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I really use in my now days teaching the outdoor learning and it is very efficient for students to be more practically learner than theory one.

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traistaru maria

The children's kindergarten is the primary link of the national education system which, along its evolution, fulfilled social, educational and instructive-educational functions with different weightings and at the same time pursued numerous general and specific objectives in cognitive, attitude-affective and psychomotor plan.The pre-school period is the stage of the most intense receptivity, mobility and psychic possibilities, a period of life with remarkable progress in all its plans. Now all basic adaptive conducts are formed, more important intellectual and creative structures - including sociability, behavioral characteristics, affective - volitional reactions

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My students had to measure their own bathroom at home. They had to calculate how may m2 of ceramic tiles they needed for renovation. They had to find out the cost of 1 m2 of ceramic tiles and the cost of all renovation.

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for my studentes their purpouse are applicate maths to software and informatic ingegnery in general

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In recent years, my students were involved in many projects based on math. Last year they wanted to renovate the local bus station. They made a project specifying costs, revenues, and materials.
Another project was based on creating a family budget: they had to specify the incomes, the expenses for his own family. The expenses must be divided into categories: basic, utility bills, loans, savings, trips or leisure etc.

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I am for the first time doing this type of online course where I am learning new realities of mathematics. I have not yet applied this type of project with my students.

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I teach for 13 years old students (2nd ESO in my Spanish educative system).

I would go for Statistics to design a challenge problem. Last year I asked my students to make a final project in this unit. They had to choose one question amongst some provided ones  to answer or find their own one. Most of them chose to describe themselves as an age group, what were their likes, hobbies, phobias, behaviours, feelings, beliefs…

On the other hand, young people are always saying that adults don’t understand them. Since the part of statistics we have to deal with is the descriptive one, why don’t ask them to describe themselves as a group.

So I think it could be a good starting point to ask them “Who are you?”

I bear in mind that they have to answer that question using statistical methods, surveys, tables, charts and some parameters.

Maybe the question is too open, but once I shape it up, it could be engaging, open ended and it could easily fit the learning standards.

Finally, they could communicate their final conclusions to our school community using our website, some panels or even local media.

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My students are high school students, and one project was one year ago "upgrading a first floor bath" where students had to measure the surface to be covered with new ceramic tiles. They went to a particular store to see the tiles, choose the models and calculate the necessary quantities. The team that had the most beautiful model, the most correctly calculated and the lowest cost came out winning. Of course, it also implied the graphic design on the drawing or computer of the bathroom.

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First of all our schools aren't so beautiful and so provided like the one in the video.Sometimes it is complicated also organize group activities because of limited space; labs are often occupied for activities that require their use. So I generally resort to real problems to introduce a topic and problem solving to taste their skills.
However, the school-work and Simulated Enterprise Project offer different ideas for PBL. For examples: market analysis, market research (creation of a questionnaire), choice of a statistical sample, analysis and representation of data

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I divede my class in several groups of 4-5 students.

Each group has 1 month to build a real pyramid symbolizing the food pyramide.
The pyramide has 4 sides. In each the students have to report the peculiar food pyramid of the language they study at school. Following this we'll have an Italian face, an English face and a Spanish face. The last face will be used as students want: let's free their imagination.

To design and build the pyramids they'll have to : find an amazing idea; make the tech drawings to design it; build it in wood, cardboard or other materials (or a mix of them); take pictures during all the process to apply all the knowledge of photography they've learnt in classroom. Realize a slide presentation with Power Point, Prezi, Google Slides or other softwares. Finally all gruups has to lecture in front of all the classroom using all the material they produced.
The last activity is to give a vote to the job. This activity is made by the whole class following an evaluating grid I prepared.

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Students contribute to the development of their communities through projects that focus on services or topics of interest to those communities, and act as ecologists, data collectors, social workers or scientists to gain insights into their community life. Products and tasks become authentic when experts are invited to school to talk and evaluate students' projects and collaborate with them. In many projects, these links with experts are essential to help students develop quality work and develop their own learning process. Many teachers may think that all this involves more work, but these connections are surprisingly easy to create and once established, they come from themselves. The established relationships are invaluable for encouraging authentic engagement and lifelong learning.

