GOAL ! - Go Outside And LearnIdeas of lessons outside a school (Maths and Science)

Please write your country, idea (up to 15th November), the approximate period of doing, the age of students + description + your name Other teachers write if they are interested to share this idea with their studentseach teacher uses a specific color (choose!):

UrszulaSiegfriedIvanaTuijaJose Benito Ambrož

Idea 1: How many trees are in your country? We can answer on the basic question "How many trees are in your country?" in three ways:-guessing- counting trees in forest (10m x 10 m or even better 100x100m) than multiply with area of country/%of forests-using Google Earth (different locations), same as above but in computer room(?average of different areas and woods) - use distance tool!-using books and net Very opened question - what is a tree (a young one included yes/no)We did it last year - in Slovenia approx. , 500.000.000 trees (250 per inhabitant),range from 1.500.000.000 to 200.000.000BIG NUMBERS, ESTIMATION, ORDERS OF MAGNITUDE, % I like this idea, i propose to try something like that and discuss the results with students (level = i don’t know yet, rather young : 6eme or 5eme) I proposed something very similar to my students this year. Which is the number of persons of a mass meeting in a street?. Which is the system to calculate this number?. And one more similar. If we want calculate the area of a burnt surface, what whave to do?. We have so many trees in Finland.. Nice idea! How many trees is needed for a daily published newspaper in participants country? How many trees are = 1 m3 -measuring in a forest. We would like to try it with fish in the Adriatic sea :) Idea 2: The Siegfried’s idea. Which is the system to calculate the height of a tower?. Or a tree.

I propose you:14-16 years1 lesson:Debate between students to find a system to measure the height of a tower (or other real thing).At the end of the class we can explain the Thales system (somebody says he used this method to measure the height of the Kheops pyramid)2 lesson:Check all methods and measure the shadow of the tower and the shadow of a wood stick. Then, we can use the Thales theorem to measure the height of our tower. I will do this activity me measure the height of a tower near our school (no access to the tower), by getting on GoogleEarth the distance between the tower and the school, by measuring each student’s arm and using a ruler. Students’ level = 4eme (age = 12/13). With students in level 3eme (age = 13/14) I would like to do the same with the handmade sextant proposed in idea 6; so videos are welcome.... Ok. I will try to convince a student to do the videos. If any student want to do it, I will try do it or do a document explaining the system with photos. I need sometime, so the video will be in Internet after Christmas. We can do the activity in January or February, if you are agree.OK What is accuracy and mean error of (your) handmade sextant? Less than 1%. It is the same, more or less, for all handmade sextants I checked. It was checked with a taquimeter. 1% of 90° or 360° ? I think accuracy does not depend on an angle - in the same conditions it is not important if you measure 2° or 350°. New activity to do to continue this way:Which is the wood volume (without branches) of one of the trees outside our school?We can suppose the tree is a cone. We need measure the height and the radius of our tree at the basis (measuring the contour of the tree=circumference). 1 lessonAnother one:When we measure the height, we use the shadow. What is the angle inclination of the sun rays in this moment? This inclination angle change along the day and the year? What is the appropriate angle of inclination of a solar panel and what is the system to orientate our solar panel?. We could install a solar panel in our schools, I think. 1-2 lessons Geometry, Geography, Astronomy Idea 3:

14-16 yearsWhich is the system to trace right angle outside the classroom?. (To trace a big square, for example. It was and it is necessary to build).1 lessonDebate between students to find systems to trace right angle2 lessonTo check all systems and choose the better system. I proposed this problem two years ago to my students. They found two systems:http://centros.edu.xunta.es/iesramoncabanillas/cuadmat/pirkheo/basepir.htm Geometry, History Idea 4:Humans rob 14-16 yearsSure there are areas people changed near our school. Near my school there are a big area which was “robbed” the sea. Which is the number of square meters robbed?. We need see the area robbed (students go to see the situation today)We need an old photo to know what was the situation at the pastWe need use a map to measure lengths (or GoogleEarth)We need use geometry to calculate the areaDepends on shape of robbed area, rather not a rectangle i suppose... Students’ discussion how to calculate it can be interesting. Topic rather difficult, because students will have to do a map of robbed area (probably ‘old’ and ‘current’ maps will have different scales) and divide it into squares (or triangles), approximate area of ‘not whole’ squares etc. 2-3 lessonsGeometry, Geography, local History Idea 5:14-16 yearsWe go to trace geometrical objects outside the classroom What is the system to trace a circle, an ellipse or a star outside?Rectangle. I did it with my students few years ago - not so easy. Circle an ellipse is very easy to do. We need only a chord and a wood stick. The system is based in the circle and ellipse definition like a “geometrical locus”. If we want do a square or a rectangle, it connects with the Idea3. The problem is to trace well a right angle. It is a task difficult to do on a field, depends if the know Pythagoras theorem or not. If yes - quite easy. My students did not know this theorem, so we used lines parallel to PE court + diagonals.

