jueves, 4 de junio de 2020

Pythagoras – Father of Harmonics



Eva de Prado shares:

Pythagoras – Father of Harmonics

Pythagoras discovered the musical intervals. He also lectured people in the healing powers of sound and harmonic frequencies. Pythagoras not only applied the principles of harmonics to music, art, and architecture but also to more social arenas like raising a family, friendship and personal development. 

From these genius pythagoreans with their mathematical formula came the basis of our music of today.

This activity will be carried on between Music department and Math department.

Click here to see the lesson

Analyzing the melting of the polar ice caps and its effects on the Earth and humanity

Eva de Prado shares:

Cross-Curricular Math, English, Science Lesson 

Lesson Focus and Instructional Purpose Students: analyze the melting of the polar ice caps and its effects on the Earth and humanity 

Unifying Essential Question(s) 

How fast are the polar ice caps melting, and why is this rate important to human life on Earth? 

Click here to see the lesson

The Curious Incident of the Dog In the night time 4th Year ESO



Marta Sánchez shares this activity: 
Click here

Activity for 4th ESO: The Curious Incident of the Dog In the night time 



Art class:  Students could be asked to draw a comic or  to redesign the book cover for a new release of the novel. Or to design the poster advertising a stage play or movie based on the book.
English class: They could be asked to write a brief summary, to make a list of the characters, to describe the main character. Plot: summary test, Full Book Quiz, 
Maths class: Mathematics is the most prevalent motif in the book, as it's the means by which Christopher best understands the world around him.

  Students could be asked to identify where Math arises in the book and do some activities:
   Prime numbers, The Monty Hall ProblemChaos theory, Pythagorean theorem, a  Game       called Conway's Soldiers, Tessellation and more...
  


HANDS -ON MATHS: Million Dollar Project


Miriam Tesedo comparte: 




Option 1: Hands-on Maths


The project I would like to share with you is called “Million Dollar Math Project”.Click here to see it.

In this project the students have inherited $1,000,000. They have to spend the money almost any way they choose. There are a few things they are required to purchase. The goal is to get as close to the $1,000,000 mark as they can. 

Of every item that they purchase they have to include an information page with the details. At the end of the project they have to complete a tracking list. On it they have to include all the items they have purchased, the starting balance before purchasing the item and the balance after the purchase. For each item they have to add the percentage of the total budget used on every item.



How ………………. use Maths

Compartido por Raquel San Juan:


How ………………. use Maths

In this activity students work in groups of two or three. I will give each group a text in which maths are brought to live. (I have selected two of them, but every group has a different one. They all are taken from the web site: www.doodlemaths.com )

The activity has three parts:

1.   They have to read the first part of the text “how …… use maths” and to look for the words they don´t understand.
2.   They have to answer the questions of the second part of the text: “curriculum links”. I don´t give the answers to the students until the end of the activity.
3.   They have to explain to the class the text and the maths used in that job. We discuss the answers given to the second part of the text and the rest of the students can make contributions. Then I give them the answers given in the text and we compare them.

How biologists use maths 

Biologists use maths to study lots of things, including animals. By collecting data and using statistics to analyse it, they can investigate how changes in the environment can impact the survival of various creatures - such as meerkats!





Hi Nino! Please could you tell us a little bit about yourself and your job?

I am Nino and I am a biologist. My main interest is the behaviour of animals and how they work together as populations. We call this field population ecology of animals, and an important part is finding out how changes in the environment can affect the survival of these animals.
For this purpose, I collect data on wild animals in the field and analyse this data using mathematical methods. The species I am researching at the moment are meerkats and sturgeon fish.

Why do you think maths is important?

Maths is used in a lot of different fields of science. This is because when we look at things, they don’t always make sense on their own. By using maths as well, we can find out if the things that we observe in nature follow certain rules. This type of mathematics is called statistics, where we find out information (collect data) and then analyse it (look for patterns).


How do you use maths in your job?

I use mathematics and statistics to understand what makes meerkats behave in a particular way. For example, I observe meerkats and the weather, so that I can calculate whether meerkats have fewer babies when it rains less and it gets warmer.
This is really important for us to know because our climate is changing and we need to understand how we can protect animals.

Do you have any advice for someone who may find some parts of maths tricky?

If there’s a part of maths that you find hard, try practising all of the steps. If you’re struggling to work out how to find 5/8 of a number, you might want to try practising finding 1/2 of a number, or 1/8.
The more you practise, the better you get to know the rules and the easier you find it. When you find the right answer to a problem you’ve been struggling with, it’s very rewarding and you learn to love it! Maths can be fun!