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I have used project based learning in math club and in class. For example, tree years ago I was implementing a project about the “history of numbers”. Students engaged in activities using a variety of resources, such as literary texts, digital material and films etc and were motivated to compare the arithmetical systems of four ancient civilization, “Babylonians’, Egyptians’, Incas’ Indians’ arithmetic systems. Thus, the structural elements of the Indian system were highlighted.”

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For the time being I can not identify what challenges or problems could work for a class project, because my students are too small, they are 7 years old, and for the moment it is difficult.

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The projects based learning devoted to solving real-life problems is effective if it involves knowledge from various disciplines. An example of a project can be focused on examining and solving problems related to the reduction of environmental pollution. It is possible to involve students in solving problems from different perspectives: mathematical statistics, chemistry, biology, medicine, etc.

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A real problem that I propose at my students 12 years old is given them a recipe for a cake for 8 people and tell that we have to prepare the cake for
12 people and we have to understand how many flour, how many sugar...
They have to identifying proportional relationships.

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I think I would integrate them into an activity connecting real life with maths such as organize, design and create a part in the school garden with plants and trees of their decision.

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An example of PBL Activity: Students must create a portfolio of pavement patterns for a given surface, specifying for each one what is the number of boards required. They will know types of plates (hexagons, triangles, squares, dodecagoans, etc.) and their dimensions.

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At the beginning of the school term, this year, I gave to my 9 years old students this real problem:
The Rossi family goes to the zoo and pays £ 55 for the entrance tickets. Mom, dad and grandmother paid £ 45, but Mattia paid less. How much did you pay the ticket for Mattia?
For lunch they buy 3 sandwiches with meat at £ 4 one and 6 sandwiches at £ 2 each.
How much have they spent for lunch? How much did the Rossi family spend in paying tickets and lunch?
They have enjoyed a lot and have invented a similar problem thinking of going to school on a trip.

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For my primary students, for those about 10 Years old, I am going to ask them to calculate an area, for the grandpa's yard, and to estimate the total costs for the
wire fence.

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In this day we are studing the solar sistem. We are creating a model of it in scale reduction

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I'm going to ask my 13 years old students to make a 2D draw of The Solar System in scale for our school's hall.

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Trying to teach maths in B grade make you be as realistic and image making you can. Chinren

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In my case, I think that it´s quite difficult to use PBL in my classroom because I work with very young student (4 years ago). Anyway I try to use, at least, one PBL per schoolyear, but not related to Maths. We play Maths using materials closed to them and the use their knowledge about numbers to solve real problems, like share pieces of toys, pencils, ...

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I think I would ask them
- to find out what is cheaper at the supermarket (calculate price/kilos)
- to apply geometry to architecture, art and to forniture design
- understand something about economics

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In a 12th grade level class we are studying solid geometry. So we can consider the challenge to build a class-library taking the most number of books in the armoire we have in class.

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The aim of STEM education; questioning, researching and developing products. The most appropriate method for this purpose is Project Based Learning. If the math course topics are explained in such a way as to find solutions to daily life problems, they can be made more fun by the students. The work in the picture is the "fractions" topic and the scenario is; Mimarın in the Children's Library planned to be made to our city. I want you to make a design using 1 full, 2 half and 4 quarter blocks.

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We calculated the area and perimeter of the school playground (5th grade students). They are exited every time we do it. I also taught them the transformation scales (meters, grams, an so on) using the steps from the school's stairs. I do this like a game (in teams/ individual they have to go up or down the marked steps and transform/ solve an exercise/ task).It is easier for them to understand the concept and they enjoy the activity (cause it's a game

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For my 5th grade students I want to propose something near to their life. I ask them to compare different offers to choose the most cheaper smartphone. Than they have to calculate the hypotetic family budget and compare it with the smartphone prices to choose one of them that the family can afford.
They will use calculus , knowledge of decimal numbers, percentage, place value and number comparison skills.

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I will ask my students to imagine to go shopping in a supermarket. They have to organize a party and they have a budget of 50 euro. That can they buy? 1How many euro left?

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I currently work at a high school where unfortunately in Greece the lessons seem to be orientated just to prepare the students for the final exams and the entrance to the University. I till know do not had the chance to used PBL in my classroom, i rather use simple activities that the children work in groups like projects for example 1) how to measure the height of a building just from the angle and similar triangles, 2) which telephone company is suitable for them, 3) how to fill the floor with specific tiles, 4) how much money we will need to paint the building, 5) what is the best (value for money) contract for the annual school trip and so more. I must say i feel a little awkward engaging my class with a so well prepared activity as the one shown on the video. I sure would like to give a try....

