TETRAGLE RATING: (a+b)2 = a2 + 2ab +b2
Area
Math
Duration
1 session
Dimension of the advised group of students
15 - 20 students, divided in 5 groups
Specific objectives
The mathematics course should be accessible and enjoyable to
all students. Through observation and interaction, students should be able to discover and understand that (a+b)2 differs from a2+b2 and ultimately deduce what ( a + b )2 equals.
The students' cooperation in groups, observation, observation skills, the
observation, reflection, the discovery method and critical thinking help
The students' understanding and achievement of the objective of the lesson.
Needed Materials
Computer or laptop, internet connection, notebook and pen
Software
The activities are carried out online and students can take notes if they wish.
Description
Students are asked to find out whether the representations (a + b )2 and a2+b2 are equal or unequal. At the end they should be able to prove that the equality ( a + b )2 = a2 + 2ab +b2 holds for any values of a and b. They have the opportunity to find out in two ways either algebraically or geometrically.
Procedure on how to put in practice
Students who choose the geometric mode are given two activities. In the first activity they are given three squares with sides a, b and ( a + b ) respectively, where a and b are positive numbers. First, they calculate the area of each square and observe whether the sum of the areas of the side squares a and b respectively, where a and b are positive numbers, equals the area of the side square ( a + b ). They experiment by moving the two cursors a and b that change the sides of the squares and record their findings.
In the second activity, students can move points E, A, B and observe what happens. Discover geometrically what the representations a2 ,b2, a∙b, ( a + b )2 express, and what the representation ( a+ b )2 equals. In algebraic mode, students are asked to give various values to a and b and to test whether the equality ( a + b )2 = a2 + 2ab +b2 holds for any value of a and b. Finally, they can prove the equality by doing operations in their notebook:
( a + b )2 = (a + b )∙( a + b )=....
The identity ( a + b )2 = a2 + 2ab +b2 is proved!
