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Please send me the link so that you can explain

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Tashi did you see my writing in hindi I wrote your name

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I knew that the property of commutative associatative properties.

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In my 12th grade level class I have to teach goniometric functions, so I can introduce them by Eratosthenes Experiment.

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With my third-grade students, we tried to make a project about family budget calculation - a family's spending and spending for a month. It was very exciting to gather information, data, drawings, see if they could do it in the future with a budget.

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I had aproject with my kids where they could estimate great or small distances and then checked actual distances using the Google Earth ruler. They could determine the area of such complex polygons as oddly-shaped crop fields. They could learn about network theory and generalize rules while drawing lines to connect islands.

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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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Lucia, Italy.               It is very important to use a teaching based on projects. Students can see the importance of the studied concepts but above all put them into practice convincing themselves of their usefulness. unfortunately however it is difficult for teachers to be able to organize training projects involving students. 

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Lucia, Italy.               It is very important to use a teaching based on projects. Students can see the importance of the studied concepts but above all put them into practice convincing themselves of their usefulness. unfortunately however it is difficult for teachers to be able to organize training projects involving students. 

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That's one of the reasons i enrolled in this course: lack of imagination in creating projects for them. Of course, calculus skills are very important (money, time, distances, areas) and the most important is using equations in solving problems. So many everyday situations can be seen as equations. If they transpose it into an equation the right way, then it becoms easier to solve

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To set up a Project-Based Learning can be quite challenging  for the teachers, but I believe that it worth. In my opinion, a good project could be this: "apply your knowledge of mathematics, technology and biology to project the power plants and the power grid needed by the area where you live."

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The interdisciplinary project is a fun way to learn math.
Interdisciplinary projects for Mathematics  and education technological:
graders 5: To refurbish the school yard and calculate the amount of materials they need
graders 6:  To make Class budget  to rearrange classroom objects and materials which they would like
graders 7: To plan a trip and calculate mileage and time required and budget .
graders 8: To make a business plan on producing and distributing electricity for their village.

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Apply of mathematics to solve the problem of pollution in the city

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Pbl is a challenging project. It make teachers reflect on what they are proposing to their students.It is not simple, in my opinion, to find the right problem to start from,  for example it could be "Which is the best rate  for my mobile according to how  I use it
?"

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PBL

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sar

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This is an incredible way to learn math. We can teach our students how to take care of the family budget, how to plan the cheapest trip, how to cook using a recipe and many more.

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Pupils' maths skills in Primary school can have a main role  in many real life contexts: - calculating rates and shopping to prepare dishes for parties or events in school
- measuring distances, heights, weighs and capacities
- calculating money to pay costs for school trips
- surveys to discover information about mates ' collections and other hobbiesinterests  using strategies to design properly  display.

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I

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Fabia Genova
Through the execution and examination of small games, such as causal walking and the coin toss, the boys begin to make assumptions about the randomness and probability .

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I did many projects with my students and they like it very much. Using the maths they organize one rock concert, the sport contest to collect the funds for changing their classroom. They had to use their creativity, marketing and organisation skills, knowledge of other subject also. They realize how the maths can be useful in real, life situations.

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A project that my students could work on using mathematics should involve their beloved smartphones...
They can look for phone operators rates and offers for calls, SMS and internet data, organize information and find best solutions depending on some average user they have to model. They'll use statistics, literal algebra, cartesian graph representation, linear programming.

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[ Example of project ] With little students (8-9 y.o.) I tried last year to let them apply their knowledges about measures by planning the restoration of a small wood gate (gateway!). They had also to make a project for a wall painting (mural) respecting proportions. They made some mistakes  when they measure the sizes, so that they had to solve the problem by adding a supplement to the planks. �

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With geometry skills my students solved many problems in real life . In this way the students work in teams and are motivated.

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Students are given the results of state exams and school marks and they have to compare those data using statistics (with no names, of course)

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The students have fun in cutting out geometric shapes and putting them together.
They organize themselves into small groups, dramatize texts of problems and find the solution into the drama.

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I think that math is realty and reality is math. Each things each    situation is

due to a mathematical problem. I asked to my student to study the USA's election day with statistic.

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First I think we must start by letting teachers have time to think about their activities in class, at least in Portugal, unfortunately, we are losing too much time with papers and bureaucracy…
Then we can use de PBL……

When designing geometric solids, is requested to students using geometric figures build solid that you are asked.

