Relationship between Area of a square and its Sidelength- Activity 1

Objectives

 * 1) Understanding the geometric meaning of square root.
 * 2) Finding square root of a perfect square number by prime factorisation.>
 * 3) Finding square root of a  number by division method.
 * 4) Finding square root of a decimal number.

Estimated Time
40 minutes.

Prerequisites/Instructions, prior preparations, if any

 * 1) The students should know tables and multiplication.
 * 2) They should know that the product obtained by multiplying the same number twice is called a perfect square number and the number itself is called its square root.
 * 3) They should know a square, its side length and finding area of a square.

Materials/ Resources needed
Laptop, geogebra file, projector and a pointer.

Process (How to do the activity)
Extending the analogy to the   area of a square and its side length helps students visualize the geometric meanings of square and square roots. [Note : Disadvantage of this activity: here we can consider only positive numbers as square roots. Hence in further classes the concept of square root should be extended to negative numbers as well.]
 * 1) Initially the teacher can discuss about a square, its sides and area of a square.
 * 2) Tell the students that each small inner square measures 1 unit.
 * 3) Formula to find area of square is side X side.
 * 4) Each inner square's area is 1 sq unit.
 * 5) Start with a outer big  square of side length 3, which gives an area of 9. Then after doing side lengths of 3-5,  put up a square and say the area is 64, so what must the side lengths be? The students will know it must be 8. Do this a few times and then introduce the new notation saying that the side length for the square with area 64 is the sqrt(64) = 8, and  that is along the side of the square. Similarly repeat for area 144 and write it as square root of 144 =12 on the side length. Tell them that a square root is the inverse of squaring a number.
 * 6) Introduce the symbols forsquare and square root.
 * Developmental Questions:
 * 1) What is the figure called ?
 * 2) How do you know its a square ?
 * 3) Why is the figure called a perfect square ?
 * 4) What are the dimensions of each inner smaller square ?
 * 5) What is the area of each small inner square ?
 * 6) What is the area of two such small squares ?
 * 7) What is the area of 9 such small squares ?
 * 8) If the small squares are of 1 unit dimension, and area of each such square is one sqcm, can  we say that the whole area is equal to the total number of smaller squares.
 * 9) (The number of cells/small squares in each row) x (number of rows) gives us ________.
 * 10) If the number of cells in each row and number of rows is same then we multiply the _________ number twice.
 * 11) Conversely if area is known, then its ___________ can be found out.
 * 12) For ex : If the area of a square is 81, then what would be its side length?

Evaluation at the end of the activity

 * 1) Did students make the connection between the area of a square and square numbers? How do you know?
 * 2) What evidence helped you assess students' understanding of the geometric meaning of square root?

Question Corner:

 * 1) If you know the side length of a square, how can you determine its area?
 * 2) If you know the area of a square, how can you determine its side length?