Angles in Ramps

Many of the children built ramps with objects like planks of wood or sheets of carboard. The angle between the ramp/board/plank and the floor changes as the children change their ramp set-up.

The picture below shows how we can think of the ramp as the long side (the hypotenuse) of a right-angled triangle, the floor as the bottom, and the supporting pillar as the vertical. Sometimes the vertical side won’t be so obvious, for example if the ramp is resting on a tabletop or if the bottom of the ramp doesn’t touch the floor.

“It’s gone little up the top now when I move the ramp up, the acute angle that’s just small.”

The angles in the triangle determine whether it is a steep ramp or a shalllow ramp, or somewhere in between. In a shallow ramp, the angle with the floor (or horizontal), angle A, will be fairly small, and the angle to the pillar (or vertical), angle B, will be larger. In a steep ramp, the angle to the floor is larger, and the angle to the vertical is smaller. Even the ‘big’ angles are smaller than a right angle, so they are still all acute angles!

Mathematicians would almost always focus on the angle to the floor (or horizontal), but we found that the children would nearly always focus on the angle to the vertical - this is absolutely fine!