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One problem for my seventh grade students would be to find out how many gallons of paint would be needed to paint the entire school and how much it would cost to do it. They will apply both notions of geometry, to find the surface of the school to be covered, and algebra notions to determine how much it will cost.

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I will give to my students of 8 years old the task to organize a library in our classroom. They will use maths to catalog the books, their cost, and they will divide them and will count them considering their type.

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I will give to my students of 8 years old the task to organize a library in our classroom. They will use maths to catalog the books, their cost, and they will divide them and will count them considering their type.

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Such an activity facilitates communication within the team, establishing a common viewpoint in terms of synthesizing knowledge and understanding the activity of an architect. Groups must learn to lose or gain as part of real life and to cope with this. I think it is an effective way to put into practice the accumulated knowledge.

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A problem that my students will work on is in the school.

We have an old building. This construction students want to turn into a gym.

Students will use a certain set of math skills. They will use mathematical skills in geometry, will make the necessary calculations.

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Year 2015 was the year of Samantha Cristoforetti, the first Italian woman who went to space. Starting with his journey, me and Mario, who taught in the same class, a first graphic classroom, we have proposed a project entitled "Planetaula". All the disciplines took part in the project and the starting point was to ask a few questions: Why? What are the motives, principles, laws governing the operation of the great clock of the Universe? Why do the objects orbit around the sun, stars and planets? So the curiosity was born to know more about orbits, stars, planets and solar system ...
Here is a conceptual map and video representing the project in the classroom.
https://drive.google.com/file/d/0B9zLiZ3ai7wsTXNZbFk5UTlCTmc/view?usp=sharing

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After the last earthquake that Mexico suffered (sept 19, 2017), I think that an interesting and perhaps useful challenge is to create a seismograph for their classroom, also to build different types of houses or buildings models to study the movements, timing and resistence of their models. With this examples they are using math skills like: data collection, graphing and analyzing them. They can learn about correlations and also about logarithm scales (magnitude of the earthquake). They are also applying knowledge of another areas like geology and physics.

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At the beginning of the school term, this year, I gave to my 9 years old students this real problem: you have 50 euros and you need to buy things for school (notebooks, pensile, pens and so on), what do you buy, how much do you spend and what is left of your 50 euros.
They enjoyed it a lot and they invented a similar problem going to the supermarket.

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THIS YEAR WE TOLD TO OUR CLASS  THAT WE WANT TO GIVE IT A NEW DRESS SO AFTER THEY PLAN EVERYTHING THEY STARTED TO SEE THE MATERIAL PLAN THE COST GIVE EVERYBODY A ROLE AND SAY HOW LONG WE NEED TO DO ALL

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Project  based ilearning is one of the key features of the kindergarten. In particular, at this time with the children we started one that is related to natural sciences, art and mathematics. The children respond to basic queries that they are interested about how colors are created, what are their grades and they are experimenting to find them. They make assumptions and find out how many were verified and how many were defrauded. They should fill a double entry board and count checks and denials. The children found it very interesting and continues.

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I think project based learning is a great way of making students learning meaningful. Giving them a purpose is a good way to get all children regardless of ability engaged and the final project seems like a great motivator. Most of my teaching has been in the younger years so I would like to look more into how this could be done as efficiently and effectively with younger children.

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Such an activity facilitates communication within the team, establishing a common viewpoint in terms of synthesizing knowledge and understanding the activity of an architect. The groups must present the project in such a way as to convince the jury that the project deserves to be put into practice. Groups must learn to lose or gain as part of real life and to cope with this. I think it is an effective way to put into practice the accumulated knowledge.

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I haved learned about PBL on a Schoolnet Academy course, but I did not tried yet to apply this method in my classroom. I think that an interesting challenge for my classroom could be to organise a yard sale, where they can sell small boxes made by themselves.

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Turkey

I use project-based learning in my class. I agree with projects that are mathematically relevant. I am learning new things there. I am developing myself in time. The activities of the project are going to the students very much.