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Mathematics in everyday life :
- shoppinsg
- pay- bills
calculation of interest rates
- calculation of taxes

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I realized with my students objects with different shapes using recyclable materials. They were exposed and filmmakers presented by their peers.

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I teach in high school. I introduced systems of linear inequalities using a real life problem: find a day or an hour in which a group of people can meet. They have to represents datas in graph that is the same one that we use in math.

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With Geogebra my students and I are searching for a function which describe a bridges, route...

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Together with students from 6th grade we realized geometric shapes of recyclable materials.

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PBL in the Maths Classroom - Adriana Fericean

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PBL in the Maths Classroom - Adriana Fericean

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My pupils are very young (7-8 years old) so I tried to tie the mathematical knowledge of their immediate experience working on a project called "Math about me" in order to revise mathematical concepts from the first school year. They have to write how old are they, how many persons live in their house(boys,girls, total), how may toots they have lost, which is their birth date, etc. It was a funny way to remember the concept on numbers.

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For younger students (5th graders, 10-11 years old), I provide supermarket leaflets and a shopping list, together with different tasks like getting the best price (buying packages), calculating the reminder or the discount, etc.

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My Bes student aged 13-18 and I suggest them to divide a square  , that is a plant of a piece of ground neither school, in many triangles. They use proportion, divition to operate.

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I could suggest the students to imagine they own a store, so they can role play the owner/seller and buyer, and use Maths notions: proportions, addition, subtraction to operate with in their activity.

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Last year I realized a project in my class with student aged 11-12. In this project we made real soap with a traditional recipe. Actually it was a Science project but there was Maths involved in it as they had to calculate the right amount of water, olive oil, caustic soda, using different measurement units. We used instruments such as scales, thermometers, graduated flasks.

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After teaching mathematical sequences and financial Maths, we have a PBL activity: Student visit a bank websites or take a leaflet from a bank with a bank offer of a loan. Then a group of students or an individual student count acording the bank offer how long they would have to spare a certain amount of money if they want to achieve their dream ( to buy a new flat, a new car, etc.) Students use the mathematical theory and compare it with the bank offer.

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1. Cooking: students must cook something. It will be given recipe for 200 people, and they must find out how much ingredients they need for 14 people using proportions. They also must calculate how much will it cost using decimal numbers

2. Travel planning: students will decide where will they go on imaginary trip. They must find out distance between two places using Google Earth and ratio. Also they must decide what transport do they take, in which hotel they will stay in, how long they will stay and which places they will see. They also can make a map of places. hey will be using ratios, decimal numbers, calculate units, Geometry (Geogebra).

3. Family budget: students will plan family budget . They will calculate what incomes and outcomes their family have. What money they must spend on everyday life and what for joy. How much they can increase incomings and where they can save some money. They will be calculate units, decimal numbers, graphs (Excel), percents, interest account...

4. Measuring the height of buildings around school using shadows, where they can use knowledge of similarity of triangles and Thales Theorem

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In the forth or fifth class of primary school, I can ask to the students to organize our school trip, projecting the destination (searching in internet the websites), the contents, the duration, the transport, the global cost and the cost for each partecipant, etc...

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First of all I would say that 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 example:  market analysis;
market research (creation of a questionnaire);
choice of a statistical sample;
analysis and representation of data

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I never use PBL as in the video , but  I often use real problems or real life to introduce a topic or to improve my students' knowledge: I uses cinematic examples in analytic geometry, the reproduction of bacteria for the esponential function, real life problems of max and min,probability...

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I think a good project for the 7th grade students is making a house and garden map with  legend and as maths application - measuring their dimensions in order to calculate areas.
Of course this project could have a sequel in the 8th grade, to calculate the volume of every room of the house.

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I teach in a seconday school and I try to use real problem to introduce a new math subject. For example studing cellular reproduction I ontroduce the study of exponential function.

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I live in a small town but there are problem of traffic. So i propose my student to use geometry to read the map of town to calculate area and lenght of roads so to solve problem of trafic by graph theory.

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We live in a small town. We have already made a study of the wonderful forest surrounding our village, but I'm thinking it would be interesting to calculate areas and estea volumnes that occupies space and the castle that is in its center. Because every year we went at different times of the year to see and photograph as they are this natural space.

