VARIATION AND MATHEMATICAL LANGUAGE NETWORK MEETING Sarah Holman and Lisa Ashmore Hello and who are we? Introductions and why are you here? What do you hope to ‘get’ from this meeting

Aims of the meeting Share good practise with other colleagues Build knowledge of the different methods for procedural and conceptual variation Look at ways to develop mathematical language To have a variety of activities that can support variation and language development Explain what the overall aims are from the meeting

Small steps are easier to take Teaching for Mastery Number Facts Table Facts Making Connections Procedural Conceptual Chains of Reasoning Access Pattern Representation & Structure Mathematical Thinking Fluency Variation Coherence Small steps are easier to take

Variation Procedural and conceptual The minuend and the subtrahend in each column of calculations have been varied. This draws attention to the relationship between the two numbers. It encourages some reasoning to explain why the answers change in the way they do. This gives an opportunity for ‘intelligent practice’ where they can explain what is going on and make up their own examples. To get a sense of what a triangle is learners need to see examples of images and concepts which show all aspects being varied (length of sides, angles, orientation; so that over-generalised do not exist It is also important to give non-examples, to discuss why it is not a triangle. Procedural conceptual

Progression in Reasoning • Describing • Explaining • Convincing • Justifying • Proving

Can you first convince yourself? 2 Can you now go on and convince a partner using talk? Can you first convince yourself? 1 4 Finally, can you convince your teacher? What about convincing a friend using jottings? 3

Ways to reason

Procedural variation What do you notice about the calculations? Can you explain what is happening and how this is changing the calculation? Can you calculate another line following the pattern? Why or why not?

Variation Theory in Practice Compare the two sets of calculations What’s the same, what’s different? Consider how variation can both narrow and broaden the focus Taken from Mike Askew, Transforming Primary Mathematics, Chapter 6

42.195 What are the different ways which we can represent this number?

42.195 10 x 4 = 40 + 1 x 2 = 2 + 0.1 x 1 = 0.1 + 0.01 x 9 = 0.09 + 0.001 x 5 = 0.005

Games to support place value Three in a row Nearest to 1000 etc Blank number line

Challenge 9999 + 999 + 99 + 9 + 5 Seen in a Y5 lesson in Birmingham

Pass the fraction George

How did this activity support conceptual variation? How could these activities be supported using concrete materials? How could this activity be differentiated? How can we make connections with other maths areas?