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Since I started teaching math I have tried to introduce real-life things in my classes. It is quite easy to do it when teaching geometry or statistics. However, with other parts of the subject is not so easy.
In the last two years I have participated with other teachers in a project  of soap elaboration. We have used project-based learning. In my classes the students have worked with proportion and percentage calculations that are needed to know the amount of each ingredient in the soap recipe. In addition, they have prepared a spreadsheet to get the expense to make a quantity of soap. Each subject has worked on some of its content relating it with the soap. As a final project activity,  they have made soap in the natural sciences class.
Students enjoy this experience while applying mathematics to real things.

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I have learned about PBL two years ago on a course. And I love this idea and also I am afraid to introduce this way of working on the math class. But this year I started to do PBL on the IT lessons. This is a subject in which I am more courageous to make changes. I will also dare to consider such changes in mathematics lessons.
How I bring the real world in to math? I thing that many teachers do that: statistics on the favourite football teams, percentage on sale, surface area on the painting of rooms.

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There are two different ways how I try to connect maths and real life in my classroom. First when we are learning about the perimeter and area of rectangle and square. Most of the examples are like: If the walls of the room are square shape with side * and we want to paint it how many wall paint we have to by? The another way how I implement PBL and connect my subject with real life is true statistics. They have to create a questionnaire, process data and make graphs, charts...

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With my students, I try to bring them to reality so that I can apply mathematics. But I usually use PBL with math and science when I do experiments!

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Two years ago I was implementing a reading engagement programme with my 5th grade students based on the book Made on Earth which takes as its subject the effects of globalisation both on the human and the natural environment. It tells the story of a red jacket and how it was manufactured in an Eastern Asian country by workers working under harsh conditions (long hours of work and low wages) and traces the trip both of the raw material and resources required for its production as well as the trip of the jacket across the world from production to first owner to recycling bin to an illegal immigrant crossing the Meditteranean. It was a great opportunity to approach subjects ranging from inequality, violation of human rights to global warming. As a warm up activity I had my students make a short survey in four groups of fifth and sixth graders about their trainers. So, off they went with their notebooks to each of the four groups and made a list of the material the trainers of each pupil were made (usually plastic) plus the country of production.Then after accumulating their data they came back and they had to present the results of their survey using statistics. They worked on Excel and then they presented their conclusions to the class. Below you can see one of the sheets they produce where they accumulated their data as well as some of their findings using Excel.If you download the attachment you'll see that they used different types of diagrams to present their findings which only confirmed what the book they were reading argued for !!!

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Αντίγραφο του ΠαπούτσιαTRYPI KOMNINI

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In my classes, students solve problems related to real life, most of which appear in the student manual. In these problems they apply what they learned. Performing PBL is something totally different and would be ideal but this is practically impossible because the math program is very extensive (mainly in secondary education) and has to be fulfilled because of the final national exam.

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I have activities in Math related to real life. For my students (6-7 years old) is very important to use things that they are familiar with, so I do a lot of activities like that and the kids are very interesting in these ( I use little rocks, money, human body, measures, paving units in the school yard, leafs from the school garden etc.)

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We were lucky to try a PBL activity after our national test was done in our grade 6 class. We spent about a month on a group project designing a park. I think it worked well for some students because they naturally wanted to challenge themselves and learn more however there was no 'problem' to solve it was just to design something. So after watching this I am inspired to adapt and alter the project so that it can be more like a challenge to fit it an area or setting etc. I also think that have real architects come in must be a wonderful touch and hope that we can make that work at our school (we are currently under construction so maybe I can get our current architects to come in and judge the end project)

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PBL is a great think-tank for taking advantage all kind of things. At my classroom we get the paintings of great Kandisky painter, so we can figure out and name the shapes, the Lines and after try to find out the equations for perimeter, square meters etc.

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The PBL is a great thing for students. I hope I do the same with may students in the future. I have some example of problems which involve the real life in the classroom. One of them is to measure oll of ungle from their school and check them if they are 90 degrees. In this situation they are not alowed to use the square but they may invent something else.

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Anna, Italy          Save money in grocery shopping

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Anna, Italy          Save money in grocery shopping

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Project-based learning can help make Maths more meaningful.
Every time it's possible I bring the real world in my classroom.
Save money in grocery shopping is a lab where student have to study the shops fliers and have to choose that where they save money.

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I would like to propose to students to plan a trip for two days considering a given price per student. They’ll have to calculate the costs of transportation, accommodation and the schedule considering the places to visit. Students will have to do calculations simultaneously with studying google maps, choosing a firm of transportation and a place to stay.

