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Stage 4: Constructing and solving equations more formally

Find out how to adapt pyramids to help build pupils' understanding of more formal equation solving. You can also find a series of examples to work through.

More formal equation solving

In the fourth stage, the examples become more complex and are likely to require more formal methods of solving equations. Work quickly through the examples in Stage 4 of Resource 6c: Pyramids 2 (PDF-41 KB) Attachments .

When working on examples like these in the classroom, aim to build on the matching method to inform the balancing method, which leads to more formal equation solving.

You can adapt pyramids to the needs of groups of pupils and individual pupils. You can do this by using larger numbers, decimal or fraction coefficients, expressions with brackets, or indices leading, say, to a quadratic equation to solve.

For more examples of pyramid puzzles, see the 'Further developments' section of Resource 6c.

Exercise

Now make up your own examples of a pair of pyramids requiring the solution of:

  • a pair of simultaneous linear equations in two variables
  • a quadratic equation with integer solutions.