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Geometric transformations

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After the last holidays I asked my 14 year old students where did they meet anything related to Math during the holidays. They mentioned only sales and converting money. I was very surprised, I expected much more.

I show a photo of a package of biscuits or cereals (or bring a package) when learning percents.

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calculate and represent the percentage of the cash outflows

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I used examples form real life when i teach percent.

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From the image of the Lisbon Cathedral, introduce the concept of symmetry. Students have to indicate in the image what is equal.

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You have to buy Nesquik. What package would you go for? Why? Do you see something weird with these prices? What should be the prices in your opinion? Can you find other examples in your favourite supermarket?

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We used a România blouse - " ia" to begin the lesson "The symmetry of a point to another point and to a line in plan."

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A topic where students can understand the connection between maths and real world is Operational Research.
For example I use the following  video when I introduce the topic on O.R.  in a CLIL lesson

http://www.learnaboutor.co.uk/flash/flash_video.htm

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I would use the shape of the door in order to teach geometrical shapes

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I used household items to explain orders and classes to natural numbers

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My pupils are 4 years old, so we are starting with the Maths world. Every day we count differents things. They are learning to connect the cuantity with the number.

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We can propose endless activities of maths, always in the form of a game: probability, fractions, symmetry, etc ...

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Optical Illusions: Calculate the  areas  and the volumes of the geometrical figures represented on the image.

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I can use a label of a yogurt cup for introducing the proportions, in the label there are the value for 100 gr of yogurt and for a cup,
with these informations the students have to estimate how many yogurt there is in the cup. Then we can talk about the nutritional requirements of boys and girls
with their same age and we can estimate if a cup of yogurt it's a good snack for them.

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Last November we had our first experience with planting. We planted beans in the  school garden and in pots and we figurative the progress of the plants. The students made measurements and wrote them down to a notebook. They enjoyed the project very mach!

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I can use rosacea from a local church to work symmetry, geometric transformations, modules...

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I have asked my nine years old primary school children to bring shopping bills into the classroom. We compared them and they invented problems working in small groups. Then we compared the problems.

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I used Lego the class clock to teach children about angles. We observed the different position of the hands every five minutes and we reproduce them on the notebooks. Then we named the different angles and measure them.

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Children have already met geometric shapes in the infant school (or at least they should have). In the primary school, therefore, geometric shapes can be introduced by presenting a path of many images of works of art in which children can easily recognize the modules that are the basis of the composition of the work: so many squares, rectangles , circles, and so on

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I am gonna develop and experiment for the little students:

we put seeds and we want to calculate how many days it will become the plant seed. It will be interesting for them, to see that it will be a different process for each of them...

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the relationship between diameter and circumference

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Greece
I use their books to teach how we meassure lenghtc

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i can use a picture of the school to teach geometry (transformations, positions, ...)

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Building a spectrocope.

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STEM + Architecture

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 Tiziana Panaro, Italy Maths can be seen  emerge from some of the most unlikely places in fact  we all use math in everyday application, Maths is, in fact,  the universal language of our environment, our  games, for playing music. Maths is vital for every real world or work-related issue and almost every  problem can be solved through Maths. One of the more obvious places to find people using math in everyday life is at a grocery store. Grocery shopping requires a broad range of math knowledge from multiplication to estimation and percentages. Also,  more math can be found in the kitchen in fact, cooking and baking are mathemathical applications  all their own and can be some of the most  delicious ways of introducing children to mathematics. After all, recipes are really just mathematical algorithms or self-contained step-by-step sets of operations to be performed. An example of a creative diferent Maths class  can be baking a pudding: making it,  you need a wide range of mathematical knowledge, including : measuring ingredients, multiplying / dividing fractions to account for more or less than a single batch, converting a recipe from Celsius to Fahrenheit, converting a recipe from metric (mL) to Uk standard units (teaspoon, tablespoon, cups) etc. 