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I'm very interested in the idea of PBL, but I still struggle with the demands of final Exams.
I can only develop projects in special classes, for witch I don't have time constraints.
In Math Applied to Social Sciences, I developed a project in witch students have to study the various offers from banks to a saving account. They have to study several scenarios and to present what they think is the best proposal.
With a tecnhical class of design, we explore pavements (constructed by hand and with Geogebra), create a art work (with the help of a Design teacher) that culminates  in a public
exhibition.
My difficulty appears when we have pre- University students that have to take final exams (I can not find interesting ideas for several subjects, and most of the times have little time to present the contents that are demanded by the curriculum)

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The project I have been thinking is about geometry and consists in designing new plates for the classroom of sciences. The school science lab needs a restyling and each class has been entrusted with the design of a classroom part. There is a sink in the classroom and behind it there is a square white tiles (a square made of 36 tiles). My class has been entrusted with the task of painting these tiles. Each group must reproduce the tiling according to the given dates and propose a new one using translations and rotations. Then drawings must be reproduced with a drawing software such as GeoGebra. The mathematical skills that will be exercised are as follows:
- recognizing and addressing problems in real contexts,
- recognize and represent forms of the plan, relationships and structures that are in the real world.

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I think that PBL is great! is the best way of learning. But it is difficult to implement in the educational sistem. The hours in each group for maths are a few, the number of students is big (35) and the curriculum is very long.
This month I´m going to make a projecto with mosaics where the students have to find out which shapes allows to make one, they have to make their own mosaic and make a tutorial of how can you make one.
I want to read your experiences to have more ideas!

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Once I spent several lessons by solving problem how to arrange the best lighting system for a town. It was a complex problem, my students were interested, but really time consuming. And I wonder if this way of teaching is really effective. Students are envolved but I feel a lack of practising during those activities.

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Geometry in art
I would ask my students to find examples of art (paintings, sculptures, buildings etc) and study the geommetrical elememnts used in them.As a finalproject I would ask them to create their own work of art.

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I share the view that PBL is the best way you can bring the real world into your Maths classroom. BPL is a wonderful tool for every classes: not only with STEAM, but also with Business  and Economics in English. BPL is really useful to solve problems, take ownership of learning and applying all diverse contents in a real world context improving skills, collaboration, creativity and critical thinking in your classes. Last year, e.g., I carried out a CLIL project based on insurance companies and related probability problems with my 5th class of secondary school. They hypothesized a problem, considered all the possible solutions and discussed their thesis in English in front of the final exam commission. 

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I share the view that PBL is the best way you can bring the real world into your Maths classroom. BPL is a wonderful tool for every classes: not only with STEAM, but also with Business  and Economics in English. BPL is really useful to solve problems, take ownership of learning and applying all diverse contents in a real world context improving skills, collaboration, creativity and critical thinking in your classes. Last year, e.g., I carried out a CLIL project based on insurance companies and related probability problems with my 5th class of secondary school. They hypothesized a problem, considered all the possible solutions and discussed their thesis in English in front of the final exam commission. 

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We were exploring isometries (line simmetry, central inversion, translation and rotation) on Croatian traditional costumes (especially on the costumes of east part of Croatia - Slavonia) and old handworks. These costumes are very elaborate, with floral designs (mostly), fancy embroidery, lace work... The students had to interview old women and investigate how did they made complicated designs and did they knew it is Math. They were collecting photos of the costumes and old handworks and then they tried to make their own designs. They also made posters about it.

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Matematika na ručnim radovima našeg kraja

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Name:

The strange world of Escher

Topic:

Paving, Mathematics and Art.

Description:

M.C. Escher has become an inescapable name in the connection between art and mathematics. His work in the field of paving was remarkable and absolutely innovative. What polygons are the basis for the pavements created by Escher? How did these polygons become to create tiles? How are these tiles articulated to generate pavements? How and what geometric transformations did Escher use in his works?

Project - Paving of Escher. Geometric transformations in Escher's work.

Skills:

- develop visualization and geometric reasoning and be able to use them;

- understand and be able to use properties and relations relating to geometric figures in the plane and in space;

- develop understanding of isometries;

- be able to solve problems, communicate and reason mathematically in geometric contexts,

- The predisposition to identify geometric transformations and the sensitivity to relate geometry to art and technique.

