View video clips Mathematics
in Context curriculum is designed so that lessons begin with
a meaningful context and the math is extracted from that context.
The context here involves a ladder positioned against a building,
what it does, and for whom and when would a ladder be needed.
The class moves outside where they help the school janitor
position a ladder. By directing the positioning of the ladder,
students see and describe how the angles and distances made
by the ladder change when the ladder moves from an unstable
position to a safe and stable position- underscoring the mathematical
focus of this lesson - the tangent ratio.
Back in the classroom, students draw triangles representing
the ladder against the wall and examine the relationships
amongst distance, height, and angles of the resulting triangles.
They discover that the height-to-distance ratio is a measure
of steepness affected by the size of an angle. The lesson
culminates with students plotting a steepness graph to determine
the necessary height-to-distance ratio for a ladder to be
safe and stable.