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 Tiziana Panaro, Italy Maths can be seen  emerge from some of the most unlikely places in fact  we all use math in everyday application, Maths is, in fact,  the universal language of our environment, our  games, for playing music. Maths is vital for every real world or work-related issue and almost every  problem can be solved through Maths. One of the more obvious places to find people using math in everyday life is at a grocery store. Grocery shopping requires a broad range of math knowledge from multiplication to estimation and percentages. Also,  more math can be found in the kitchen in fact, cooking and baking are mathemathical applications  all their own and can be some of the most  delicious ways of introducing children to mathematics. After all, recipes are really just mathematical algorithms or self-contained step-by-step sets of operations to be performed. An example of a creative diferent Maths class  can be baking a pudding: making it,  you need a wide range of mathematical knowledge, including : measuring ingredients, multiplying / dividing fractions to account for more or less than a single batch, converting a recipe from Celsius to Fahrenheit, converting a recipe from metric (mL) to Uk standard units (teaspoon, tablespoon, cups) etc. 

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ROMANIA
If Maths doesn't  have  real life  contexts  to apply  it  at  school it  is boring to  have Maths. Project  based  learning  are  useful  when  dealing  with Maths  contents.

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Sticks and modeling dough - areas, volume, height, apotema .

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Teaching All about cylinder :)
I did use these simple materials of everyday use to teach what a cylinder is created with

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I used geometrical shape to reconstruct a city

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Finding the center of a coin as if you were Euclides

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I teach the fractions slicing an apple in slices of different sizes or I use a clock.

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Numbers

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I use tangram to analyze shapes.

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I'll prove it, like a dish in the form of a disc. Students can get the Pi number

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fractions

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Perhaps for introducing statistics, the students have to count and classify the cars they see when they go to school, home or another day / route by color, size, shape, brand, etc. After they collect some data they can select what color or brand was the most popular.

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I ASK TO MY CLASS TO OWN SOME  RUBBER MONEY WITH DOING SOME  SKILLS AND AT THE END OF THE MOUNTH THEY CAN BUY ,ON A STORE CREATED BY THEM, WATH THEY WANT.

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All young children delight in participating in concrete, everyday activities, all of which support math concept development. Those of the home or kindergarten environment are especially accessible at this age: setting the table, picking up toys and putting them away (ordering), sorting the onions from the potatoes (sets and classifying), sorting laundry...

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I often use the sale time to speack about percentage, terms and proportion.

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Ιn order to realize children the application of mathematics in everyday life we visited the corridors of a school and we found that the surface of the floor had geometric shapes that enclose perimeter surfaces and felt the challenge of finding the largest.

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my Pinterest board with symmetry

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Matika - symetrie obr. // School - Symmetry pic.

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Objevte recepty, rady pro domácnost, stylovou inspiraci nebo další nápady, které můžete vyzkoušet.

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Last year I ran  a geometry and literature after school club with a colleague - also a participant in this course. We organized a short trip in the neighbourhood of our school which we called "geometrical walk". Armed with tablets, the students took photos of various shapes they found, then we projected them, we printed and grouped them in categories of shapes, identifying common elements between them. So, this session was based on material that was "mathematical" and could be found in their surroundings.

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Bitcoin - starting with decimal number or money.

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I would go on a shape walk in the classroom and around the school. I would ask children to find different examples of specific shapes.

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We can use the famous Russian dolls, Matryoskas, to introduce the concepts of figures´s similarity, proportion or scales.

image source: The creative mind

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To introduce pi number I ask my students to bring circular objects and a thread to surround it. In class I tell them to surround the object with the thread and measure the length. Then I ask them to measure the diameter of the circle and divide both lengths. They observe with surprise that the final amount they get all is almost equal (pi).