What’s your favourite number and why?

My favourite number is 3 because that is the average number of babies a meerkat has in its litter.

If a school wanted a biologist to visit their school, what advice would you give them?

You may want to contact your nearest university and find out if any research scientists would be willing to come in to school, or a parent may know somebody.
The research scientist could give a small presentation about their topic that is easy to understand and the children should be asked a lot of questions, for example, how they would use mathematics to solve a problem in the scientist’s field.

Thank you, Nino!

Curriculum links (*I don´t give the answers to the students until the end of the activity to compare with their own answers)

How do biologists use maths?

Statistics: One of the biggest parts of Nino’s job is to be out in the field (that means he is out in the real world rather than sitting in an office) collecting data on the animals he is studying. A lot of this is tracking the meerkats and recording the information. Nino will need to use statistics to analyse it and look for patterns, or trends. He may also need to be able to find averages of the data he collects in order to draw conclusions.

Measure: Nino has to be able to measure the amount of rainfall to see whether this affects the meerkats. He may also have to be able to measure things such as the quantity of food available to them, or the distance that they cover, and may need to convert between metric measurements (millimetres, centimetres, grams, kilograms etc) and imperial measurements (ounces, pounds, feet, yards etc).

Number: While he is observing meerkats, Nino may have to be quite fast with his mental maths. Because animals move quickly, he might need to count them before they disappear. This means that he needs to be able to count in multiples, and he also needs to be able to add or subtract those numbers in his head. He may also need to multiply or divide, especially if he’s looking at litters of meerkats and making predictions.

Fractions and percentages: When Nino has finished measuring, counting, recording and analysing his data, he has to write a report which tells people what he has found. He might use fractions and percentages in his report to explain trends. For example, one fact about meerkats is that they live in groups (called mobs) of between three to 50, and it’s usually one male and one female meerkat who have 90% of the baby meerkats in the whole group!

How pilots use maths 

Pilots use addition, subtraction, multiplication and division to help them work at key calculations, such as working out how much fuel they have and how much runway there is to land on.


Hi Hannah! Please could you tell us a little bit about yourself and your job?


My name is Hannah and I’m a commercial airline pilot. I’ve wanted to fly since I was seven years old and did everything I could to become a pilot. This meant a lot of studying, as the most important subject for flying is maths.

Why do you think maths is important?

Maths is very important in flying as we use lots of numbers. You need to be good at problem solving and be able to do lots of calculations quickly and correctly.

How do you use maths in your job?

Pilots use a lot of maths everyday. We have to make sure we take enough fuel for the flight; work out how much the plane weighs so we’re not too heavy to take off and land; decide how fast to fly; how far we need to descend and when to slow down; and how much runway we need to land on. A lot of this is straightforward arithmetic: addition, subtraction, multiplication and division.

Do you have any advice for someone who may find some parts of maths tricky?

Times tables are very helpful. They make maths a lot easier, as you don’t have to work it out if you know if off by heart! But the best way to make maths simpler is to practise: if you do it every day it slowly becomes easier until you can do it in your sleep!

What’s your favourite number and why?

343! The speed of sound is 343 metres per second … and some planes can go more than 3 times as fast as that!

If a school wanted to ask a pilot to visit their school, what advice would you give them?

Most airlines have a careers department who arrange school visits and presentations. Air Cadets and The Air League provide older children with the opportunity to experience flying and gain valuable skills tailored towards a career in aviation. 

Thank you Hannah!

Curriculum links

Number: Hannah needs to use a lot of addition, subtraction, multiplication and division to calculate things like how much fuel to take (too much fuel would make the plane too heavy and slow it down and too little would mean they couldn’t get to their destination!) and to work out how far they have left to go, so she can decide whether they need to go faster.

Geometry: Geometry is also needed to plan routes and keep the aircraft on course. Hannah needs to think about angles and be able to work out how many degrees she needs to turn the plane in order to land on a runway – you don’t want to miss that! Angles are also really important for landing and take off, deciding how much the nose of the plane has to tip up or down so that the wheels or the back of the plane don’t scrape along the ground.

Measure (time and money): Hannah also needs to be able to work out time and money problems – as a pilot, you’re always flying to different countries and need to be able to switch between different currencies. She also needs to be able to calculate the length of the flight and what time they will arrive so that she can update her passengers.

