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Multiplication Times Tables and Variation Theory.

Make links and connections using variation theory to look for patterns and links using variation theory. Available in the shop or in the members are as part of your subscription.

Each resources starts with a shared example for an adult to expose the link or pattern to the multiplication times tables.

In intelligent practice, children should use the calculation(s) they have completed in order to calculate the next one. Looking for what is the same and what is different.

What's the same? What's different?

Variation theory draws attention to maths concept by keeping one (or more) elements the same and varying another element. Procedural variation can allow children to make links, connections and spot patterns when applying a method. Asking 'What's the same? What's different' can be a powerful way to sharpen the focus of all learners.

Pedagogy and approach.

Start by explicitly teaching children to look for that is the same and what is different. Explore the relationship between the first and second question to introduce the relationship or concept. Allow children to practice carefully designed tasks in silent fluency practice with questions they can quickly recall. Then vary the questions to expose a pattern, link or concept you want to focus in on. At this point, children can share their thoughts with partners or in a group and may need more intelligent practice to embed and strengthen. This process can happen as many times as needed. Then teachers may explicitly discuss answers and the relationships and offer children some more questions which vary elements of questions carefully to strength and deepen understanding.

In the example below, teachers may explore the known facts that 4 x 4 = 16, teachers may then draw attention to the next question (8 x 4 = 32) and note that one factor has doubled and so the product has to double. Again, looking across to the next set of calculations, children may apply their understanding of 4 x 4 to solve 4 squared.

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