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Proportions in the kitchen and conversions

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I used some pics of famous human sculptures to introduce the idea of proportion: in a brainstorming we debated about proportion in the real world, its meaning and utility, and also we reflected on human proportion after seeing a "real" Barbie by  Nickolay Lamm

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Reading and comparing nutritional values ​​on food labels

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Coming out to the street, students take measurements and apply  triangls similarity, Pythagorean theorem and learnconcepts of trigonometry

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This is a photo of the church of the locality where we live. How can we know the heoght of the tower with the bell? What measures do we need to know? What math can we use?

Coming out to the street, students take measurements and apply  triangls similarity, Pythagorean theorem and learnconcepts of trigonometry.

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Teach fractions through the division of pizza

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Pentagon :)

we try to find the math into the nature....

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“The mobile phone company is going to spend two million euros to construct mobile phone towers in our country.  The company has hired you to decide where to place the cell phone towers.  The company has only one rule: towers must cover all of the major cities.” This could be an example of an activity where the goals are:
students will be able to proficiently use a compass to make circles with a given radius; students will be able to support their decisions with sound mathematical arguments expressed in a grammatically correct form;  students will be able to apply ratios to a real live situation;   students will experience a real world situation involving mathematics.

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I think that students can go over the school and take pictures of the cuadrilaterals they find all over it. Then we can share in the screen in the classroom and see that there are cuadrilaterals everywhere.

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We use  product wrappers  to teach fractions, proportions,  percent and healthy life

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Tiziana Panaro, Italy I like working with graphs and pictograms related to every  aspect of the life around the students: e.g. Italian vs British biofuel resources, their  expenditure during a period of time,  the weather, daily temperatures, favourite movies genres, sales of DVD players per month or number of TV sets each city has,  are only some among the innumerable examples.I think that using Statistics with Economics and English in Maths classes is a wonderful way  of bringing the real world into my  Maths classroom. The students can learn geometry, calculus, analysis, logics while observing changes over a period of time,e.g. changes in the currency values , the inflation rates, or company profits. While discussing about a pie chart they have created themselves,  they can learn at a glance how a total amount is divided up such as a budget, their expenses, etc.... They find out  they are surrounded by Maths every day. It is surely  a great way to start a lesson. 

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Tiziana Panaro, Italy I like working with graphs and pictograms related to every  aspect of the life around the students: e.g. Italian vs British biofuel resources, their  expenditure during a period of time,  the weather, daily temperatures, favourite movies genres, sales of DVD players per month or number of TV sets each city has,  are only some among the innumerable examples.I think that using Statistics with Economics and English in Maths classes is a wonderful way  of bringing the real world into my  Maths classroom. The students can learn geometry, calculus, analysis, logics while observing changes over a period of time,e.g. changes in the currency values , the inflation rates, or company profits. While discussing about a pie chart they have created themselves,  they can learn at a glance how a total amount is divided up such as a budget, their expenses, etc.... They find out  they are surrounded by Maths every day. It is surely  a great way to start a lesson. 

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Gmail is email that's intuitive, efficient, and useful. 15 GB of storage, less spam, and mobile access.

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Tiziana Panaro Italy

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Shapes and lines: Draw your itinerary from home to school!
Fraction: Split your pizza/ chocolate/ birthday cake with your friends!
Symmetry: Make a butterfly: paint on a half of paper, than press on the other side!

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We talk about real life math a lot in our classroom and I even start some topics by asking the students where they would see them so it is not just me telling them. I still constantly get told that Algebra is not applicable to real life and noone solves problems using it. I do tell them that we may not actually use variables when solving something in our heads but we are probably using algebraic thinking and that it gives us good strategies and starting points to solve more challenging problems. Along with the fact that nobody can predict their exact future and it is important that they get the basics in all areas of math in case they need it in their future

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real life math.
Geometry: shapes, lines and angles

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Kiriazis, Greece
One method I used and it causes excitement to my students is when I ask them to bring a chocolate bar per person. Chocolate bars are already divided into small pieces, but also in pieces that you can cut. So students learn to split, divide and learn fractions. For example, you eat 4/12 of the chocolate, show me that piece. After finishing your teach, your students can enjoy some chocolate and have a sweet taste of maths!