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Donato; Italy

Use very often problems of everyday life. With the fifth primary we worked with large numbers comparing worldwide city dwellers and assuming world population growth for the continent. In this way children have also worked with charts and tables

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We live in a city rich in monumental art. We have already done a study of ancient building techniques but I'm thinking it would be very interesting to calculate volumes of stone, weight and energy to perform some simple concrete construction. It would be a PBL and our students continue to build new parts of a previous project.

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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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In my third primary school class I'm planning to ask children to design a playground area next to the school. They will able to measure, to calculate perimeters and areas of objects looking at them as shapes on maps, to calculate how much the plan could cost.

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At the 4th year of mechanics it would be interesting to suggest that students open their own garage to study the economic management.

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I totally agree with the need to put students to apply their Math knowledge in real life situations.
The problem is sometimes the fact that the curriculum does not allow the time for that - there are a lot of notions that need to be taught in a limited amount of time.
In my class I do try to include lots of examples from real life, but I have never tried PBL. Maybe it is the time to start...

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PBL is really engaging for teachers and students.
In second grade  it could be nice to play "At the grocery store" or something similar it's useful to understand the meaning of simple operations

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My opinion is that children should  presented math through specific examples from life or different job

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I think the need to connect mathematics with life and nice things. We call it the lessons more integrated. We practice mathematical tourism. We use a variety of measuring instruments, exploring the mathematical objects, visualize, calculate. I support STEAM.

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I am thinking of a simple problem such as creating a family budget. Calculating how the money is being spent at home. Simple addition and subtraction  skills and perhaps the use of Spreadsheet Application for the analysis of data.

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I am thinking of a simple problem such as creating a family budget. Calculating how the money is being spent at home. Simple addition and subtraction skills and perhaps the use of Spreadsheet Application for the analysis of data.

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I think a nice challenge would be to decide how to make a tunnel for carrying water through a mountain that goes in a straight line, and starting from both edges meet in the middle. They have to plan it using only knowledge from ancient times. As a matter of fact, it is a project that Eupalinos carried out in ancient Samos, a greek island. The knowledge they need is how to make right angles using only a compass and a ruler, and similarity of triangles.

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Apply Math to real problems is more interesting

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interesting and engaging way of learning mathematics.
Design and work in a group improves motivation

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I used PBL last schoolyear with my 5. - 6th graders.  Through autumn, winter and spring students found in the nature the geometrical objects. They took photos, share them with each other on groups´ GoogleDocs, import them to GeoGebra to show geometrical shapes and put the scale on the GeoGebra worksheets . In the groups they create the set of worksheets with exercises. For them it was very interesting and motivating.

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It's an interesting method to learning Maths. I use this for example to explain the velocity. The students have to calculate different measures in group, different times, to put the results in graphs. They are able to analyze different graphs and discuss each other ideas.

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It's an interesting method to learning Maths. I use this for example to explain the velocity. The students have to calculate different measures, different times, to put the results in graphs. They are able to analyze different graphs.

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I use to make encourage student to remember What we done in the lesson before. I pratice brain-storming, to start lessons or simple discussion to repeat the last knowledge. This is a way to make integrations between life, language and skill. I also create moment to repeate alltogether what we done.

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I think PBL and the idea of applying math skills to solve real-world problems as a lot of positive aspects and the one shown in the video is amazing. First I think we must start by letting teachers have time to think about their activities in class, at least in Portugal, unfortunately, we are losing too much time with papers and bureaucracy…
For instance, as lots of students have low financial knowledge we can explore the offers of loans and savings banks have searching their sites. Then, taking account of the variables that matter to set the conditions of a loan or saving, students can build simulators using Excel. This way they will improve not only mathematical skills but also other essential skills for the twentyfirst century.

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I Think that in the teaching-learning process is very important the integration between real and mathematical worlds. Necessary to encourage children to use the Knowledge acquired at school in real life to orient themselves in modern society. I like to bring PBL into classroom.

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BPL will be the next challenge for me and my young students.
I think I will follow the main idea of the video: a project based on geometry skills. I will ask them to bring a shoes box. Pupils have to look around them and find the forms of the objects that are in our classroom. Then they have to build our classroom minature in 3D.
An other theme for a BPL could be "Organising the end school party". They have to calculate the quantity of goods and the amount of money we need to buy sweets, drinks, etc... considering parents too. Then they have to choose who buys what and spend money carefully. Finally, they have to move the desks in order to form square tables on which to place the goods. They must also draw and cut invitations. My pupils are 8 years old. At the end of this school year, I think they will be able enough to use the four operations in order to calculate how many things and how much money we will need for our party.

