B1.2 Identify and represent perfect squares, and determine their square roots, in various contexts.
Activity 1: Using the Concept of Area to Understand Perfect Squares
Ask students to take a grid sheet or whiteboard. Have them draw 3 squares of different sizes (limit to squares of size 12; times 12).
Example
The student must identify the dimensions of each square and their respective areas.
If necessary, the teacher reactivates prior knowledge related to the area of the square by asking them this question:
- How do you find the area of a square?
Students should be able to relate the area of a square to its formula (base x height).
Discuss with students the observations and meaning of perfect square numbers and possible notations to define the concept.
In this situation, students should notice that the areas of the squares represent perfect squares or square numbers.
Activity 2: Using the Dimensions of the Square to Introduce the Concept of Square Root
In order to make connections with the original activity, give the area of a square.
The student must then devise a strategy to find the length of one of the sides of the square.
Discuss the properties of the square of a number and introduce the square root as the inverse operation of the squared number. Later, introduce the symbol for the square root as well as the notation to be used.
Consolidate new learning by asking them to calculate the square root of perfect squares less than 144.
Activity 3: Find the Perfect Squares
Hand out number cards randomly to students (number on cards from 0-150). The student should be able to determine if this number is a perfect square (put emphasis on student justification).
To check for understanding, if the number is not a perfect square, ask the student which 2 perfect squares the number falls between.
Example
Number on card: 40
This number is not a perfect square, because 40 is not the product of 2 identical whole numbers. It is between the perfect squares 36 and 49.