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We can use this picture when we start to study trigonometry. This is an example of the real life.

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When talking about the infinity (with older students), fractals are a good starting point to "bring students to infinity". For example, Sierpinsky carpet in the picture - we can talk about how the picture was made. And students can find some examples of fractal patterns in nature.

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I found this craft into Banffy Castle. We may try to reproduce at Math class this geometric figure using our instruments and using Geogebra'

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In everyday life you meet Math. Also in a chocolate cake!
It could be funny cook a cake (or biscuits) with children at school.

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Showing students contrails of air-planes you can make a bit of geometry: you can explain what incident lines are.
Giving them some different photos, like the one I posted, you can let them discover that for each triangle the measure of its internal angles is 180 degrees.
...it would be more involving asking them to make the photos...
and they could also discover that sometimes planes leave in the sky parallel contrails. And in this case, you could even study the properties of parallel straight lines.

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With my 8th grade students (13 years old), when we studie translations and other isometries, I take a picture of the frontage of the school building and point out what can be seen mathematically. Here is an example:

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This photo of a tax receipt could be used to start a lesson about decimal numbers and operations with these numbers. I could ask my students: "If to calcoulate faster I account only the full part of the numbers and ignore the decimal point, what could happen when I came to the cash? The total I calculated would be combatted with what I really have to pay?"

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Estimate how small are objects on the pictures.

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Math is everywhere and I'm learning my students to find it and to see it.

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Matematika na ručnim radovima našeg kraja2

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In many streets of Portuguese cities you can set foot in mathematics. Seriously! Symmetries, rotations and translations, all you can find in the black and white geometric drawings of the Portuguese sidewalks! Mathematicians call them 'friezes' and 'patterns', as the drawings repeat themselves in one or more directions. They are so beautiful and important that the Municipality of Lisbon and the Portuguese Society of Mathematics have an agreement to classify and complete the symmetries in the city. That is, although there are 7 types of friezes and 17 of patterns, on the sidewalks of Lisbon there are only 2 and 9 of each, respectively. And in your city, how many there are? Find out more about the theme at the Atractor Association website: http://www.atractor.pt. Then just tell!

https://www.math.tecnico.ulisboa.pt/~acannas/Simetria/desdobravel.pdf

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Turkey
In the real world we see mathematics all over the place. For example, we say that the geometry of the students is like a rectangle ball in the windows. In this way, students see the environment. They can think of more concrete ones. We need to learn the numbers. We give examples from the shapes in our circles, which are about symmetry.

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We have the project "Big for Kids" in our school. Our school pupils prepare (with kids) cakes, fruit salad, frappe for the kindergarten children. At the end of Sway you can see how our students calculated all that they have done. Sway is in Croatian language but you can imagine atmospher on that day with this pictures.

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Srednja škola Markantuna de Dominisa Rab ugostila je jednu vrtićku grupu od 23 djece u sklopu projekta Veliki za male, mali za velike. Naši ugostitelji pripremi

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After I'd presented them with two pictures, one of our class's library and one of the school's library, I would ask them to observe and compare their size, their content, their shape. Afterwards, we could continue by estimating the average quantity of the books in both of the libraries. As a result, the two pictures could be a starting point for us to study lots of aspects concerning Maths and even become a stimulus in order to combine Maths with other subjects, such as literature.

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Measuring time
This is an actual photo from my classroom. There is a combination of a clock and a calendar. We can start a discussion about time and how we measure it, why we have so many different time units like seconds, minutes, hours, days, months, years, etc.

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Through the project "Mathematical Challenges" we had a part devoted to math in life. A part of the students did the purchase of prescription foods that they called "Fine Mathematical Balls", the other students measured and made. At the end, they were treated honestly with them.