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I usually do brainstorming to start a new theme. Sometimes I also propose to students conducting research activities. For an example, to study fractions. The last activity fulfilled on my classroom was "As frações e os chimpanzés". The only thing I gave to them was the task. With this task students can explore their ideas and also test it. They work with concepts an feel the need of mathematical Knowledge. Students also work with motivation

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For example when I introduce the theory of geomethric figure . I ask to each group to write a relation about different maths models that involve this theory: solar sistem.The idea to connect with real life is amazing.Using PBL approach and my students like to do it.

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- Plan a class trip
I have an IT group with 14 students. Their project is to plan a class trip. The first step was to figure out the destination. In groupwork they have looked for reasons why sould they go there. After that they'll decide where the trip will be going. The math part will be planing the costs.
- Process some algebric problem with geogebra. Students make excipients for other students to better understanding these problems.

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When we learn geometry, we use to lauch a challenge to the students: they have to pave the classroom floor. They need do messure, to make a project that simbolises the classrrom floar, they chose a figure that can be used to pave (al figures together have to pavement the rectangle) and to pave at the scale they chose. The skills they develope are: solving problems, messuring, using geometric tranformations like translate, rotation, and so on, proportional figures, using scales and social skills, like working in group.

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This PBL is amazing!
I have been trying to introduce some PBL related to real world (proportionality by calculating recipes or organizing a volleyball tournament, solid geometry by the construction of a real model for example), in my classes
and I've seen a positive answers from my students. I have to say it requires a lot of work and more than this a different way of thinking.
But I believe it is the best way to involve students with Maths and create a significant learning.

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Arrange a trip

This year with  5th graders we should arrange a 4 days trip in Tuscany.  Therefore pupils  should compare different option and combination: calculate price of ticket flight; train or bus ( with different price and kilometres); hotel with only breakfast, half board or  full board option. Tickets for  museums and other historical site. Calculate also time needed for visiting and draft an itinerary. My proposal is to work in group and each group should  propose the best value for price.

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For example, "How much material do we need to make a dog house?" for 7th grade. They have to use trigonometry for the roof and the quadrilaterals geometry.
A few years ago, my students drew on the computer and they animated those drawings using coordonates. They had to use formulas of analytical geometry. They liked very much.

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When we worked weights and measures they are supposed to create a cookbook with recipes or in groups surveying some of the objects in the schoolyard and compare them by size. They are 9 years old

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For example when I introduce the theory of logarithms I ask to each group to write a relation about different maths models that involve this theory:

1. Stellar Magnitudes

2. The Earthquakes

3. The PH

4. Financial maths

5. Perception of sound

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This is a great video! As a PBL in my class I would go with sweets because we have school theme this year that involves healthy food. They will have to calculate how much ingredients they need to bake cookies for the whole class and throught that they will have to recalculate various units of measurement.

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I try to search some example in the real life when I present a new topic, even if it's very difficult for some arguments. I use the trigonometry for many example in the real life

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In the study of exponential and logarithmic I tried to show as much as possible the real world applications: exponential growth, growth with logistic function, decay of radioactive substances, Richter and momentum scales for earthquake and so on.
Students also realized a physical experiment to "discover" th Newton's law of coooling. The students worked in groups, made the measurements and worked out the data with a spreadsheet.

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PBL: If we're working a history lesson as The Medieval Period, children will  like a lot everything refers to castles, knights, dressing,.... In that way we can ask our pupils for making a Medieval castle, with towers, dungeons, walls,...places and rooms they have to make using a scale, making three dimensional parts (3D shapes and their properties) and preparing a story to explain when each collaborative group (3 or 4 students) does the castle presentation to the rest of the class.

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Problem-based approach:"We don't have any pitch at school to have Ph. Ed. lessons: how can we solve this problem?"
-Groupworking to elaborate different solutions, identify tools and materials needed, quantify the costs, prepare a presentazion for the rest of the class.
Maths skills required: organizing, sorting, calculation, spatial organization, measuring,geometrical shapes.

