4 mistakes learners make with real-life graphs, each one named and explained.
On a real-life graph the gradient and the area underneath each mean something, and the units on the axes say what.
You read a gradient triangle off a falling line and write 4 instead of -4.
The triangle you drew has two positive side lengths, and the minus sign lives in the direction rather than in either length.
Question. A line falls from (0, 8) to (2, 0). What is its gradient?
A common answer. 4
The answer. -4
Why. y goes down by 8 while x goes up by 2, so the change in y is -8 and the gradient is -4.
Look at the line before you divide. If it falls, the answer carries a minus sign.
You work out the area under a speed-time graph and label the answer in m/s, or in square units.
Area has meant square units in every lesson until now, so the unit comes along with the method.
Question. A speed-time graph in m/s against s. What does the area underneath represent?
A common answer. the speed, in m/s
The answer. the distance travelled, in m
Why. Multiplying m/s by s gives m, so the area is a distance and not an area in square units.
Multiply the units on the two axes. Whatever they make is what the area means.
You call the gradient the speed on every graph, including a speed-time graph.
Distance-time graphs come first and their gradient is the speed, so the name sticks to the word gradient itself.
Question. What does the gradient of a speed-time graph tell you?
A common answer. the speed
The answer. the acceleration
Why. Speed divided by time is acceleration, the same way distance divided by time was speed.
Divide the vertical unit by the horizontal unit. That is what the gradient means.
On a speed-time graph you say the lines crossing is the moment one car passes the other.
On a distance-time graph crossing really does mean meeting, and the two graphs look the same at a glance.
Question. Two cars on a speed-time graph. Their lines cross at t = 5 s. What happens then?
A common answer. one car overtakes the other
The answer. they are travelling at the same speed
Why. A speed-time graph says nothing about where anything is, only how fast it is going.
Read the vertical axis first. It decides what crossing can possibly mean.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.