We could use this method. It isn’t mine. It is a method proposed by one of my students years ago. We need only chords and wood sticks. Or we can search for other method. but I think it is interesting students could understand is different to do a thing on a paper and to do the same on a field You can see an example here:http://centros.edu.xunta.es/iesramoncabanillas/origcrop/praticas.htm Part 11 lesson:Debate between students....2 lessonTrace a circle and an ellipse outside the classroomPart 21 lessonWorking with GeogebraStudents have to do a star (based in a polygon) in GeoGebra. They have to include lengths and they have to think the system to do his star outside the classroom. They must choose one, two or three (depending the number of students involved) of all stars to draw outside2 lessonStudents have to trace their stars Geometry, ICT Idea 6:14-17 yearsMeasuring angles The sextant. How to do a handmade sextant (video?)How to use a sextant to measure angles (video?)We use a sextant to measure anglesWe use a sextant and a metric tape to solve trigonometry problems (15-17 years in Spain)We use a sextant and a metric tape to solve a problem different that appears in a text book Number of hours: more than 4

Geometry, Trigonometry, Topography, etcMeasuring angles is quite difficult, so - respect :-)Can be compared with an angle calculated with 3 lengths + a law of cosIt is a good idea to compare the obtained result with a sextant and using the cosinus theorem.I could do a thing:I can try to convince one student to do a video explaining the steps to do a handmade sextant and I could try to convince another to do a video explaining the system to use a sextant. If we do this, the number of classes could be two because students could do before a handmade sextant at home.You can see an example of use here (English):http://www.xplora.org/shared/data/pdf/measuland.pdf interesting, i looked at this and i have some questions:1) which angles were really measured in the terrain? <A =180, it is impossible to measure.2) why <AGF=90 and AG‖EF ?3) why students divided this figure into 5, not 4 triangles ?4) was measuring angles compulsory for students? if 2) =true, much easier to measure only distances and divide into 1 rectangle, 2 trapeziums and 1 triangle, or 2 trapeziums and 1 triangle. 1) I don’t know.2) <AGF was measured with the sextant, I suppose. If AG seems parallel to EF it is not important. They did’t use in their work this fact.3) I don’t know. It was their option to do the calculate4) No. They had to do a trigonometry problem. What to do and how to do it was a part of the problem they had to do. It is an open problem. I don’t introduce corrections in their work. I read their work only. I publish in internet their document without changes, if they want publish it. If I read their work and I talk with my students to correct their mistakes, the work is mine too. I run a risk of they can deceive me easily but I prefer this option. And my experience is that a student hasn’t interest in deceive me. A part of them because they want see their work in Internet. Other part, I suppose, because they know I will be angry if I discover their deceit.And you can see more works here (“Trigonometria” section. Spanish):http://centros.edu.xunta.es/iesramoncabanillas/cuadmat/index.htm Idea 7:14-16 yearsCan we measure the inclination of the stairs of our school?Can we measure the slope of the hadicapped ramp of our school?Can we measure the slope of the road? We use “eye to eye” system.lol, i feel like in the forum for surveyors...It is a good idea to continue the work later. You can see the system used to do this by my students two years ago (spanish language). It was the method found by one of the students:http://centros.edu.xunta.es/iesramoncabanillas/cuadmat/pirkheo/nivterr.htmGood, quite simple, i miss a spirit level in this instrument

