# Maths in the Solar System

Author: Malgorzata Konik in cooperation with Daniele Brioschi

Introduction

A series of 4 workshops were a part of a 5-day Learning Teaching Training Activity of Erasmus+ project INTERNATIONAL SCHOOLS’ STATION held in Poland on 10 -14 February 2020 with the representatives of 4 partner schools from Italy, Poland, Portugal and Romania on 10 – 14 February 2020. The 4 workshops were held in the period of 10 – 12 February.

The whole school week was dedicated to extending the participants’ knowledge of different aspects of the solar system as well as exploring the solar system as a means of teaching various science issues. Thus, among other activities (e.g. visiting science museums, school observatory, radio telescope centre etc.), the series of 4 workshops were organised to explore what the solar system provides us with in the field of Maths.

The first 3 workshops were prepared and carried out by six 16-years-old students of the Portuguese school for their 12-14 years old mates, coming from the other partner schools. The fourth workshop, with an original idea of a teacher from Italy, was prepared by the Polish students and involved all the participants (at different levels) to complete it. During all 4 workshops, the students worked in mixed international groups so that they used English as a means of communication in learning scientific issues.

Workshop 1 – Where are the Planets of the Solar System?

Aim: making a solar system model on a scale to have students practise calculating ratio and converting units of measurements.

Description:

The workshop started with the revision of the characteristics of the solar system’s main planets like mass, radius, distance to Sun, rotation and revolution periods. For this revision, a PowerPoint presentation was made. Then, the students cut out paper models of the Sun and the planets (without keeping up exactly to the ratio as the aim of the activity was to determine the ratio of the planets’ position). The main task was to scale correctly the position of the main planets on the wall, using a measure tape and a duck tape with the following clues given:

• Distance between the Sun and Neptune is 30 AU.
• Distance between the Sun and the Earth is 30 times smaller than the previous distance.
• Jupiter is about 7.8 x 108 km far from the Sun.
• The planet with the most comprehensive set of rings is ten times further from the Sun than the Earth.
• The planet closest to the Sun is 0.40 AU away from it.
• The solar system´s hottest planet is 0.70 AU far from the Sun.
• Uranus is 18.6 AU away from the Earth.
• The Red Planet is 0.60 AU further from the Sun than the Earth.

Workshop 2STEM: Simple Tool Enables Measurements

Aim: to measure the acceleration of gravity using a pendulum.

Description:

Having prepared a pendulum of a given mass and length, the students put the pendulum in oscillation (less than 10 degrees) and measured the time interval related to 10 complete oscillations. They repeated the previous step four times. Next, they created charts that included the collected data, in each step, the oscillation period and its most likely value, besides pendulum mass and length. They retraced all the previous steps for another pendulum with a different mass but the same length. After that, the students converted the pendulum oscillation time period formula in order to calculate the gravitational acceleration. Finally, they expressed the experimental error related to the real value of g (acceleration of gravity).

Workshop 3How Heavy Is Water on Mars? (and on other Planets in the Solar System)

Aim: to explore how the weight changes on planets using bottles and water.

Description:

Working on the concept of density, the students related the mass of the water content of a plastic bottle with the respective volume. Then, they compared g on the Earth with g on the other planets of Solar System and tried to explain the physical significance of it. Using identical plastic bottles, the participants calculated the mass of water they should take to answer the question “How much water should we put in a plastic bottle to simulate the weight of a kilogram on the surface of each planet in the Solar System?”. Finally, they sensed the different weights by holding each bottle in one hand, while holding the plastic bottle related to 1kg on Earth in the other hand.

Workshop 4STEM: Sun towards Earth – Measurements

Aim: to make an art installation to show the real proportion between the Earth and the Sun.

Description:

Students were asked the question: If the Earth was the size of a bottle cap, how many bottle caps would you need to make the Sun? Students, divided into 6 groups, started with calculating the radius of the Sun to be drawn and filled in with the bottle caps. They knew that the radius of the bottle cap was 1.5cm and they found out the average radius of the Sun (696,340 km) and the Earth (6,371 km) so by arranging proportion, they calculated the size of the Sun’s shield. After drawing the Sun’s circle, they younger students started to fill it with bottle caps (and counting the caps) while the older ones were supposed to find out how many caps would be necessary for the project by calculating the surface areas of the models of the Sun and the Earth and dividing the values.

The activity was designed for kinaesthetic and visual learners in order to teach some maths issues (ratio, radius and surface area calculations). It also provided students with bits of knowledge of some dimensions in the solar system and made use of English as a communication means for teaching and learning STEM.

Dissemination:

All the young pupils of the Primary School no. 1 in Kruszwica, Poland, where the workshops took place, were shown the results of the workshop 4 as its visual proprieties seemed very suitable for school children of any age for introducing them to the topic of the solar system dimensions.

Wiktoria: …at 1:30 p.m. all visiting and host students had a workshop together. We calculated the relative position of the main planets of the solar system. It was cool.

Francesca: I was amazed to see in small but faithful dimensions how much the Sun is bigger than the Earth.

Igor: … we started our first workshop about the distances between the planets of the solar system. It had been prepared and now carried out by our Portuguese friends. We made paper models of the solar system indicating distances in scale. An interesting experience! A lot to learn!

Weronika: … after lunch, we had another workshop: we sensed weight on different planets of the solar system. Then, in the gym we completed a visual task to compare the size of the Earth and the Sun. We enjoyed the workshops very much!

Zosia: The workshops prepared by our friends from Portugal were very interesting. We learned different things in Physics and Astronomy, and we made some experiments.

Antek: The workshops were about astronomy in general but I learnt some new maths formulas and a lot of English words. I liked them a lot and I hope we will be able to have more such classes.

Kuba: What I liked the most was that we built the Sun of bottle caps and compared it to the Earth. The second thing that I liked was that we all use English to learn Maths, which I had the first time in my life. Overall, the time of the workshops was nice and it passed fast, which meant that the workshops were great.

Mikołaj: During workshops we learned some Maths in English. It was a very interesting experience and I certainly won’t forget this.