多角形と正方形


כל תלמיד יקבל 3 ניירות אוריגאמי ממניפת הצבעים.
לפעילות זו הכינו את המודד וטוש אדום

Spread the sheets and hand out 2 sheets to each pupil.
The measurement tool is described in the lesson, ‘A Measuring Tool for Comparison of Lengths’.


הוראת קיפול: לקפל את הנייר כך שאחת מהצלעות תתלכד עם הצלע הנגדית לה. (בנייר אחד בלבד)


הוראת קיפול: לקפל צלע ארוכה לצלע המקבילה. (בנייר אחד בלבד)


המודד: לסמן זווית ישרה רק באחד מקדקודי המודד.


A discussion question:
What is the shape of the sheet in front of you?
In what way can we find out the correct name?
Explain. 
We measure the sides of the square using the measurement tool.
The next slide should not be shown before the end of class discussion.


Aswer: The shape of the sheet is a square: 4 sides and 4 vertices.
With your measurement tool, check that all of the sides of the shape are equal in length and that the 4 angles at the vertices are rightangles.


Folding instructions:
Fold one vertex to lie on top of the opposite vertex. Do this with both sheets. 
It is suggested not to give any aid to the pupils with their own folding. The teacher should pay attention to the folding of the pupils in the classroom.


A discussion question:
What shape do you have now? How do you know?
Explain.


Answer:
We have a triangle. The polygon has three vertices and three sides. Two sides are equal and one angle is a right angle, so the triangle is a ‘right angled isosceles triangle’.


Question for Discussion:
How many different polygons can you make by putting together the two triangles, so that two sides of the same length will always touch? 
Point out to the pupils that when joining the shapes, adjacent sides must be of the same length.


Answer:
Two triangles will make: A parallelogram
– A square
– A big triangle
 A parallelogram

מומלץ להעמיק בסוגי המצולעים שהתקבלו ובתכונותיהם בהתאם לרמת התלמידים.


Folding instructions::
Fold one vertex to lie on top of the other, then open the paper to a square. 
The other triangle shape should be put aside for a further activity


Question for Discussion:
How many congruent triangles can you see in the square? 
Two shapes are congruent when they can cover each other exactly


Answer: Looking at the shape we can identify 4 larger triangular shapes and 4 smaller triangular shapes.

Two shapes are congruent when they can cover each other exactly.


Question for Discussion:
What kind of triangles do you find in the square?


Answer:
All the triangles are right angled isosceles triangles.


Folding instructions:
Fold two opposite vertices to meet at the line of symmetry. 
It is important to take notice of the folding done by the pupils.


A discussion question:
In our folded shape, what are the various polygonal shapes that can be seen?


Answer:
The paper shape is a hexagon. Inside the hexagon we can find:
– 2 squares
– 2 isosceles
– trapeziums
– 2 pentagons
– 4 rightangled trapeziums 
It is not necessary to find all the different polygon shapes only as shown in the animation, as there is also a hexagonal shape and a parallelshaped polygon.


Folding instructions:
Fold together two parallel sides as shown in the animation. 
It is important to take notice of the folding done by the pupils.


Question for Discussion:
What kind of polygon can you see? Describe it.


Answer:
The polygon is a quadrilateral called an isosceles trapezium. Two sides are parallel.


Folding Instruction:
Mark in red the nonparallel edges of the trapezoid and also the line of symmetry. 
At this stage, it is important to stress the need of proper markings which will aid the pupils in a later folding. Take notice that the pupils have done all of the necessary markings.


Folding instructions:
Fold the 2 nonparallel sides marked in red to the line of symmetry, as shown in the animation. 
Pay attention to the correct folding of the pupils. Before folding, it is important that the pupils will point out which sides are to be folded and which is the line of symmetry.


Folding instructions:
Fold inwards the marked vertices. 
The size of the fold is not important and pupils can decide in which direction they fold the marked vertices.


Folding instructions:
Turn your shape over to the other side.


A discussion question:
Which different polygon shapes can be seen in your folded shape?
Explain. 
At this stage there will be a variety of answers depending on the size of the folds done by each pupil.


Answer:
– 1 hexagon
– 2 quadrilaterals 
Due to different folds of the pupils, they may notice different polygon shapes.


Folding Instruction:
Use your markers to draw the face of a rabbit.


Final activity:
Take the other sheet that you put aside and make 3 folds of your choice, but do not open the sheet. Then, press to tighten the folds and open your sheet.. 
The pupils can mark each fold with a clear line or color to highlight each shape as seen on the opened sheet. They should write the matching name to each polygon on their sheet.
This can also be a homework activity.


Folding Instruction:
Open the paper and with your paper ruler (straight edge), go over the lines with a marker pen. 
בשלב זה עלהתלמידים לשרטט את הקווים ולכתוב אילו מצולעים קיבלו במקומות המתאימים .


Folding Instruction:
Look at the polygons in the paper. Write inside each polygon the name of the polygon.
 Lesson Aims
The pupils will fold and identify shapes according to their properties.
The pupils will use paper folding in order to make geometric shapes and investigate their properties.
 Name of Model
A rabbit finger puppet
 The lesson structure
Triangles activity A, Triangles activity B , Polygon activity A, Polygon activity A, Polygon activities B 1/2 , Polygon activities B 2/2 , Polygon activity C , A measuring tool for comparison of lengths , Quadrilaterals A , Quadrilaterals B: Square & Rectangle – same and different, Line of reflective symmetry 1/2, Line of reflective symmetry 2/2, Quadrilaterals C: Square & Rectangle , Lines of symmetry in quadrilaterals, Translation of shapes
 Lesson content
In this lesson the pupils investigate polygons that are formed during the folding process. There is a surprise at the end of the lesson. The pupils learn new concepts and refresh their previous learning.
 Prior knowledge
If during the folding process there are cases of inexact folding by some of the pupils, then these cases will be used to identify differences between the polygons and their properties. The pupils will also learn the concept of polygon sides and vertices.
 Materials
Origami sheets 15 cm x 15 cm, 3 sheets per pupil