Imagine a broom laying on a wall. Refer to diagram. Observe what is the difference before and after, and describe.
You will notice that the height of the broom from the floor to the upper end of the broom decreases and the distance of the lower end of the broom from the wall increases when tilted further downwards.
We say there is a change in the slope of the broom. In mathematics, we can measure slope and help us to measure the steepness of any slope. This is how we calculate slope or in mathematics we call it 'GRADIENT'
Before, the gradient is 5/2 = 2.5 and after that the gradient is 3/6= 0.5. We say 2.5 is steeper than 0.5. Hence by looking at numbers, we can imagine which slope is steeper and which is not.
We can conclude that gradient is the 'rate' of changes in height against changes in the horizontal distance of two points.
Now, let us look at the following diagram.
The first diagram, the broom is vertically upright, hence the gradient is 6/0 =? What do you think 6 divided by 0 is? Try to figure it out using a calculator. Next the broom is laying horizontal on the floor and the gradient is 0/6=? What do you think 0 divided by 6 is? Try to figure out using a calculator. You should get the first answer is math error and the second answer is 0.We say, anything which is vertically upright, the gradient is undefined. Meaning, take a cliff as an example. Cliff has no slope but it is very steep right? Yeah it is very steep. So when anything is horizontal , there is no slope, or the gradient is 0. A flat road has no slope, therefore there is no gradient.
To make our lesson more fun, try to figure out the standard gradient of a ramp in buildings!
Thats all i want to share for now have fun and we will continue in the next lesson.
