Maths lesson: Pythagorean theorem. Demonstration
Teacher’s name; José Manuel Rodrigues Henriques
Escola Horácio Bento Gouveia, Funchal, Portugal,
Summary
With my teaching experience over the years, I know it is hard for pupils to understand the maths contents only in the traditional lectures, without connection to the facts of their everyday life and practical demonstration.
The Pythagorean theorem appeared as a necessity of the man to solve problems of everyday life and that are related with innumerable and different applications that require the calculation of inaccessible measures. The Theorem is therefore an important and indispensable tool in the different areas of geometry and that only applies to rectangular triangles according to the law “the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse”.
Name of the activity
Introduction
The activity is very important for pupils as they are able to learn the concept of the Pythagorean theorem in an open space that is familiar to them, the schoolyard. The understanding of the concept will become more effective when the pupils are able to apply it to real situations. They will identify the situations, measure them, do calculations and finally they will come to conclusions.
Learning objectives
General Aim: To apply the Pythagorean Theorem in the resolution of problems using real images of the schoolyard.
Specific aims: To understand the Pythagorean Theorem and to know when to use it.
Resources
Book; worksheet; writing tools; ruler;; tape measure, laser meter;
Activity
Step1: Pupils will be informed of the procedures.
Step2: A worksheet about the theorem, with examples and challenges will be handed out.
Step3: The teacher will read the worksheet and pupils will clarify their doubts.
Step4: Pupils will measure the stairway, as one the examples of the worksheet.
Step5: During 15 minutes pupils will discover other real situations where they can apply the theorem. They will choose one of them and they have to measure and do calculations .
Step6: Pupils will be placed on a triangle rectangle. In one of the legs there will be 8 pupils and in the other one 6. The aim is to discover how many pupils will be necessary to the hypotenuse.
Step7: Consolidation and evaluation.
Comments from the learners´ surveys
With this activity pupils had the chance to apply the theoretical concepts to real situations in the schoolyard. The fact of having an outdoor lesson has motivated pupils, In their opinion, the acquisition of the concepts became easier, more dynamic and funnier. The interaction among the pupils was one another positive factor, because they had the chance to chat about the theme, to contact with existing real situations, as well as being able to visualize, to measure, to calculate and to solve the problems.
The only disadvantage was some noise that other outsider pupils were making.
Final remarks:
The activity was great . Pupils have assimilated the new concepts. The activity was done in other classes and the results were also great: pupils were motivated, interested in learning and explore.
Links: http://www.escolavirtual.pt/
https://youtu.be/CkWUcB8YX5k
September - October 2018:
Math lesson-I.C.Laura Lanza. Carini-Italy
Title:” Discovering flat figures all around”
Teacher Debora La Cascia
School I.C. Laura Lanza-Baronessa di Carini-Italy.
Geometry outdoor lesson-
Introduction
Drawing real objects where to highlight the presence of flat figures
Learning outcomes:
- Drawing flat figures by using simple tools like a ruler, a set square, a compass.
- Analysing significant elements (sides, angles, diagonals, medians, height, bisector, axis) of the main polygons.
- Classifying polygons with reference to the lenght of sides and measures of the angles.
Tools:
- Sketchbook
- Pencil and rubber
- 30, 60 and 45 degree angles set squares
- Compass
- Ruler
- Interactive whiteboard.
Activity (description)
- The first step of our activity will take place in class. It is a summarized lesson on the main polygons and their features by using the interactive board
- The second step of our activity will take place outdoor. Students position themselves on chairs arranged in a circle, they observe the space surrounding and draw real objects ( trees, houses, etc). after that, they highlight the presence of flat figures by using simple tools, ( ruler, set square, compass).
- The third step of our activity will take place in class, students analyse the main features of polygons relative to the lenght of sides and measures of the angles.
Teacher’s comments after learning checking
I find extremely useful take advantage of outdoor activities, students through the direct observation of surrounding spaces, experience the pleasure of drawing, exploring and analyzing shapes to practice basic geometric principles.
FINAL COMMENTS
Through the direct observation of reality, Students can find the chance to focus some geometrical notions . The period of the whole activity is three hours, or more if you want to go into techniques in more depth
Supplementary material
Links to blog, videos, etc.
https://animoto.com/play/UhfFXISqwHRFrMftzGjTUg
https://twinspace.etwinning.net/45380/materials/videos
Maths outdoor lesson: “Measurements”
Melinda Nagy
Liceul Tehnologic Octavian Goga Jibou, Romania
Summary
A CLIL outdoor lesson about measuring, comparing results, talking and listening
Introduction
This is a CLIL (Content and Integrated Language Learning) outdoor lesson, in which pupils learn specific words and expression related to measurement in English.
Learning objectives
To enable students to:
-to compare, describe and solve practical problems for lengths and heights (e.g. long/short, double/half)
-to use natural materials to measure length and height
-to understand why it’s important to use standardised measurements
Resources
-natural surroundings: leaves, sticks
-rulers, notebooks, writing tools
-worksheets
Activity
Step 1: Introduction – the pupils will be introduced the key vocabulary in English for length and height measurement units (Millimetres, Centimetres, Meters, Kilometres)
Step 2: Pupils work in groups to transform from one unit to another, to practise in English the names of the measurement units.
Step 3: Pupils are encouraged to explore the outdoor environment and collect natural materials, using only the natural objects (sticks, leaves, pine cone, etc.) the children will be asked to measure various body parts (arms, legs) then compare and contrast their findings with each other.
