Sadie computes the perimeter of a rectangle by adding the length, \(l\), and width, \(w\), and doubling this sum. Eric computes the perimeter of a rectangle by doubling the length, \(l\), doubling the width, \(w\), and adding the doubled amounts.
Sadie first adds \(l\) and \(w\) to obtain \(l + w\) and then doubles the sum. So her expression is \(2(l + w)\).
Eric first doubles the length and the width, getting \(2l\) and \(2w\), respectively. He then adds these amounts to obtain the expression \(2l + 2w\) for the perimeter of the rectangle.
With \(l=30\) and \(w=75\) using Sadie’s expression we have \(2(l+w)=2(30+75)=210\).
Using Eric’s expression we have \(2l + 2w = 2(30) + 2(75) = 210\).
Commentary
The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent. This is another variation of the Rectangle Perimeter problem shown in "6EE Rectangle Perimeter 1" and "6EE Rectangle Perimeter 2." It goes one step further than "6EE Rectangle Perimeter 1" by asking students to explore the idea of equivalent expressions in addition to writing and using an expression.