Applying Maths skills to a real-world problem:

http://www.educationworld.com/a_curr/mathchat/mathchat019.shtml

https://www.edutopia.org/

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My students are 6-10 years old and I can give them problem based learned activity in math, geometry and geography in this area: design a new school -play yard; organize a one day trip and visit in a new town, organize a new learning timetable, organize the space for the vegetable garden, plan the Christmas' market activities, organize a visit of your village, realize a game with numbers to play with your friends, realize a recipe,

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My student is in the age of 7-11 years. I am teaching mostly with things that are encountered in daily life. I have activities with cartons. I use the things they use in daily life. I want them to do them by touching. At the same time I ask where the numbers are seen. When I use the money, I take markete. We bring the money to the class.

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In PBL are several skills that students can develop/use:

some math skills

organisation skills

collaboration

way of presentation

creativity

correlation with some other subjects in curriculum

socialization

discover some new talents

each team member can be useful.

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Romania,

Unfortunately I do not use the PBL class. Indeed, we often use brainstorming sessions to solve the problem, but it is not enough. We learn in college about PBL but when it comes to applying it always is like in theorea.Programa is loaded and the classes are with 7-30 students.

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Last year I produced with a colleague a stop motion animation (in primary school).
For this activity children had to create the setting. So they used maths to measure and divide the set, to count frames, to measure time....
This activity involve a lot of different skills and Maths is one of these.

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My students are 14 years old and have been taught in project teaching. Through eTwinning projects and research they easily master the elementary school maths.

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An example of activity may be the following: Determine the smallest distance between two European capitals. Specify the identified cities. Students will work in pairs and use the Internet to solve the requirement. The mathematical ability used will be the organization of data in a matrix array.

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I have once applied a didatic sequence  based in a problem-situation that was intended to study (a one-bedroom construction project) and to contemplate the mathematicians content refering to the theme “Direct proportionality” and others:  geometric design, measurement units, área and volume, proporcionality, equations and information treatment,worked in the 7th year. This proposal was developed from the everyday life of students, with the aim of developing mathematical knowledge and capabilities.

In fact, students learned to build plants, through geometrical drawing instruments, working the whole idea of ptoporcionality, building graphs using Excel, searching products prices, critically analysing the cost-benefit of furniture and, mainly, developing the critical sense of a citizen, the autonomy to builg and research.

There is no doubt that when we contextualize our lessons from everyday situations we lead students to be aware of the need for specific knowledge to resolve the problema and, consequently, the constructions of new ones, however the implementation of this type of projects need time. On the other hand, it also requires a new posture of the teacher.

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Our school needs to be painted and have its front and back yard redesigned and reconstructed. So, would it be easier and less expensive for us to do these by ourselves or would it be 'wiser' to hire sn do the job? How lond would it take to do them?

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Mathematics is everything that surrounds us.

Each type of movement in physics is described by a motion law that is given by one
function or equation of several variables (spatial, temporal, spatio-temporal). Trajectory
followed by a moving material point is, in fact, the graphical representation of the function that
gives the law of motion. To determine the magnitude of earthquakes on the Richter scale is used
logarithmic function.

Simple motion issues are solved using first-degree equations.

The hardness of a material, with
the help of the Brinell sphere is solving a second degree equation.

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Should we buy an electric car or a conventional one?

Our family considers buying a new car. What’s the best option? Can we afford buying an expensive electric one or a car which runs on fossil fuels? Are electric cars really environmentally friendly or is this a hoax? The videos bellow can help us start a debate among our students and analyze many mathematical concepts.

Are Electric Cars Really Green? https://youtu.be/17xh_VRrnMU

Benefits of Electric Vehicles: https://youtu.be/G3wzulCMFVg

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Unfortunately, the hours of math in each class are few. Projects can be:
- organization of a trip (with calculation of costs, distances, ...)
- organization of an event (example "math party" with preparation of games)
- design of an environment (with measures, scale design, costs)
- design of a room with energy saving
- conduct a statistical survey and analyze the data

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I could think about several real problems that involves maths skills...just keeping in mind they are not children, but adults. This year I would like to ask them to prepare a project for the local community to be financed by a public or private body. The project should aim to enhance tourism in the territory, giving job places or possibility of career for local people.

