Aims:
•  To elaborate sequences of numbers according to given mathematic patterns.

•  To solve problems in mathematical contexts, adapting and understanding different strategies and assessing results;

•  To develop reasoning and mathematical communication, formulating and testing conjectures, processes and ideas, justifying and explaining results;

•  To communicate orally and in writing, using natural and mathematical language, interpreting, expressing and discussing results, processes and mathematical ideas.

Materials:
Sheet of paper with the problem, parchment paper, colour pencils and pens.

Introduction:

• Oral explanation of the work to be done in the classroom (10 minutes);
• Distribute the pupils in groups of four;
• Give out the materials;
• Silent reading of the task to be carried out;
• The teacher clarifies some important questions which may arrise after the reading of the task;
• The pupils try to solve the problem in pairs (15 minutes).

Main part:

• Pupils presentations: one sheet of parchment paper, drawing paper and colour pens
• Pupils purpose the resolution of the task;
• Discussion of the task (55 minutes) – large group
• Final Synthesis and contents systematization(10 minutes) – large group

Round up:

• Pupils should solve the task autonomously but under the supervision of the teacher.
• Thus, students will be the builders of their own learning since they are responsible for the acquisition of knowledge.
• Pupils can easily solve this activity and the conclusions which they come to allow them to acquire some knowledge of the main mathematics issues.

Clarification of some main concepts:

• To find out the number of phone calls made by any number of people using a chart; combine all the numbers starting from zero to the previous number of students because there is always somebody who makes no calls.