A very common reason why students fail to do well in physics is they struggle to do the mathematical questions. There are many reasons for this

- Lack of maths skills
- Inability to transfer skills. from maths lessons. Maths tends to deal with numbers, and physics with quantities. In maths, many students who can rearrange something like a=bc and do calculations cannot do the same thing for F=ma. They also fail to see how the formulae can be used to give the units.
- Graphs in physics tell stories, in maths, they tend to be abstract relationships. The gradients calculated from y = mx+c do not represent a quantity as they do in physics. In physics, the gradient of a displacement time graph tells you the rate of change of displacement, which is the velocity. The gradient of a velocity-time graph tells you the acceleration. The area under a velocity-time graph tells you the distance travelled.
- A line of best fit in maths is nearly always a straight line. In physics, it may be a curve.

It seems evident that the physics and maths departments should work together to produce a common approach.

Before we look at Science stories it may be helpful to see how we might change the subject in English and Maths lessons to show commonality.

**Literacy stories**

- The cat sat on the mat
- The mat is where the cat sat
- Sitting is what the cat is doing on the mat

These three statements all tell the same story but have been rearranged to change the subject

**Maths Stories **

- 6 = 2 x 6
- 3 = 6/2
- 2 = 6/3

These three statements all tell the same story, the relationship is the same, but has been rearranged to change the subject

**Science Stories**

- F = ma
- a = F/m
- m = F/a

These three statements all tell the same story, the relationship is the same, but has been rearranged to change the subject

This can be a revelation to some students!

**There are 4 main types of stories our students encounter at GCSE **

- F = ma – Proportional eg F = ma
- Ratio eg a = F/m
- Accumulation s = vt
^{ }Squared relationship – Ke =½ mv^{2 }squared with with velocity

**Proportional Relationship**s

We mostly teach proportional relationships. Doubling a factor on one side of the = sign doubles the other side. These give rise to straight-line graphs

So for F = ma if the force is doubled, then acceleration is also doubled (if the mass is unchanged)

For V = IR if the resistance is doubled, then the potential difference must also be doubled to keep the same current

**Ratios**

- a = F/m
- I = V/R
- x = F/k

Ratios usually tell better stories in all of the above the **consequence = cause/constraint**

acceleration is the consequence of the force, with mass being the constraint

current is the consequence of the potential difference with the resistance being the constraint

If we want a large consequence we need a large cause and a small constraint.

What effect does doubling the cause have on the consequence?

What effect does doubling the constraint have on the consequence

So what story does a = F/m tell us?

Is this a better story than F = ma?

**Accumulations **

- s = vt
- E = `Pt
- E = VIt

Accumulations (which are also proportional) tell us that over time that the quantity increases.

The longer you move for the further you travel

The longer you leave an appliance on for the more energy is transferred. Note that the more powerful the appliance the more energy is transferred in the same time compared to a less powerful one

Leaving an appliance on for twice as long, doubles the energy transferred (and hence it’s cost to run)

Squared Relationships

- Ke =½ mv
^{2} - P = I
^{2}R

Squared relationships tell us that doubling the squared quantity eg the velocity, quadruples the kinetic energy

With the power relationship, we should be able to tell the story of what we want low currents through power lines in order to reduce power losses.

Have your students practice telling the stories, models for all are attached below

Stories of Graphs – Coming Soon!!