# Algebra

The ability to use scientific formulae relies on the ability to communicate algebraically. Students will need to be confident and fluent in their use of algebra.

Students often use letters in algebra without understanding what they mean. Common misconceptions include believing that a letter can only stand for one particular number, different letters must stand for different numbers or letters can only stand for whole numbers. Such misconceptions often arise when students generalise from a restricted range of examples.

Make sure you talk about the formula you are using in words so that you reinforce the meaning of the operation used in the formula. For example:

Resultant force (F = ma) “is equal to the mass of the object being moved multiplied by the acceleration of the object being moved” So for example it takes more force to produce the same acceleration for a larger mass. In some cases there is the opportunity to use units as a means of checking the validity of the formula being used. For example velocity must be measured in m/s as it is calculated by dividing a quantity measured in metres by a quantity measured in seconds.

A common error when solving equations can be applying rules regarding order of operations incorrectly and a lack of confidence and fluency when manipulating negative numbers. Science gives a huge range of opportunities to encourage students to develop the habit of checking whether their results make sense.

It is important that students can use their mathematical skills to rearrange formula. Try not to resort to memory aids such as the triangle as it can reinforce misconceptions and lead to mistakes, and students will struggle when moving to post-16 study if they rely on this method.

Instead encourage students to write the formula correctly and then rearrange it:

Distance = speed × time

or

D = ST

Discuss how you can change the subject of the formula by rearranging it and the effect of changing the variables on the result of the formula. This would be a good point to check students are confident with the idea of the inverse relationships between addition and subtraction and multiplication and division.

A large proportion of the equations in Appendix 1 of the science content specification can be written in the form:

X = YZ.

So once they have learnt to rearrange this once they can apply the same logic to the other examples without relying on memory aids.

The ability to use algebra, including substitution into and the rearrangement of formula is mainly needed across almost all of the Physics topics however it will also be needed in Chemistry for calculations involving chemical analysis such as the molar amounts of gases and their volumes as well as calculating concentrations of solutions.