Lesson 21 Expressions and equations

# Expressions and equations

Overview Resources
An activity to explore linear expressions and equations with one variable. Algebraic manipulations require prior understanding of number identities, so the first episode on breaking and building up whole numbers is used to establish the notions of expressions, commutativity and equations, before using the associative property (brackets) and symbols, Both the inverting and balancing methods of solving equations are used. TM26: Chunking in algebra takes these ideas further. Worksheets 1, 2 and 3
• Links between inverse operations and equivalence in algebra,
• Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way).
• Understand addition, subtraction, multiplication and division of integers,
• use the laws of arithmetic and inverse operations. Know that algebraic
operations follow the same conventions and order as arithmetic operations,
• Begin to distinguish the different roles played by letter symbols in equations, formulae and functions,
• Manipulation of algebraic
expressions.
• EPISODE 1
Expressions, the equal sign and breaking up numbers
Using two small numbers, pupils write down all the eight different expressions possible using the four operations. Each of the four operations is then explored in terms of commutativity through comparison of the expressions. The meaning of the equals sign is a focus. This is followed by breaking up and recombining numbers in addition and multiplication as a means of simplifying calculations.
EPISODE 2
Handling expressions and equations
This episode focuses on the differences between an expression and an equation, including that the expression is a variable while the equation defines a value for a given unknown. Pupils work on examples to clarify two methods of solving simple equations with understanding. One is the standard procedure of balancing, or ‘doing the same to both sides; which needs rehearsing with language. The other is ‘splitting! or ‘breaking up numbers to suit the solution’ practised in mental arithmetic, and on paper is an intermediate approach that allows ‘doing the same to both sides’ to remain visible.
EPISODE 3
Constructing an equation to solve a problem
Pupils solve equations where the unknown is present on both sides of the equals sign, using ‘splitting up’ and ‘balancing’ methods, This consolidates the understanding that the equals sign has a meaning other than ‘the answer is: Pupils see the power of the equivalence and the splitting-up methods, and may go on to devise equations for each other. They construct and solve an equation, using algebra in context to solve a problem.