1 lessonDebate between students to decide what are the data necessary to solve the problemInclination of the stairs - measuring 1 stair. Did your students do it ?No. I talked them about this problem today. They asked for the next lesson dedicated to measure the slope of a ramp and I told them they will measure the stairs inclination of our school. Two of them thought about the problem some minutes (when they have to do exercises about percentages I had wrote to do) and they said: “ Teacher, is the same problem of the ramp” and show me a drawing where appears several stairs with a straight line at the top of each stair.Measuring 1 stair by each student would look funny... Calculating average from many data can be more precised than 1 measurement between top and bottom of stairs. To check. 2 lessonTo apply the method to measure the inclination of the stairs (degrees) and the slope of the ramp (degrees and %) We can talk our students about the maximum angle to do a ramp for disabled people in our countries. We can compare these angles (or %) between our countries.We can go to the computer room to do a graphic of our stairs and ramp (GeoGebra). We can do an applet to calculate the slope of a ramp easily (and the same with the stairs). We can do a video with students doing the work to measure lengths and doing the calculations in a paper (my students have to do the calculation of the angle with a scaled triangle on a paper and they have to measure the angle with a graduated semicircle. They haven´t trigonometry knowledge at 15 years)I checked in Poland - it is of course precisely described in a regulation (75 pages) to “A Buliding code” (next 75 pages). I do not think students are able to find it and understand ‘lawyers’ language’, maybe...H < 0,15 m 15% outside without a roof 15% inside, or outside with a roofH < 0,5 m 8% 10%H > 0,5 m 6% 8%There are also regulations concerned stairs, but all related to width and high, not inclination. We have such a ramp in our school. I also looked for legislation on slopes of such ramps. Not easy to find but interesting to learn how to look for, select information and find (needed to become a citizen with critical sense, can be helped by the documentary/library teacher).Then I would like to do this activity with my oldest students, find % and angle, and draw on Geogebra maybe too. One of my students told me the legislation is difficult to read. I said them they could send a e-mail to one handicapped association asked for the concrete information they need. Or they could use the telephone to obtain an answer. One student asked his sister (she is an architecture student) and she gave him a book containing the information. In the book appears the % is 12.5 in Spain. I have seen 12% in other documents. For me all possibilities to obtain the data are good. ok, we will do this, with 1st class. We also have a ramp in our school. Geometry, ICT

Idea 8Solids of revolution1 lesson.Objective: To practice solids of revolution and have different view at them.Students divided into groups do from snow (sand?) a cone, a ball, a cylinder. Their task is to measure needed data and calculate volume. They have to do drawings and calculations at home. We can’t use snow. We haven’t snow on winter. If we try to use sand...difficult to do a solid with sand. But in Spain we can use other material. I will try it with sand...and water (we have both...) lol, I know you do not have snow in Cambados - same in France and Croatia I suppose. At last 1 advantage of living in a country with cold winters. A cone would be even better with sand.Ok for me Idea 9Number game1 lessonObjective: To practice basic terms and calculations related to numbers.Each student has a big number on his/her back and chest, can be from a school register e.g. 1-24. During the lessons a teacher ask them for:1) introducing themselves (“I am a rational odd number, I have .. dividers/ I am a prime number etc.)2) matching into pairs: even numbers, sum=24, etc.3) queueing: start=5, add 3 -> 8, multiply by 2 ->16, ...4) dividing into 2 groups (left-right): even/odd, prime/not prime, divided by 3, ...5) creating bigger numbers in sub-groups: e.g. (1, 2, 5, 18) - create a number divided by 4 ->51812 funny.. I like it too. I will do. Idea 10Step measuring1 lesson (or even half)Objective: Learn/practice statistics (average).One of the useful information is length of a personal step. Straight ‘base’ with known length should be traced (e.g. along PE court), 30-50m. Students walk and count number of steps, calculate average etc. And we could connect this system with the Mathematics history. One of the versions to describe the system used by Eratosthene to measure the distance between two points maintain Eratosthene used your idea.I propose something closer to students: calculating length of a route from student’s home to school. Should be measured 2-4 times.Good idea to complete the activity.

Nice idea! Idea 11Oil and waterWe go outside Maths classroom to go the laboratory roomA environmental disaster happened. A big stain of oil is on the sea (we can see the stain in a photo. It is a GoogleEarth image where we have included a stain). What we can do to measure the numbers of liters of our stain?.1 lessonWe work in the laboratory room. We will drop oil on the water to obtain a table of values: x:oil (in ml) y=diameter of the stain (in mm) (see: http://www.youtube.com/watch?v=3q6pAHzEq6s)2 lessonWe go to the computer room and we insert our data to obtain points in Cartesian axes (GeoGebra). We will try to obtain a function who approach our points (square root, f(x)=K*sqrt(x) ) (see:http://www.youtube.com/watch?v=szs7hH59fAw&feature=mfu_in_order&list=UL)Then we can we can measure our oil stain on the water and use our function to calculate the volume.