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I'd like so much to be able to do something similar... I will try with  a little project. In the past i did a similar activity with experts and pupils. the goal was to make a nice yard outdoor my school...but what we did...now is  dead. may I could restart the project with a new area.

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What I do with my students is a project about Statistics. They are supposed to do a small survey on the topic they choose - there should be one question about quantitative and one about qualitative variable. They are supposed to calculate mean, median and mode, variance and standard deviation. They are supposed to do a presentation on their findings. It is not much, but some of them can be very creative and resourceful. I would like to prepare a special lesson about measurements for my high school students - something using shadow method:)

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Unfortunately there is not so many free time to solve problems like thisduring Math classes. I knoe that the main goal is to make ss possible to use Math rules in real problems. In a real life ther is lots of percents, statistics and comparing. In almost every situation people have to use logical ans critical thinking. Thats what I want to develop in my ss.

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I think that a good project could be amking previsions about the election of students and parents delegates. It involves statistics and applies it in an authentic task.

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My pupils have problems in math..

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It happens every year that my students ask to me "What this argument is useful for? Why we should study it?" and I try to answer, to say that  the argument is inside your every day life  but  I know I'm not convincing.
Experimenting with PBL on Maths subjects could be a more effective way to lead students in understanding that maths is in every day real life. But I have not spent yet enough time to experiment myself in finding new ways to explain maths subjects and lead students to this understanding. I have to understand first by myself!

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The discovery of the fractions
https://drive.google.com/file/d/0Bynw2m6iGiuTbEJQY1pLZUZnSFk/view?usp=sharing

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Learning goal at the end of V Primary

• Read, write, compare decimal numbers and perform confidently, considering resorting to mental calculation, written or with according to the situations calculator.

• Understand the concept of fraction and equivalent fraction.

Brainstorming questions

You can always split?

Record all student responses.

The fraction is

•         Part of a whole

•         Quotient

•         a straight point

•         Operator

•         Decimal number

•         Rational number

•         Probability

·       Common language

It is necessary to reflect the students that a single definition is not enough!

Watching the video taken by Khan Academy

https://www.youtube.com/watch?v=jgWqSjgMAtw

https://www.youtube.com/watch?v=U44my48zgFE

Now proceed concretely!

Construction unit fractional ½ "as part "and" as "operator of magnitudes continuous and discrete variables

Construction of other fractional units: ¼, 1/8, 1/16, ... 187����d�+

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this year I introduced a base of statistic using electronic sheets and every "excuse" to project a new chart: the timetable, if we had to control if everyone brought requested things... now students ask to build tables and project them on their own

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Students can make a research where they have to come up with good questions to ask to find out answers to a specific real world problem that concerns them. Find out how to collect good data and how they can use the data to analyse and interpret on.

An other would be to find what math can be found in their hobby and introduce to their classmates.

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A way to introduce linear systems is to propose

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Many arguments, both of mathematics that science, can be introduced starting from real problems; for example, when I start to talk about the extent I ask all students what is the measure of an object (bench width), I leave them free to measure by the instrument is most convenient, then by the comparison of the measures we try to find ways to give only one answer.

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5th grade: decimal numbers- calculate the direction in the apartment

7th grade: poll in class and presentation of survey data using charts

7th grade: similarity of triangles- measuring the height of tree using shadows

8th grade: Pythagorean theorem- what is the length of the ladder needed for climbing on the balcony

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In a fifth class of primary school it would be interesting to organize a charity collection where pupils realize the products to sell, set prices and programming time also, places and invitations.

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I love PBL! I remember that 10 years ago, when I hadn´t heard about this methodology, a new pavillon as a sport center was built in my school. We asked our students in Maths to design a map to optimize the lines to paint on the floor for the different sports: tennis, football, etc. It was a real work, with a jury composed by the PE Department and the principle. The students did a very serious work! Thank you for make me remind it! We should try another PBL like this. Here you´re our pavillon.
Anyway, sometimes it is difficult to find a significative question, a real one. That is to say, it doesn´t sound to Maths just from the beginning. Frequently we, teachers, adjust the PBL to our contents, and that is unfair, in my opinion.

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I like the idea to bring PBL into classroom. I explore with my students real examples with video material by using “Virtual School” or others so they can understand that math is aplied to reality all the time.

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Using the concepts of geometry can solve many practical problems