# Free samples

## Variation theory

Our variation theory arithmetic papers focus on procedural variation of key concepts in each year group and promote intelligent practice.

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Variation theory draws attention to the essential concept and allows teachers and learners to see, understand and experience concepts.

Asking what is the same and what is different? can be a powerful way to expose essential and non-essential mathematical concepts.

We can consider variation in two ways: conceptual variation and procedural variation. Conceptual variation draws attention to what a concept is and is not.

Conceptual variation.

Lets take the concept of a half. The image below draws attention to what half can look like. It exposes two equal parts but shows the non-essential concept of a half being the way in which an object is halved.

Our concepts maps also show the essential and non-essential concepts of mathematical concepts.

Procedural variation

With procedural variation, the focus is on what is kept the same and what is different so teachers and learners can draw attention to what has changed and what has stayed the same. In essence, the design of the task becomes less random and numbers are kept similar to expose relationships and patterns. In doing so, teachers and children can draw attention to patterns and relationships between numbers. Take the example below and see which set uses variation theory and the impact it could have on learning.