It is a project for 4 classes. The age of students is 16-17 and it is a project to work functions and their operations. It is no a easy project. If somebody wants read all project, I can send a copy in English. But we can use the idea to do an activity for students of an age of 14-15 (even 16-17 but without parts of the complete project). Idea 12A cup (or a mug) and a spoonWe go outside Maths classroom to go the laboratory roomIf we have two equal cups (or smugs) with warm water at the same temperature but we put in a spoon in one of our cups, which is the cup where the water cool dawn earlier?1 lessonLaboratory. We will measure the temperature of the water of our two cups at the same time and each two minutes (or each minute, or each three or each four). We will obtain two tables of values. One for the cup without the spoon and another for the cup with the spoon.2 lesson

Computer room. To compare our two tables of values, we will use a graph. We will use GeoGebra to generate points in Cartesian axes (x: minutes, y:temperatures). We can compare our two graphs and obtain conclusions. Age of students: 14-15 Idea 13Optimal cans14-1516-17Previously: Students have to see cylindrical cans at the supermarket and in their larders.1 lessonDebate: If we see cylindrical cans, we can see different sizes. To make a can is necessary to use brass. But if we have two cans with the same volume but different dimensions, the amount of brass used is the same?Which must be the dimensions of a can to economize brass? (if we know the volume of our can and it is a cylindrical can)2 lessonEach group of students (or each student) have a cylindrical can. They have to measure its dimensions (with a caliper) and calculate the brass used to made it. They have to do calculations to obtain the optimal can for the volume of their cans and compare the result with the dimension of the “real” can. If it is different, they will make with a card the optimal can.The method they will find will be different for students of an age of 14-15 and 16-17. The old students will do the work using the derivative of a function. My students, some years ago, have to do something more: the old students have to read the works wrote by young students and criticize their work. Idea 1414-15Which is the weight of one corn grain (or other cereal) To continue the work:The legend of the chess origin Which is the number of grains king gave to the inventor of the chess game?They apply the data obtained previously to calculate the weight of all grains the king gave to the inventor of the chess game.Students search in Internet the production of corn in their country and in other countries and compare their result with this data to obtain conclusions. In Spain the legend of the chess origin appears like an example of a sequence in the textbooks. The textbook says the number is big, the weight is very big but never explain the reason. Idea 15Which is the number of fishes in a lake?

We won’t measure this number. We will do something similar. Which is the number of cars blue, red, yellow of our country?Students, divided in groups by colour, will count the number of cars that appears in the street during one hour. They will write the total number of cars and the number of cars of their colour.cars of their colour/total=cars of their colour in our country (x)/total of cars in our countryThey must search in Internet for the numbers of cars in our country to do the calculations.It will useful to know the number of cars of each colour we must make if we work in a car factory. A system very similar is used to obtain the answer for the first question sometimes. They use a proportion or, at least, this method was used sometimes. They mark some fishes and later fish a big number of fishes. They count the number of marked fishes and then they do the proportion.The idea is not mine. One teacher of the University told me this activity some years ago. They proposed me to do this activity but with a bag filled with chickpeas. I must mark some chickpeas and move round the bag. Then...etc Idea 16We are painting our school, classroom, school kitchen … outside walls … What we have to do?

- measuring, calculating areas- calculating how much money we have to spent for the colours- if we want to hire someone to do this job instead of us, calculating the costs and compare- compare the price between paying per hour or fixed price by square meter

Idea 17Making pancakes or apple pie(We have school kitchen) PROBLEM: recipe is for the 4 people we need to prepare for more people

- different measurements (spoons, cups, ml, l, g …)- different numbers (decimal, fraction …)- we have to by all ingredients, how much money we have to spend- how to make cakes for more people (17 students ;)- at the end taste the cake

I like this idea (cakes too, unfortunately :-). I think at school will be easier to prepare something cold: salad for example, with fruits or vegetables. Last week few classes in my school did salads on Technology lessons and then brought it to the teachers room - we really liked it! Nam, nam.. Idea 18Equation race1 lesson