They would face to the chance to receive a certain amount of money so  based on that they should estimate the needed budget.  They should have every idea or implication clear, including advertising and necessary employers (including themselves). They will face to financial issues such costs, distances and areas (in the territory), graphic designing, and furthermore no mathematical subjects like natural resources, archaeological/historical sites and communication with local activities and professionals.

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I think it will be interesting for primary school students, let say about 8-9 years old, to develop a geometry PBL using LEGO first and then building some boxes by wood. They could be helped by their parents. I love to involve parents in homework. The builded boxes could rapresent their houses, their room, a imaginary classroom.... best ideas come from students as well!

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There is a church next door to the school yard. I ask the 9th year students to estimate the height of the steeple. I then ask them to work it out accurately and provide them with a range of tools- some will be useful and others are a distraction. The toolkit includes a clinometer, a ball of string, large tape measure, a yard rule, graph paper, a compass, a mirror. This lesson can incorporate measurement, scale drawing, trigonometry and similar triangles.

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I think Project Based Learning is the best way to involve students in the study of Math often so hated. It can make Maths more interesting, but at the same time not easy to realize. Really my students were interested in maths working in groups in the study-statistics last year. We saw how statistics can be used in real life by survey on former graduates of our school. They had to cooperate to make a questionaire, collect data, represent data with tables and charts, make a final report .

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Using the ratio theory i would ask them to make miniatures of real life objects  i.e a car, the school design etc.
Using the line theory i would ask them to calculate the slope of certain objects i.e various stairs in the school.
Using geometry i would ask them to calculate the volume of various objects i.e a bottle of water, a water tank, a classroom etc. Also the area of objects, like a classroom and the cost of painting it given the cost per sq.m.

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I teach in a primary school and I've used PBL in Science and Geography, but never in Maths.
Last year, for example, my students realized a self-sufficient ecosystem using fish and plants.
Anyway, I'm determined to introduce PBL in my Maths classes. I would like they will design how to use the different areas of the schoolyard (games, reading, green areas...) using recycled materials such as plastic bottles to make vases, wood pallets to create benches and everything fantasy suggests them.

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I never used PBL in my classes, and it’s very difficult for me thinking about challenges or problems for this kind of methodology. There are logistic difficulties (we don’t have a maths laboratory and I always teach in small classes poor of technology), but I think that the biggest difficulty is in my mind: I’m not really a creative persone, but I hope to learn something new from this course and to apply it in my future classes.

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It's not simple because I work with very young students (age 7). We always play maths with them simulating real problems. The children can use their knowledge about numbers to solve little problems.

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My country's education system which is full of hard tests does not allow to apply pbl in the class. But I am sure that there is a way that I can integrate it to the maths programme. Actually tomorrow I will want mey students to build a maths class

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Sometimes, I use Lego Mindstorms kits to build some kinds of robots to demonstrate certain parts of the curriculum. For example, when talking about the circumference of the circle, pupils are instructed to build a simple chassis with wheels, and then to program the robot to travel the distance of exactly 1 meter. Pupils can find out that the best way is to measure the wheel diameter and calculate the circu

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As in our school most of the students are specialized in IT, so I would make a project connected to IT. For example, making real-life statistics in spreadsheets. I can imagine it as: the students need to get data from the news, and they have to draw consequences from the data. It would need their problem-solving and analytic skills. An other idea is to find ways of using Maths in programming. As they study a lot of programming, I would ask them to come up with a plan for a programme that can be used in the real life. At the end, they would also make the programme running. It would need their problem-solving, analytic and also their logical skills.

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In our school there is a big room on basement where once upon a time there was a canteen. My 3th Class students could designing what they would like to be in this space. They should draw the map,  make a model, predict the costs and present their work to the class. They will certanly have to use their Geomethric and Maths Skills (technical design, area, measures, reports, proportions, forecasts) but they will also have to use their imagination and inspiration!