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I am starting a revision of geometry with my 12th grade students before introducing three-dimensional geometry. I will start the revision with a presentation, and as introduction or warm-up I want to collect some geometric shapes from the real-world (e.g.: kitchen supplies) they can see every day. I am thinking of asking them to tell more objects that are in a certain shape form. After that I want to deal with triangles (revise everything we have learnt before), so I would ask them to tell triangular shapes from the real-world.

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Today we talk about how to organize our time in the morning calculating the unexpected events that make us arrived late. For example on my way to school the probability that I have to stop at the first set of traffic lights is 0.3. The probability of stopping at the second is 0.75. Now we find the probability that on one morning we stop at both sets of lights.

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Primary school (4th grade).
This image could be the starting point for a PBL regarding the following topics:
-metric units of mass
-food education

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In order to give my students how useful and practical is maths in real life and understand the meaning of functions we made a virtual market in class and using virtual money we tried to figure the amount of products we could get with the money each one had. So all students understood the meaning of fuctions/norms

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Why is it important to recycle?
Because,

plastic bottles, being petrochemical products, decompose in 500 years.

Knowing that of 10 recycled plastic containers  can produce one t-shirt or a square meter of carpet. How many plastic bottles should be recycled to produce 10 shirts? but 5 square feet of carpet?

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Primary school, 9-10 years old.

Can you show me the best way to reach Genoa center by bus?

How long it is far from here?

How much time do I need?
Let's go on the way and check it!
OR
Let's go to the Genoa's tourist information point and see if we have discoverd the best way to reach Genoa center or they have any other suggestions for us!

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Last year there was an advertising on the Italian radio; a factory was promoting their couches and selling them with a 50% discount, but there were special days with a further discount of 40%. I immediately used in my lesson this ad that we all were hearing every day. I asked my students in first year in secondary school how much  the total discount would have been.

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Buying toothpaste. Provide them with a picture of the supermarket shelf or some supermarket advertising. Different sizing and pricing. How do we know which is the best value? What about blocks of chocolate? A block of cheese? This can introduce ideas about quality versus economy, brand names, deceptive packaging.

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I use the example of a grocery store to explain my students the concept of a function! I use the prices of fruits, the quantity and the according cost as a means to explain to them the term of the independent and non-independent value! Also in this way i found it easier to explain them how to identify a function.​

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Turtle shells are fractals, we can teach you an easy program that older students have done with matlab to reproduce the shell you want. The students are very fond of this activity and are presented by the higher education courses.

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When I teach numbers to one hundred I start with something my students use every day. Each pair, or a group can collect 10 pencils. We put all ten collections together in order to get the picture of how many that is.

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If we have to go somewhere we have to know about numbers: kilometers, civic number, floor number, room number, ....

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I always use art to attract students in my lessons. The picture below belongs to Escher. I can teach parallel displacement, symmetry or turning of shapes by using not only his art but also Leonardo Da Vinci. I use the astrology or the billard to teach angles. There ara too many examples that I cannot remember now.

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Real life Math
Math is always around us.

Take a look around!

You can find geometric shapes in man-made objects just like as all the road signs…

Began searching in Your city.

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How to show our students that "Math is everywhere, so you cannot escape it" ? (insert here: scary face & malicious laughter)
Applied Economics is a good place to start: our students are often economical illiterate  (it's worst than Math), only if they take an Economics' course they can hope to learn something about money management. That's a real problem, because they are going to need all the capabilities they can get to survive next years of economical crises, with low wagers and high life costs (to say nothing about planning and saving for retirement insurances).
I'm really interested in implementing some of the ideas that the suggested site Econedilink proposes.
This site is interesting because offers idea for activities to involve 10th, 11th and 12th grade (the grades I teach to), which seem to me quite hard to find.
I'd like to explore the idea of a lesson on the topic "Owning a car", it should be interesting for my 11th grade students who are about to become of age and be eligible to get a driver license (I suppose the topic should be felt as quite "near" and real).
It contains the topic of this year (interest) and some important skills like decision making.