HANDS ON MATHS: STUDENTS CREATE A GAME RELATED TO MATHS


Marta Sánchez comparte:





I have done this evaluation with my students (1º ESO)

OBJETIVES OF THE PROJECT:

·        Develop creativity
·        Interaction between students
·        Change the point of view of mathematics
·        Relate fun and math
·        Demonstrate that mathematics is part of everything

TERM FOR CARRYING OUT THE PROJECT:
·        Four weeks

START UP:
·     
     Firstly: they have made groups of a maximum of five people and a minimum   of three (as they have chosen)
·       
      Secondly: I have asked them what is playing and what is mathematics
·        
     After that: I have given each group a sheet where the definition of playing and mathematics was written.
·   
     Then: I have explained what is the project that they have to do
·    
     Afterwards: I have told them that all questions can be consulted by mail




TASK

They have to create a game. They have to invent a name for the game, some rules and everything necessary to be able to play in class or at home. They can get ideas from other games: chess, parcheesi…but it has to be a game that doesn't exist anymore, with a name that doesn't already exist and with some rules that don't exist anymore. Each team will have to present their project in front of their classmates, explain the rules of the game and why math appears in their game.


Every year I do this project with my students and every year there are several teams that surprise me with their games It is a very nice project, the students love it because they can vote which game they like the most and, on the last day of the term we play with their games. 




UNITS OF VOLUME: What's the capacity of a can?

HANDS-ON MATHS: EXPLORING SIMILARITY WITH SHADOWS AND MIRRORS



Compartido por Francisca Arpa:


One of the most effective ways to shape knowledge and cognitive skills is conducting manipulative activities or projects to engage students in the hands-on learning of History.

Option 1: Hands-on Maths

SIMILAR TRIANGLES : EXPLORING SIMILARITY WITH SHADOWS AND MIRRORS

The aim of this Project is  to identify similar triangles, corresponding sides and angles and to apply Thales’s theorem to calcule measurements of distances to inaccesible points .

Thales of Miletus wondered about the height of the  Great Pyramid in  Egypt. Thales notices that the sun’s  shadows  fell from every object in the desert at the same angle, creating similar triangles from every object. Thales’s research allowed him to use similar triangles to measure the height of the pyramids of Egypt and the distance to a ship at sea




MEASUREMENTS OF DISTANCES TO INACCESSIBLE POINTS

1.- Calculation of the height of the cypress in the schoolyard

We just need measuring tape, paper, pen and a sunny day

The students will be divided into groups of four, one of them will be the benchmark for the measurement, the other two will measure the height of the student and the respective measurements of the shadows of the tree and the student, the fourth member of the group will write down measures.

Then using Thales they will calculate the height of the cypress





The groups will present the measurement obtained and check if they have reached a similar result

2.- Working with a mirror


A mirror placed on the floor can also be used to determinate measures indirectly. When teh mirror is placed at a particular distance from the wall, the distance that and observer stands from the mirror determines the reflection that the observer sees in the mirror.




In groups of four students, they will perform the following steps
*     Find a spot on the floor 8 m away from one of the walls of your classroom.
*     Place a mirror on the floor, 2m from that wall
*     Each gropu member should take a turn standing on the spot 10m from the wall and look into the mirror. Other group member should help the observer  locate the point on the Wall that the observer sees in the mirror and the measure the height of this point above the floor.
*     Before moving the mirror, each group member should take a turn as the observer.
*     Repeat the same process by moving the mirror to locations that are 3 m and 4m away from the Wall

I.-The students can use this table to record results:

Distance from the Wall to the mirror (in m)
Height of the Point on the Wall reflected in the mirror ( in m)

Person A
Person B
Person C
Person D
2




3




4





b) Measure the eye-level height for each member of the group and record it in the table :

eye-level height for each group member
Person A
Person B
Person C
Person D







c) - Consider the data collected when the mirror was 2m from the wall
     On the diagram below, label the height of each  group member and the height of the point on th e wall determined by the group member




d)- For each person in the group, determine the ratio of the height of the point on the wall to the eye-level height of the observer

Ratio  of height of the point on the wall  tp eye-level of observer

Person A
Person B
Person C
Person D
Ratio as a fraction






Ratio as a decimal







e).- Repeat when the mirror was 3 from the wall and  when the mirror was 4m from the wall
 f).- Express regularity in repeated reasoning. What appears to be true about the ratios you found?

     Finally you can propose to the whole class that they discuss how they would use the mirror method to calculate the height of their classroom




Pythagoras – Father of Harmonics

Eva de Prado shares: Pythagoras – Father of Harmonics Pythagoras discovered the musical intervals. He also lectured people in the ...