Difference between revisions of "Introduction to a square and its properties"
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===Learning objectives=== | ===Learning objectives=== | ||
===Notes for teachers=== | ===Notes for teachers=== | ||
| − | ===Activity No # === | + | ===Activity No # 1. Constructing a square by drawing circle.=== |
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|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | ||
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This activity has been taken from the website :http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Mylod/Math7200/Project/Square.html | This activity has been taken from the website :http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Mylod/Math7200/Project/Square.html | ||
*Process: | *Process: | ||
| − | # | + | # To construct a square of a given length, draw a line segment AB of given length. |
| + | # Draw perpendicular to the line AB at A. | ||
| + | # Taking AB as radius draw a circle with A as centre. | ||
| + | # The circle intersects the perpendicular at a point. Name the intersecting point as C. | ||
| + | # Similarly draw perpendiculars to AC at C. You get third side of the square. | ||
| + | # To get the fourth side of the square construct a perpendicular to AB at B. | ||
| + | # Name the two intersecting perpendiculars as D. | ||
| + | # ABCD would be the required square. | ||
*Developmental Questions: | *Developmental Questions: | ||
| − | *Evaluation | + | # What is the measure for side of the square ? |
| + | # What is a perpendicular line ? | ||
| + | # Why are we constructing perpendicular line for constructing a square ? | ||
| + | # Why is the intersecting point of circle with square considered as a vertex of square ? | ||
| + | # How do we determine the fourth vertex of the square ? | ||
| + | *Evaluation: | ||
| + | # What are perpendicular lines ? | ||
| + | # Why is a circle being drawn ? Which purpose would it solve ? | ||
*Question Corner | *Question Corner | ||
| + | # Can a square be constructed without using a compass ? | ||
= Hints for difficult problems = | = Hints for difficult problems = | ||
Revision as of 07:48, 17 December 2013
| Philosophy of Mathematics |
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Teaching Outlines
Concept #1. Introduction to a square and its charactristics
Learning objectives
- A square is a 4-sided regular polygon with all sides equal and all internal angles 90°
- A square is the only regular quadrilateral.
- It can also be considered as a special rectangle in which two of its adjacent sides are equal.
- It encompasses the following properties:
- All four sides are congruent
- Opposite sides are parallel
- The diagonals bisect each other at right angles
- The diagonals are congruent.
Activity No #
- Estimated Time:15 minutes.
- Materials/ Resources needed: Geogebra file, laptop, projector and a pointer.
- Prerequisites/Instructions, if any:
- The students should what are 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:
- The teacher can project the geogebra file, move the red dot and ask the students if it still is a square.
- Let them reason out for the answers.
- Developmental Questions:
- what figures do you see ?
- On moving the red dot, what figure is it now ?
- Is it still a square ?
- Why so you think so ?
- Evaluation:
- What are the properties of a square ?
- Question corner:
- Is rectangle a square ?
- Is parallelogram a square ?
- Are all squares parallelograms ?
- Can a square be considered as a type of kite ?
- Differentiate a square and a rhombus.
Concept #2. Measurements in a square.
Learning objectives
- The students learn that the four sides of a square are equal.
- They understand that the adjacent sides are at right angles with each other.
- The area of a square is side x side sq units.
- The perimeter of a square is the length of distance around its boumdary which is 4 times its side.
Notes for teachers
Activity No #
- Estimated Time:
20 minutes.
- Materials/ Resources needed:
- Laptop, geogebra file, projector and a pointer.
- Prerequisites/Instructions, if any
- The students should have prior knowledge of lines and measurements.
- Multimedia resources: Laptop
- Website interactives/ links/ / Geogebra Applets :
- Process:
- The teacher can project the geogebra file and explain about the formula for area and perimeter of a square.
- Developmental Questions:
- Identify the shape ?
- What is the measure of each small square ?
- What is the area of each small square ?
- What is the area of the bigger square ?
- What is the perimeter of the small square ? and larger square ?
- Evaluation:
- What do you understand by the terms area and perimeter ?
- Question Corner:
- How do you find the area and perimeter of an irregular shape ?
Activity No #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Concept # 3. Construction of a square.
Learning objectives
Notes for teachers
Activity No # 1. Constructing a square by drawing circle.
- Estimated Time :40 minutes
- Materials/ Resources needed : White paper, compass, pencil and scale.
- Prerequisites/Instructions, if any:
- The students should know a square and its properties.
- They should know a circle and that all its radii are equal in length.
- They should have the skill of drawing a circle.
- 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:
- To construct a square of a given length, draw a line segment AB of given length.
- Draw perpendicular to the line AB at A.
- Taking AB as radius draw a circle with A as centre.
- The circle intersects the perpendicular at a point. Name the intersecting point as C.
- Similarly draw perpendiculars to AC at C. You get third side of the square.
- To get the fourth side of the square construct a perpendicular to AB at B.
- Name the two intersecting perpendiculars as D.
- ABCD would be the required square.
- Developmental Questions:
- What is the measure for side of the square ?
- What is a perpendicular line ?
- Why are we constructing perpendicular line for constructing a square ?
- Why is the intersecting point of circle with square considered as a vertex of square ?
- How do we determine the fourth vertex of the square ?
- Evaluation:
- What are perpendicular lines ?
- Why is a circle being drawn ? Which purpose would it solve ?
- Question Corner
- Can a square be constructed without using a compass ?
Hints for difficult problems
Project Ideas
Math Fun
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