# Substitution

Students are required to understand what variables in a formula stand for and to be fluent substituting values for variables in formulae in order to solve problems. Where appropriate, examples should be taken from other areas of the curriculum, for example science. This resource list contains a variety of activities in which students use formulae by substitution to calculate the value of a variable.

Visit the secondary mathematics webpage to access all lists.

### Algebra Makes Sense

This resource contains twenty activities focusing on algebra. The activities requiring students to substitute numbers into a formula are:

**Matching mappings **- substitute into expressions and formulae, express functions in words then symbols.

**Complete the mappings **- substitute into expressions and formulae, express functions in symbols, represent mappings algebraically.

**Algebra game **- substitute into expressions and formulae, express functions in symbols.

**Random code -** construct and solve linear equations, substitute into expressions and formulae.

**Letters for lengths **- use index notation, construct and solve linear equations including brackets and negatives, substitute into expressions and formulae.

**Fibonacci-type sequences **- construct and solve linear equations including brackets and negatives, generate sequences, find the nth term, substitute into expressions and formulae.

### Evaluating Algebraic Expressions A4

In this resource students learn to distinguish between, and interpret, equations, inequations and identities and substitute into algebraic statements in order to test their validity in special cases.

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. This resource builds on students' knowledge of substitution to reconsider such interpretations.

### Algebraic Expressions

This resource requires students to consider different algebraic expressions in order to expose and discuss common misconceptions. There follows a number of rich collaborative tasks to develop an understanding of how to multiply out brackets. Students also sustitute values into formulae in order to expose misconceptions and to evaluate formulae to solve problems.

### Formulae

The resource, **Formulae**, covers a number of algebrac concepts. The sections relevant to this resource list are:

**Substitution into simple formulae:** substituting positive and negative** **numbers into more complex formulae using BODMAS.

The activities sheet contains a number of interesting activities using substitution. **Codebreaking** explores how substituting numbers for letters can be used in code breaking and **One to Twenty Eight **asks students to create different formulae such that when values are substituted the results cover all the numbers from one to twenty eight.

### Reading Age Formula

Students need to be familiar with the term 'reading age' and are required to apply different formulae to a selection of text samples, before comparing and considering the accuracy of the results obtained.

Substitution into formulae is the key aspect of this resource which includes detailed notes for teachers that provide a structure for planning lessons.

### Working with Formulae

This video resource from Teachers TV uses the length of a runway at an airport to demonstrate a practical application of mathematics. Graphics are used to demonstrate how to rearrange a formula.

Measurements, taken at an airport, are substituted into relevant formulae to calculate acceleration and the length of runway required for take-off and landing.

Calculations are performed in stages throughout the video, offering a pause point for teachers to hold a freeze frame on screen while students discuss the problem and perform the calculations themselves.

### Algebra: Substitution

This Virtual Textbook excel program contains a series of interactive spreadsheets designed to give practice in substitution values into expressions containing either one or two variables. Positive or negative values may be selected.

The workbook contains a further six worksheets providing further questions for use in the classroom. The expressions to be evaluated develop from simple linear to more complicated expressions involving brackets and simple powers.

### Formulae, Rearranging, Evaluating

This excel file contains a series of sheets which give practice in rearranging formulae and substituting values. Clicking on the subject of the formula reveals the rearranged form. The answers to the calculations are also available.

The topics of the formulae include dynamics, elastic strings, pendulum, force, electricity and lenses.

The workbook contains a further nine printable worksheets providing further questions for use in the classroom. Some of the later worksheets include the substitution of negative numbers, graphs of functions and quadratic graphs.