Teaching in distance (still in progress).**Teachers**: Sabrina Nappi in collaboration with Mario Di Fonza and Riccardo Di Pietro **Students:** 14-16 years**DESCRIPTION:**

Analysing situations and problems of daily life with the aim of their mathematical formalization, we naturally introduce mathematical concepts and tools. Reading and interpreting data in a chart or, vice versa, filling in a chart with provided data, is not always so easy for our students.

**Introduction to statistics **

The starting point of the activity is the question “What does statistics study?” that we ask the students using the software “Mentimeter”.

Students reflect on the topic and make a list of some examples with statistics statements: “The average mark in maths in this class is 6”, “The average height of the students is 1.67 cm”, “Making pizza at home is a very trendy habit this year”.

Statistics helps us to move on from the outstanding variability of phenomena (economical, demographic, social ones etc.) to interpretive models of the surrounding reality, going through classification and abstraction.

Statistics tools are introduced through Eurostat’s TED statistical educational website in which statistical concepts are described in a few steps**, **main subjects are especially variable types, charts creations, frequencies distributions, bar charts and column charts, mean and median.

An E-learning tool is also proposed for the explanations, animations and exercises about statistics and you can find them on ‘Statistics online‘.

**Activity: From data reading to graphic interpretations.**

This video “Statistics on prices” on Eurostat’s is part of Eurostat video series and can be used to easily integrate statistics in mathematics classes. It tackles the topic of price statistics, including inflation or consumer prices, and shows students how to use the information on prices and inflation in their assignments. After watching the video the students do the proposed exercises searching for relevant data and they create appropriate diagrams on Google documents.

In these exercises students read the chart containing annual data about price development of 29 European countries over a period of ten years. A skilled reader can sum up all the information deduced from these values only observing the chart, but this is not ordinary.

However, data can be better interpreted if represented in a graphical representation such as a diagram or a graphic because images can give us an overview of the investigated situation and easily understandable information.

Moreover, using graphics students can compare different phenomena, underline the phenomena development (for example points of maximum and minimum, increase, decrease, etc.) and make future predictions.

The activity ends with the time quiz.

**Activity: Relevant data research **

The students attending the first year of the school for tourism are taking a course in remote and, sometimes, in presence, with the title “Me and my territory” whose aim is to let them know and observe the territory in which they live in order to safeguard it. For this reason the most important contents they deal with are population, urban density, square kilometres surface and they are asked to create thematic maps with Google Maps in order to locate heritage sites of the territory in which they live.

It is important for students to compare national data with European ones to have a complete and detailed view about what is happening in the European Union.

**Online sources: **https://ec.europa.eu/eurostat/web/regions-and-cities

Students consider the statistics Eurostat has developed for some regions, for other European Union countries and specifically for Campania, the region in which they live and, eventually, they analyse the provided data.

https://ec.europa.eu/eurostat/cache/RCI/#?vis=city.statistics&lang=en

**From the chart to the diagram**

After reading the chart data, students, divided into small groups, create mathematical modelling challenges starting from a specific situation they choose in which they either evaluate increase and decrease over an observation period or make future prediction.

Here is the description of a challenge created by a group of three students:

**Less and less..**

**1 – **Please analyse data in the diagram and define the average decrease variation of population in Campania over the last five years. Assuming that the average annual variation of Campania population remains the same as the one revealed in 2015-2019, what will the number of population be in 2022? Make a future prediction and illustrate the evolution trend in a diagram with a comment.

**2 –** Please choose another European Union region with the initial value of the population in 2015 between 5 mln and 6 mln and proceed in the same way as in point 1.

https://ec.europa.eu/eurostat/cache/RCI/#?vis=nuts2.population&lang=en

1-We draw a chart with reference data:

We define the average variation (A.V.) of the period we took in consideration: 2015-2019

A.V.= (5.801.692-5.861.529)/5= -11.967

In order to define the number of population in 2022, assuming that the upward trend is equal to the average one of the observation period and considering the passage of three years, the solution is:

Population 2022= (11.967×3)+5.801.692= 5.765.791.

**These data let us reflect upon the territory of our region whose risk of desertification is very high.**

2- Let’s consider Provence-Alpes-Cote d’Azur France

Proceeding in the same way as in exercise 1, we have

A.V.= (5065696-5.007.977)/5=11.544

Population (2022)= (11.544×3)+5.065.696=5.100.328

Unlike Campania, The population in the Region of France will increase.