KS2 Mathematics: Two Unknowns and Using Formulae

Algebra in Year 6 is about using letters for numbers in situations pupils already understand. The national curriculum lists five things to learn: use simple formulae, generate and describe linear number sequences, express missing number problems algebraically, find pairs of numbers that satisfy an equation with two unknowns, and enumerate the possibilities of combinations of two variables. The last two are the ones that surprise pupils on the reasoning papers of the Key Stage 2 tests, because there may be more than one answer and you have to find them all, or use an extra clue to pick the right one.

The twelve quiz questions practise each of these skills. You find two numbers from their sum and difference, and from their sum and product; count every pair of whole numbers that fits an equation such as 2a + b = 11 by working systematically; decide how many pencils and rubbers were bought for exactly 31p when two combinations are possible and a clue rules one out; turn a 'think of a number' puzzle into an equation and solve it with inverse operations; use a perimeter formula with a decimal length and a taxi-fare formula backwards; describe a sequence with a rule and continue a decreasing sequence into negative numbers; choose the expression equal to 3(a + 2); and substitute two values into an expression.

The flashcards explain the language of algebra at Year 6 level: what a letter stands for, what 2a means, what a formula and substitution are, why an equation with two unknowns can have several solutions, how to work systematically so that no possibility is missed, what inverse operations and equivalent expressions are, and what a term-to-term rule is.

The printable written work has eight problems that ask you to show every step: two numbers from their sum and difference, a full list of solutions of 3a + 2b = 20, the two ways of buying tickets for exactly £50, a 'think of a number' equation, a cooking-time formula used forwards and backwards, a sequence with a rule and a check whether a number belongs to it, two expressions that are always equal, and formulae for a hexagon and a cuboid used to find a missing length.

In the oral exam an examiner gives you one puzzle at a time and asks how you know you have found every answer, which is the key habit for questions with two unknowns.

The material is aimed at Year 6 pupils preparing for the end of Key Stage 2 tests. Keep a pencil handy: a small table of values is the quickest way to list possibilities systematically.

• Find pairs of numbers that satisfy an equation with two unknowns
• Enumerate all possible combinations of two variables systematically
• Express missing number problems algebraically and solve them with inverse operations
• Use simple formulae, including working backwards from the answer
• Generate and describe linear number sequences, including with negative numbers
• Recognise equivalent expressions and substitute values into expressions

Practice material written by Zestly, based on the Year 6 mathematics programme of study in the national curriculum for England (DfE, 2013): algebra (use simple formulae; generate and describe linear number sequences; express missing number problems algebraically; find pairs of numbers that satisfy an equation with two unknowns; enumerate possibilities of combinations of two variables).