Introduction to a square and its properties

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= Concept Map =

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=Additional Information=

Reference Books
= Teaching Outlines =

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

 * 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

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enableRightClick="false" showAlgebraInput="true" enableShiftDragZoom="true" showMenuBar="true" showToolBar="true" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
 * 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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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
 * 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 ?

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.

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.
This activity has been taken from the website :http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Mylod/Math7200/Project/Square.html
 * Estimated Time :40 minutes
 * Materials/ Resources needed : White paper, compass, pencil and scale.
 * Prerequisites/Instructions, if any:
 * 1) The students should know a square and its properties.
 * 2) They should know a circle and that all its radii are equal in length.
 * 3) They should have the skill of drawing a circle.
 * 4) They should know to draw perpendicular lines.
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets:
 * 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 ?

= Hints for difficult problems =

= Project Ideas =

= Math Fun =

Usage

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