Course Guide - USAID Teacher Education Project

Unit 3 GeometryWeek 5, Session 2: Squares, Tilted Squares, Square Roots (Surds)1. What are the important concepts?a) The side length of some squares will be rational numbers. Other squares will haveside lengths that can only be expressed as an approximation or as the square root ofthe square's area.b) Numbers have two square roots, one positive and the other negative.2. How do children think about these concepts?a) When asked to draw squares on grid paper or dot paper, most youngsters drawonly “upright squares.” Until prompted, they do not consider “tilted squares.”This is similar to a very young child's perception of a triangle, not seeing a three-sidedfigure as a triangle unless it is oriented with its base "down."Even older children may look at a tilted square and call it a "diamond," not perceivingthat it has all the characteristics of a square.b) When asked to name the length of the side of a square with an area of 2,youngsters usually say, "One." This is because they do not have the words to describean irrational number.c) When looking at a square cut in half along its diagonal, youngsters oftenincorrectly say that this results in "two equilateral right triangles" with sides of 1, 1,and 1.They do not perceive that the hypotenuse is longer than the other two sides.3. What is essential to know or do in class?a) Have students use dot paper grids to draw both upright and tilted squares.b) Introduce the concept and notation of square root.