Objective: To practice Cartesian system and solving equations.Students’ task is to solve equations in envelopes hidden under stones (->idea 19). Warm and not rainy day is necessary.- teacher give envelopes with written coordinates to students- students put envelopes in correct places- teacher gives to each student coordinates of ‘his/her’ envelope. Can be related with Maths skills of him/her. - students find their envelope and solve the equation- 2 students who did it first get extra equation and solve it together, then next 2 etc.For each activity students collect points -> note. We could do the same in few countries and do ‘International ranking’. Idea 19Descartes on the parking2 lessons (related to idea 3)Objective: To practice Cartesian system and basic geometry (tracing right angle and squares)To Idea 18 the Cartesian system is needed. I propose to paint such ‘drawing’ on the school parking I asked my headmaster - he said OK. I do not know when we can do this because of weather:cold and humid. The parking surface must be dry. x axis =<-5, 5>, y axis =<-5,5>, +0,5 m to each direction, 1=1 meter, lines 5cm. Y axis should be directed into north. Students have to draw the plan, divide tasks, decide what will be necessary etc. and ...paint it.I will do it :) Older student for my little one!

Sometimes I used this geographical star (my students made it some years ago) to trace cartesian axes and to do exercises with straight line equation and polar coordinates (it is difficult to use cartesian coordinates directly outside).Why? Did you do it? Because if you want use Cartesian coordinates directly, you have to trace two right angles (a right angle is difficult to trace outside) and to measure two lengths.

I think it is the easiest way to do “Descartes on the parking” (except N E S W), but i am open for students’ proposals:

green line is a string, 15-16 m. Of course it should be repeated for each quarter. So to do this is needed a compass (if we decide to have orientation NS, not necessary), chalk, string and measuring tape 25m. Sometimes the surface is not plain so the problem to measure two long lengths outside is a problem. With the polar coordinates you need measure only one length and one angle. Three years ago I proposed my students of a age of 16-17 this problem. Is it easy to obtain the Cartesian coordinates of a point outside? They begun trying to trace the rights angles but after 20 or 30 minutes one of my students says: “we could obtain the Cartesian coordinates using a angle and a distance from origin to the point”. The polar coordinates appears like a form to solve a problem. It was a good lesson. If we want the “real” north direction, we have an activity for one lesson to trace the North-South direction. If we use a compass, we can trace our Cartesian axes in some minutes. I don’t know which is the better option. We can do:1 lessonWhich is the system to trace a right angle outside? (and trace a right angle outside)2 lessona) Which is the system to mark the North-South direction?. We can use a compass or use the shadow at the noon. Or both of them and calculate the magnetic declination of our school.b) To mark the four geographical directions outside. So we have a Cartesian axes. I can’t use the Cartesian coordinates at my school to do the “Equation race” competition. I haven’t a big field to do it. Also, I prefer use the drawn Cartesian axes to explain, for example, the polar coordinates with a metric tape and a sextant.To polar coordinates students have to know trigonometry, younger ones - don’t know it.Yes. it is an activity for my students of 16-17 years if you want to calculate Cartesian coordinates through polar coordinates. But if you want work only with polar coordinates is a work for students without knowledge of trigonometry Idea 20 : drawing and measuring circles

Who : youngest students (level = 6eme, age = 10/11)1st class in Pol, so 12/13When : around 26th January 2011How long : 40 min outsideneeded : rope, chalk, meters How : students are in groups (3 students), they already learnt the definition of a circle as a set of points. They draw in the playground a circle, write the radius and measure with a rope the length.Back in classroom, all the data are gathered in a spreadsheet and students discuss and make a conjecture on a formula.The file with data is sent by mail to students; they have to add formulas to compare theoretical and practical results and send back (in our curriculum, we have to learn them to use a spreadsheet) I would also like such easy activity for conjecturing the area, any idea?What about car tires? We can even ‘organise’ in our school something bigger, a tractor tire for example, or smaller - a barrow, a bike? Students will roll tires along line with known length (30m?). Then... many possibilities, depends what we want to achieve/practice.I think students will enjoy this activity (teachers too...) Idea 21 : axial symmetry in the schoolWho : youngest students (level = 6eme, age = 10/11)When : around 1st may 2011How long : 30 min outsideneeded : camera or mobile phones How : students are asked a few days before to observe symmetries in the school (inside/outside). During the lesson they go out in groups and take photos.The use of a graphic program is explained to students.Photos are sent by email to teacher after resizing and drawing the symmetry axis.Photos are used in the classroom to conjecture the conservation properties of the symmetry. ok for me, i would like to use mobile phones.We could use GeoGebra. GeoGebra allows insert an image and work symmetry. Idea 22 : an activity with all participants ?If we would be all ok, Benito... would you organize for our 6 countries another gnomon measure session to get the radius of the Earth?? The measure of the radius of the earth is an activity for several lessons, you now. It is difficult to fix a day our countries are all with good weather (we are six countries). Etc. We cannot choose the weather, but as i remember in previous measuring took part 4 schools, with 6 schools - higher possibility that in some will be a good weather. I think the most important would be weather in Finland and Spain/Croatia, because of their latitude difference.

