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.
Improving Learning in Mathematics: Challenges and Strategies
The materials use active learning approaches originally designed for post-16 mathematics but for use across the secondary phase.
You may want to have a quick look at the following sections to inform your planning. Section 4 page 16 describes the different types of activity used to develop different ways of thinking. Section 2 pages 6 – 10 describe some of the research based strategies that underlie the principle of good teaching identified by the research. Although written with a mathematics class room in mind these principles could also be used in the science classroom.
Nuffield Science Calculations
This resource has a comprehensive set of equations and calculations from across all the science subjects. There are step by step worked examples, questions and answers (at the back) for pretty much any topic that may crop up across all the sciences. Some of the advice in the opening sections may approach things differently, for example the authors seem to favour the triangles advised against above however there are lots of good examples here.
Ohm's Law and Visualising Equations
The simulation on the PhET site for Ohm's law provides a way to help students to visualise the relationship between the three variables (Potential difference, current and resistance) and the effect of the change of one of these upon on the others. Whilst this is subject specific example, it could be used to support students when dealing with other three quantity algebraic equations. (Note: you can turn the annoying sounds off)
Creating and Solving Equations A2
This resource is an excellent way of checking students understand how to solve equations using inverse relationships as well as understanding the rules on order of operations (BODMAS).
If you look at the section called “Starting Points” on page 1 of the resource this will introduce you to the different methods and related terminology used in mathematics when solving equations. It will also review some of the classic misunderstandings that arise when students try to learn rules without understanding them. Spend a little time thinking about whether you have seen examples of these type of mistakes in your classroom.
Building equations is easier than solving them because it postpones the need to be confident with what operations lead to the desired goal and so is an easier place to start.
You start by writing a letter and a value on the board for example x = 5.
Using learners’ suggestions for operations, build up an equation, step by step, using each of the four rules, +, –, ×, ÷ and whole numbers between 1 and 10. Clear guidance and an example is provided on page 2 of the resource.
Ask the group to check that the original value of x still satisfies the final equation (page 3). This is very important if students get into the habit of checking in this way they should rarely, if ever, make mistakes with algebraic manipulation.
For example if they started with x = 5, multiplied it by 2 and then subtracted 3 the final equation would be:
2x – 3 =7
If you now substitute x = 5 into this equation you will get:
2 × 5 - 3 which is equal to 7, therefore they have manipulated both sides of the equation correctly.
Student then unpick the equation they have created step by step, again clear guidance on this and an example is provided on page 4.
Doing this a couple of times before working with the equations you need to use will make sure students are happy with the inverse relationships they need to use as well as the use of BODMAS. The checking will also give them practice in substitution. Depending on the equations you need to use you may want to introduce squares and square roots at some point.
Maths Is Fun - Algebra
A basic review of equations and how to solve them Once students are secure, they can move onto some complex examples here.