to practice all the Timetables.

In order to be able to participate and contribute to this lesson, the students need to be able to recognize the different shapes (e.g. what a rectangle is). It is important for students to know how to collaborate effectively. In case this will be their first time, students should follow the routines established by the teacher. Lastly, students should have a very good knowledge of all the timetables (1-10).

Introduction:

The teacher shows the video about the Parc Guell in Barcelona, known all over the world thanks to the decorative technique by the artist A. Gaudì who combined ceramic fragments and coloured glass pieces, reproducing a sort of mosaic with waste materials and materials from everyday life. After the video, a brief discussion is carried out:

• Did you like the video? Yes or No and why.
• Have you ever visited this place? If yes, how was your experience?
• What do you know about mosaic art?
• Do you own a mosaic art piece and/or do you have it at home?
• Have you ever created an art piece using the mosaic technique?

The teacher informs students that mosaics have a long history, starting in Mesopotamia in the 3rd millennium BC. Pebble mosaics were made in Mycenean Greece. Mosaics with patterns and pictures became widespread in classical times, both in Ancient Greece and Ancient Rome.

*Also, an alternative would be to schedule an educational visit to a museum/art gallery.

STEP 1: Formulate a problem statement

The teacher informs students that their today’s mission is to learn how a mosaic artist calculates the tiles needed for a rectangle mosaic art piece. But first they will identify their main characteristics.

STEP 2: Identify key facts

Each group is given 4 pictures representing ancient and contemporary mosaic art pieces (Annex 1).

Following the group work, students share their thoughts in the plenary. The discussion should lead to the following findings:

• A mosaic is a pattern made of small regular or irregular pieces
• Those pieces have different color (e.g. natural or processed. In the past, artists mainly used neutral colors)
• They can be made out of stone, mineral, glass, tile, or shell
• Mosaics are often used as floor and wall decoration
• The topics represented in the past: persons, nature, life situations, religion, culture, geometry.
• Nowadays, the mosaic art pieces are also more abstract and modern.
• In most cases, the artist of an ancient art piece is unknown.

STEP 3: Brainstorm

The teacher refers to the problem statement “How a mosaic artist calculates the tiles needed for a rectangle mosaic art piece?” During this activity, the groups work on the computers (or tablets) using the online tool “ Make a mosaic” (Annex 2). The teacher calls students to draw random rectangles on the working area. In order to do that, students choose a colour/colours and then click on each box or click and drag the mouse over the boxes.  Allow some time for students to experiment with the tool. As soon as all the groups have created a number of rectangles, the teacher asks:

• How can we count the total number of the tiles in a rectangle shape? (The teacher shows with his/her hand the interior of the shape) Could you think of more than one way to count them? (The teacher introduces the concept of area)
• How can we count the total number of tiles that surrounds the rectangle? (The teacher shows with his/her finger the outline of the shape) Could you think of more than one way to find out? (The teacher introduces the concept of perimeter)

The teacher writes down the above questions on the board as a reference for the students.

Step 4: Analysis of potential solutions

Students work on solving both questions and search for potential solutions. The teacher strolls around and supports the groups whether needed. When all the groups prepare their proposals, the teacher calls them in the plenary to discuss their suggestions. The students are prompted to explain how they worked and what they suggest. For the first question (perimeter), students are expected to say that they can count the tiles one by one until they count them all (expected answer) or to follow a “quicker way” by multiplying the number of tiles of the first row with the total number of rows (desire answer but since it is an introductory lesson, not all students are expected to use this method).  For the second question (area), students are expected to count the tiles on the outline of the shape (expected answer) or to count the length and the width and multiply by 2 because the opposite sides of a rectangle are equal.

The teacher along with the students will conclude to the following:

• To calculate a rectangle’s perimeter = length + width + length + width or (length + width) X 2
• To calculate a rectangle’s area = length X width

Step 6: Apply the knowledge gained

Each student calculates the perimeter and the area in the given rectangle shapes (Annex 3). They are encouraged to discuss with their group if something is not clear or they need assistance. Also, the teacher strolls around and supports whether needed.

Step 7 - Present and reflect

The students are gathered in the plenary and discuss their findings. With the aim to broaden students’ knowledge, the teacher challenges students to reflect on the following question “What if I know the area of a rectangle backyard (56m²) and the length (8m²), how can I find the width?”. This activity could serve as an introduction to the division as the inverse operation of multiplication.

• Reading text
• Videos
• Pictures
• Hyperlinks