Sibenik 43 43 N 15 54 EVantaa 60 17 N 25 02 E When I did it with you, my students worked at least five lessons to do all work and they published the work in Internet. I prefer other options. I don’t like repeat activities other students of my school did and my students can see in our web page. They prefer to do something new. Of course, you can do the work, if you want. I think it is no necessary all countries do the same activities. We have a different curriculum, ages of students, authorities recommendations, etc. But if all of you are agree, and you are interested in calculate the radius of the earth, I will do the work with my students too. We could try to do something different with a gnomon for all participants and to use all data obtained in our countries. There are several experiences to do with a gnomon. This experience is only an example. We can use the gnomon and its shadow at the sunrise. If we mark on the floor the shadow line, people says we have the est-west line but it is true only if we do this work certain days of the year. Maybe we can do every possible measuring on 21st March? It is Monday. Equinox is on 20th at 17.32 UT. Measuring a shadow of a gnomon on the solar noon. It is a classical school experience. We could try 21 December.Free days in France. If this day the weather is not good, we could try 21 March. We could use the obtained data to:- Determine the North-South geographical direction and East-West direction- Measure the radius of the Earth- Calculate the ecliptic inclination- Calculate the magnetic declination of our schools.Last two far far away from my curriculum... I did this calculations several times. I could do a document explaining the most important questions to do all activities and questions If we do this work on the Cartesian axes described in “Idea 19”, we could see the difference between the two lines: the East-West line and the obtained line measuring the shadow at the sunrise. It is useful to compare the difference of the angle in our countries and to explain the difference of the day duration in each country a fixed day (it depends of our latitude. It is easy to explain the day duration is different in Spain and in Finland with a globe and a lantern). The problem is locate a good place to do the measure. Our school is situated with mountains at our east.In Poland the school is surrounded by mountains, so it is impossible to see a moment both of sunrise and sunset precisely. I think in Slovenia is the same problem. Sibenik as i remember has mountains on east and north EastOK. Shadow at the noon For us is better if we do the work at the sunset because we are at the coast. So, each school must decide if will do the work at sunrise or sunset. The angle is the same, so it isn’t a problem. These data were obtained using an Internet web page. Are the data for September 24 and November 22. The data were obtained for the coordinates of several schools. Times is from noon to sunset. It was

a part of a Comenius project but we didn’t the measure with a gnomon. It is a new experience for me.:

18h13m-12h10m=06h03m (Italie)

18h34m-12h32m=06h02m(France)

19h30m-13h27m=06h03m(Spain)

18h29m-12h26m=06h03m(Germany)

17h32m-11h30m=06h02m(Poland)

16h44m-12h04m=04h40m (Italie)

17h03m-12h25m=04h38m(France)

18h08m-13h21m=04h47m(Spain)

16h39m-12h20m=04h19m(Germany)

15h38m-11h24m=04h14m(Poland)

idea 23.Measuring for ex. a foot length of students foot (number of a shoe), length of students, observe colour of eye or natural hair colour etc.Make a diagram compare different countries. And can be combined to genetics in biology - one visible feature and many allele at the same time.age 15-16duration 2-4 lessons how big groups? i think we can ‘compare’ students involved in the project. extending it to the whole country will be fake because of small groups being compared. you are right!I like it!about 30-40 students Idea 24Are we going to ‘use’ solar eclipse on 4th Jan ? Observing quite risky, taking photos - very difficult, but on the other hand it will be in the morning when students will go to school. (by the way: what happens with the calendar i sent? i don’t know if you will be at school on this day) In Spain we are in holidays we are in holidays too Idea 25My colleague Dorota (Maths) proposed to build near the school a court to petanque - do you know this French sport / game? We played it with students both in Poland and France and really enjoyed it ! The court is just a flat rectangle 15 m x 4 m (can be bigger), covered with rubble. Idea 26 16-17 years

What was the system to locate a ship in the middle of the ocean at the past (before the GPS and other modern systems)? Students must to do a research to solve the problem and they must write a document where they do a description of the method and apply the method to obtain the geographical coordinates of a point (their home or the school).