Quadrilateral activity 2


A discussion question: What shape is the sheet of paper you have? What is special about this shape?

The properties of the paper should be checked using the measuring tool.


Answer: The sheet has the shape of a square. A square is a polygon with 4 equal length sides and all of the angles are right angles.

The answer should be shown only after the class discussion.


A discussion question: Using only two folds can you show the square sheet after opening the folds as 4 congruent triangles?

The concept of the congruence of shapes should be discussed withe pupils enabling them to explain why these 4 triangles are congruent.


Answer 1: In order to obtain the 4 congruent triangles the sheet has been folded with opposite vertices and then adjacent vertices are folded.


Answer 2: The folded triangles are congruent as they cover each other exactly. Congruent shapes have the same measurements.

I t can happen that some pupils will not fold exactly and the triangles will not be congruent. This allows the opportunity to discuss congruent and non congruent shapes.


A discussion question: What can you say about the two segments that can be seen in the opened folding? (Make a mark on the point of intersection).


Answer: The two segments are lines of reflective symmetry of the squared shape sheet and they are perpendicular to each other.

The pupils will understand that the two segments are lines of reflective symmetry of the square by folding on these segments and discovering that the triangles are congruent. Check that the segments are perpendicular to each other using the measuring tool.


Folding instructions: Fold two adjacent sides of the square onto one of the lines of symmetry.


Folding instructions: Turn over the folded sheet.


A discussion question: What can you say about this shape? Explain.


Answer: The folded shape is a quadrilateral called Kite. A kite has 2 pairs of adjacent sides having the same length.


Folding instructions:Turn over your folded shape.


Folding instructions: Fold the two shorter sides of the kite onto the line of reflective symmetry.


Folding instructions:Turn over your folded shape.


A discussion question: What can you say about this shape? Explain.


Answer: The folded shape is a quadrilateral called Rhombus. All the sides of the rhombus are of equal length.


A discussion question: What can you say about the two diagonals? (the two folded segments).Explain.


Answer: The two diagonals are perpendicular to each other and are the lines of reflective symmetry of the rhombus.


Folding instructions:Turn over your folded shape.


Folding instructions: Fold one of the vertices of the rhombus as shown.


Folding instructions:Turn over your folded shape.


Folding instructions: Fold the vertex as shown.


Folding instructions: Fold the shape into two parts as shown.


Folding instructions: Partially open the triangle as shown.


Folding instructions: Pull up slightly the inside triangle as shown.


Folding instructions. Using finger pressure the folded bird will begin pecking.


A final question: What properties of the square and the rhombus are the same? What properties are different?

When pupils are asked about the same and different properties of polygons they relate to properties of polygons with which they are familiar. It is suggested to make write down the two lists.
 Lesson Aims
 Recognition of quadrilaterals especially the Kite and Rhombus.
 Recognition of perpendicular diagonals of the Square and Rhombus.
 Model Name
The pecking bird.
 Lesson Structure
Measuring tool,introductory lesson on composition and decomposition, Quadrilateral activity 1 and 3.
 Lesson Content
In this lesson the pupils investigate the properties of different quadrilaterals during the folding process, especially the Kite, Rhombus and Square. The pupils will investigate the same and different properties of the Rhombus and Square.
 Prior knowledge
The concepts of sides and vertices of quadrilaterals.
 Materials