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

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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)

  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.

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.]

  • 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?
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