Step 4: Next, they need to measure and note down the length of leaves or sticks and calculate how many leaves long are their arms? How many sticks does it take to measure their leg?
Step 5: Consolidation and evaluation: Students work in groups of 3 to complete a worksheet and reflect on what we realised there.
Comments from the learners’ surveys
Pupils appreciated the practicality of the lesson and the innovation of it. It was their first CLIL lesson.
Final remarks
A very active, practical lesson. Lots of opportunities to work together with their classmates. Opportunities for speaking and listening in English. Appealing for pupils due to lots of touching and feeling of resources and the practical element.
Supplementary material
The worksheet used:
ENIAIO EIDIKO EPAGGELMATIKO GYMNASIO-LYKEIO AGIOU DIMITRIOU
TEACHERS: CHARALAMBOUS ANNA, PAPPA FANI
Εnjoy counting the perimeter and the area of α rectangle
Summary
A group of 15 students from classes C and D participated in an outdoor maths lesson in the school yard. The students were divided in smaller group and were asked to measure the football field , in order to give the results to a worker that would replace the fence and the plastic sod. After discussing the measurement units they had to use ( meters) as well as all the calculations they needed to make ( perimeter and area) they were given 20m and 50m measuring tapes and started measuring the sides of the field. They made notes on a worksheet and finally had the necessary results.
Introduction
This is an important activity as students have the opportunity to implement mathematics in real life and not just view them as numbers on a paper.
Learning objectives
- Make observations
- Learn about standardized measurements
- Use of measuring tape.
- Learn basic maths-geometry rules
- Enhance team work and coordination
- Promote problem solving skills
Resources
Worksheets, pencils, measuring tapes (20 and 50 meters), two colored chalks, a calculator.
Activity
Step 1:
The following problem was presented to the students as we were all in the school yard: The fence and the plastic sod of the school's football field had to be replaced and we would have to order the needed material.
Step 2
Students were divided in groups and were asked to find what they would have to measure, what instruments they would have to use and how to use their results.
Step 3:
After each team answered the previous questions correctly they were given a worksheet, that reminded them how to calculate the perimeter and the area of a rectangle. Then they were asked to measure the football field using a measuring tape.
Step 3:
The students wrote down the outcomes of the measurements and then calculated the perimeter and area of the football field.
Step 4:
Each team presented their results and mistakes were discussed .The result of the measurements were drawed with coloured chalk on the floor of each side.
Comments from the learners’ surveys
The students had never seen or used a measuring tape,so they were impressed by its size. They said they liked the activity and understood why and how maths are so important in our everyday life.
Final remarks
Before starting this outdoor lesson it was really important to explain to students very well the meaning of a rectangle, perimeter, area and units of measurement. Otherwise students would be bored and consider maths as chinese! We noticed that students were more interested as usual in that lesson, especially some of them that are very reserved in the classroom. They were really concentrated in their task , they had a chance to understand what Maths means in our real life and seemed to enjoy it.
Supplementary material
https://www.facebook.com/pg/Ενιαίο-Ειδικό-Επαγγελματικό-Γυμνάσιο-Λύκειο-Αγίου-Δημητρίου-189143001818475/photos/
SURVEYS! IES MADINA MAYURQA (SPAIN)
Summary
Statistics refer to numerical facts. Statistics are very important in education as they help students to collect, present analysis and interpret data. It also helps them to draw general conclusions. This activity was done with our 3rd of ESO students (aged 14-15 years old) in October 2018.
Introduction
Why are statistics important in our lives? Statistics are the set of mathematical equations that we use to analyse the things that surround us. Statistics are important because today we have access to many data and much of this information is determined mathematically by statistics.
Learning objectives
- To collect data and to interpret it.
- To represent the data collected in a visual way.
- To be able to work in group.
- To be able to explain the extracted conclusions to the rest of the class.
Resources
A notebook to note down the results of the survey. 1 piece of card for each group of students. Drawing supplies (coloured pencils, rulers, etc.). Access to computers in case they want to use them to make their tables.
Activities
Day 1
Step 1 (in class): The teacher explains that they are going to work on improving their statistics skills. They watch the video: “Frequency tables”. The students take notes on key statistics terms that they will use in this lesson:
- Sample Size: The total number of people that answered the survey.
- Measure of Central Tendency: The approximate middle of a data set.
- Normal Distribution: When data creates a normal curve with 50% above the average, 50% below the average, etc.
- Outlier: An outlier is a data that falls quite far from the average.
Step 2 (in the park next to our school): Students work in small groups. First they think of 4 questions to ask.
Then they collect data from people in the street or from other students in the class.
Day 2:
Step 1 (in class): Every group of students synthesises, analyses, and represents their data set. Students must include an analysis of each question, and information about their sample size, central tendency (when appropriate), and any outliers.
Step 2 (in class): Students present their findings to the rest of the class.
Comments from the learners’ surveys
Our students enjoyed the lesson very much and learnt to read and interpret statistics. What they liked the most was to ask their questions to the people in the street and to work in small groups.
Final remarks
An outdoor lesson is always welcome, especially if it is Maths! This activity was really engaging and it promoted different competences such as respect towards options different from ours, creativity and interpersonal communication.
Supplementary material
Video: Frequency tables (07:18): https://youtu.be/gdE46YSedvE
Video: Creating a histogram (07:21): https://youtu.be/gSEYtAjuZ-Y
Video: Interpreting a histogram (04:28): https://youtu.be/c02vjunQsJM
Video: Shapes of distributions (05:06): https://youtu.be/2oJldeE4JcU