As with all introductory lessons in the Montessori system, "area" is introduced to the students with a story. For the Area of a Rectangle lesson, the students are invited to the lesson and the story begins:
"A long, long time ago, in Ancient Egypt, there was a man with three children. This man lived on a beautiful farm, but according to tradition, only one of his children could inherit the farm after him. Since he loved all of his children equally, he thought up a way that he could decide who would inherit and he called his children to him one day.
'I have decided," he told them, 'that the one who can tell me how large our land is shall inherit the property.'
Well, they all went to bed that night thinking over the problem. The next morning, Jack, excitedly told his dad that he had solved the challenge. He knew exactly how big their land was and he could prove it. Their land, Jack told them all, was 5. He got out some string and showed them all that their land, indeed, was 5.
Their father was ecstatic and happily told Jack that the land was his to inherit when it was time. Sami, the younger brother, and Lindsey, their youngest sister, went to bed that night disappointed that they had lost the land. But, in the middle of the night, Sami realized that Jack was wrong and he went out that night with a new set of string to prove that he knew how large their land was, and not Jack. The next morning, Sami told everyone that the land was not 5, as Jack had stated, but 10 and he could prove it. He took everyone out to the land and showed them that the land was, indeed, 10.
Their father was thrilled with this new knowledge and told everyone that Sami had indeed shown how large their land was. Sami was to inherit the property. But that night, when everyone had gone to bed, Lindsey realized that both Sami and Jack were right--yet neither one had seen the whole picture. The next morning, Lindsey gathered her family together and told them that each one had a piece of the puzzle in determining the size of their land, but they did not have the complete picture. She showed her family how the land was indeed 5, as Jack had claimed. But it was also 10, as Sami had shown. Their land, was, in fact, 50 square units and she proved it.
As promised, Lindsey inherited the property showing their father that by making perfect square units of the land, she could show the area of any rectangular or square shape."
Once the lesson is given, the students are asked to see if they can figure out how Lindsey was able to determine that the land was 50 square units. They share that she multiplied the length (l) of the land and got 10--Sami's amount--by the width (w) of the land and got 5--Jack's amount. In this way, they determine that the formula for the area of a rectangle is L x W.