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It's not an easy question because it would be easier for me to work with Physics, but that should make the Math's challenge more interesting (at least that's the philosophy I'm selling to my students, so now I can get a taste of my own medicine :lol).
Last year I worked with my English Literature colleague to analyze data coming from an online test for a eTwinning project. I worked with the students to make data understandable with tables and graphs. That implied the knowledge of statistics and the use of Excel for data analysis.
I would like to implement something for my 11th grade class, last year I made the students build a simple clinometer, to determine highness of objects/building using distances and angles. This year I'm going to do it again, but I want to make the experience more significant, having them build the clinometer in groups and taking measure of the school to, maybe, build a model of that (I'm still not sure of which final task give them). This unit implies the knowledge of goniometric functions and trigonometric theorems on triangles. They can learn how people apply trigonometry to estimate dimensions of big objects when they cannot measure them directly (such has constructors with buildings or agronomists with secular trees).

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I have used PBL in Science to incorporate environmental studies, engineering, design and technology but with mixed results. The main difficulty is time and individual learning needs. I can see possibilities in Maths around projects like landscape design, alternative energy, networks and catering. However, I think the key is to start with small real life tasks, at an earlier age, to

ative, perseverance and problem-solving skills necessary for PBL. I also have to get better at not providing answers but rather to ask more questions.

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I find the idea of using PBL is very interesting, Because my students often ask me "how will I use math in my future life?". In my opinion by using projects I can show them in which cases they are really going to use math and solve their problems. Of course, it is going to be hard to start using PBL, but it is wirth trying!

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I don't use pbl in my math classes exactly. Yes we speak about problem state and make brainstorm to solve the problem, but this is not enough. We learned pbl in theory at university but the real world isn't like this. Our curriculum is intensive and the classes are very crowded (40-50). On the other hand we do etwinning projects and scientific projects so we use pbl in small groups. It is enjoyable. I want to learn how can ı entegrate it to my crowded classes.  I plan to watch the pbl in math classes videos from edutopia :) May be it can be helpful.

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I have very good experience with the PBL. I do eTwinning projects with my students (14-18 years) and they are very fond of this kind of learning. I ussualy connect math with economy (because I work in High school of Economy) and with history of mathematics. Kids love eTwinning because they learn many things on a different way and they connect with their peers from all over Europe.
But, here is an example of a project wy students do in pair. It is  a statistical research. They have to:
- cooperate to choose a topic of research
- determinate the hypotesis, sample and objectives of their research
- make a questionaire for examinees
- process the results of examnination (graphically and statisticaly)
- make a report of their research
- present their research to their classmates
The best part of this is their great creativity in choosing topics of researchs :-

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Hello everyone, I give math classes to students between 14 and 18 years. In recent years I have been working in this direction in collaboration with Universities and Institutions. For example last year we won the first prize in Science in Spain in the field of sustainability with a work on bees, mathematics and climate change. The students, in addition to using and learning new tools, were very sensitized and we made an environmental awareness campaign. My experience is very good, it is true that it requires a great effort on the part of the teaching staff.

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Romania
I teach in a secondary school and I can use math skills to make my students discover the meanings of statistics in every day life. They can collect real data and calculate afterwards, using math formulas and EXCEL functions, their meaning and the impact in their life. Using diagrams they represent the results; we all know that "an image has more impact than 100 words..".   :)

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Considering that I usually work with students aged 7-10, PBL is part of my lessons but with an emphasis on the creative part of it. For example, we take part in our school’s Christmas bazaar by creating our ornaments in teams and calculating how many will we need to create in order to reach a specific goal referring to our profits. The students, also decide the way we are going to promote the ornaments during the bazaar, so that the sales are successful. Although, at first, they seem a bit overwhelmed by the process of calculating and trying to figure out how to come up with a plan that will meet our goals, in the end they always manage to achieve them and be happy and excited while they do it.

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I never used PBL in my classroom, mainly for one reason: it takes a lot of time and in Italy we faced a drastic reduction of maths hours in every curriculum. Moreover we have under pressure for Math program to be covered in some kind of schools (the scientific ones) in order the student can get the final exam (I teach in a secondary school).
From this year I am in a school of Arts, so there is no such pressure and maybe I will try to prepare something for the next year.
I agree with the fact that the only way to be effective in Math teaching is to let the students to be active. In my classes I make students work in group and solve problems, possibly related to real world situations. I want they practice a sort of "brain gym", I don't want them memorize formula. In these years I have learned that they often prefer to memorize!

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My students are often unable to associate mathematics with everyday life. If we work more on this, we can make progress

I 'm hıgh scholl teacher. my country curriulum is very intensive. we can't make a lot of activity

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A real problem would be building a bike lane in our city. To do this they must use tools such as scales, graphs and economics tools.