TAS: Ladder Problem

Objectives

• Build algebraic expressions with the aid of an animated diagram
• Use calculus to find the minimum / maximum of a function
• Understand the importance of domain restrictions, sign and absolute values
• Align the result to the practical problem and reflect upon the answer

Vocabulary

• Maximum / Minimum
• Similar Triangles
• Signum function
• Absolute value
• Derivative

About the Lesson

Maddi the painter needs to work out the longest ladder that she can get around a tight hallway corner. Students formulate an expression, step by step, to build a relatively complicated expression for the total length of the ladder. Students use the CAS to differentiate and make equal to zero. Then what? Why does the function minimum value align with the longest ladder? This activity encourages students to reflect and think about their answers to what might otherwise appear as an automated response.