Introduction to a square and its properties

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Concept #1. Introduction to a square and its properties

Learning objectives

1. A square is a 4-sided regular polygon with all sides equal and all internal angles 90°
2. A square is the only regular quadrilateral.
3. It can also be considered as a special rectangle with both adjacent sides equal.
4. Its opposite sides are parallel.
5. The diagonals are congruent and bisect each other at right angles
6. The diagonals bisect the opposite angles.
7. Each diagnol divides the square into two congruent isosceles right angled triangles.
8. A square can be inscribed in a circle.
9. A circle can be inscribed in a square touching all its sides.

Activity No # Pull me to see if I still remain a square

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• Estimated Time:15 minutes.
• Materials/ Resources needed: Geogebra file, laptop, projector and a pointer.
• Prerequisites/Instructions, if any:

1. The students should have prior knowledge of lines, vertices, angles and plane figures.

• Multimedia resources: Laptop.
• Website interactives/ links/ / Geogebra Applets :This geogebra is from the website : http://www.geogebratube.org/material/show/id/2474

• Process:

1. The teacher can project the geogebra file, move the red dot and ask the students if it still is a square.
2. Let them reason out for the answers.

• Developmental Questions:

1. What figures do you see ?
2. On moving the red dot, what figure is it now ?
3. Is it still a square ?

• Evaluation:

1. What are the properties of a square ?

• Question corner:

1. Is rectangle a square ?
2. Is parallelogram a square ?
3. Are all squares parallelograms ?
4. Can a square be considered as a type of kite ?
5. Differentiate a square and a rhombus.

Activity No # 2. Properties of a square

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• Estimated Time: 40 minutes
• Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
• Prerequisites/Instructions, if any

1. The students should have prior knowlede about line segments, angles and bisectors.

• Multimedia resources: Laptop
• Website interactives/ links/ / Geogebra Applets : This geogebra file has been created by ITfC-Edu-Team

• Process:

1. The teacher can use this geogebra file while teaching the properties of a square.
2. Can move the vertices of the square to depict the properties.

• Developmental Questions:

1. What type of lines is a square made of ?
2. What is a right angle ?
3. The lines meet at what angles ?
4. Compare the two diagnols.
5. What is the meaning of diagnols bisecting each other ?
6. What is angle bisection ?
7. What is the measure of each bisected angle ?
8. How many triangles do you see in the figure ?
9. What type of triangles are they ?
10. Identify the circumcircle and incircle ?

• Evaluation:

1. Can square be considered a rectangle ?
2. Is square a parallelogram ?
3. What is the difference between a square and a rhombus ?
4. Are all squares quadrilaterals ?

• Question Corner:

1. List the properties of a square ?
2. Can you add some more to the properties list ?

Concept #2. Measurements in a square.

Learning objectives

1. Four sides of a square are equal.
2. Adjacent sides are at right angles with each other.
3. The area of a square is side x side sq units.
4. The perimeter of a square is the length of distance around its boumdary which is 4 times its side.

Activity No # Understanding the area of a square

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• Estimated Time: 20 minutes.
• Materials/ Resources needed:

1. Laptop, geogebra file, projector and a pointer.

• Prerequisites/Instructions, if any
• Multimedia resources: Laptop
• Website interactives/ links/ / Geogebra Applets : This geogebra file was created by ITfC-Edu-Team

• Process:

1. The teacher can project the geogebra file and explain about the formula for area and perimeter of a square.

• Developmental Questions:

1. Identify the shape ?
2. What is the measure of each small square ?
3. What is the area of each small square ?
4. What is the area of the bigger square ?
5. What is the perimeter of the small square ? and larger square ?

• Evaluation:

1. What do you understand by the terms area and perimeter ?

• Question Corner:

1. How do you find the area and perimeter of an irregular shape ?
2. Explain the association of the term 'square' in the unit square cm.

Concept # 3. Construction of a square.

Learning objectives

1. Construction of a perfect square.
2. Use of equal radius arcs to get equal sides of a square in the construction protocol.
3. Use of perpendicular lines to draw sides of a square.

Activity No # 1. Constructing a square.

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• Estimated Time :40 minutes
• Materials/ Resources needed : White paper, compass, pencil and scale.
• Prerequisites/Instructions, if any:

1. Basics of square, circle and constructing perpendicular lines should have been covered.

• Multimedia resources
• Website interactives/ links/ / Geogebra Applets:

This activity has been taken from the website :http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Mylod/Math7200/Project/Square.html

• Process:

1. To construct a square of a given length, draw a line segment AB of given length.
2. Draw perpendicular to the line AB at A.
3. Taking AB as radius draw a circle with A as centre.
4. The circle intersects the perpendicular at a point. Name the intersecting point as C.
5. Similarly draw perpendiculars to AC at C. You get third side of the square.
6. To get the fourth side of the square construct a perpendicular to AB at B.
7. Name the two intersecting perpendiculars as D.
8. ABCD would be the required square.

• Developmental Questions:

1. For what measure are you drawing a square ?
2. What is a perpendicular line ?
3. Why are we constructing perpendicular lines for constructing a square ?
4. What is the purpose of drawing a circle ?
5. How do we determine the fourth vertex of the square ?

• Evaluation:

1. What are perpendicular lines ?
2. Why is a circle being drawn ? Which purpose would it solve ?

• Question Corner

1. Can a square be constructed without using a compass ?

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