Students are presented with a calculation ‘trick’ – a method for working out the squares of two-digit numbers. They then use algebra to explore the reasons why the method works.

Overview of task

Students are presented with a calculation ‘trick’ – a method for working out the squares of two-digit numbers. They then use algebra to explore the reasons why the method works.

Strand

Number and Measures; Algebra and Graphs

Prior knowledge

Students should have basic GCSE-level understanding of algebraic manipulation. This task provides an opportunity to probe and develop their ability to relate algebraic formulations to patterns in calculations.

Relevance to Core Maths qualifications

- AQA
- C&G
- Eduqas
- Pearson / Edexcel
- OCR

Suggested approaches

This task is suitable for work in pairs, perhaps as a starter for a longer session on algebraic manipulation (e.g. the difference of two squares).

Resources/documentation

Use either the supplied PowerPoint or the ‘middle’ part of following video clip (from about 2.00 minutes to 6.00 minutes) to introduce the ‘trick’ for squaring numbers:

https://www.youtube.com/watch?v=1JW9BA57aR8

Then ask students to give a convincing explanation of why the method works. You may want to prompt them to ‘use algebra’, or leave this for the students to decide; it may be useful to compare other types of ‘proofs’ (e.g. verbal and pictorial) to algebraic methods.

Relevant digital technologies

Apart from the clip indicated above, there are many other video resources available on the Internet that demonstrate (and in some cases explain) mental mathematical tricks and shortcuts.

Possible extensions

Explore other methods for mental maths: for example, using algebra to justify the method for multiplying by 11 shown at the start of the video above, or explaining why the ‘standard’ divisibility tests for 3, 7 and 9 work.

Acknowledgement

Developed by Ihsan Eltom of Fareham College.