1. 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

2. 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

3. 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

4. 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

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

6. 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

7. Ways to reason

8. 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?

9. 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

10. 42.195
What are the different ways which we can represent this number?

11. 42.195
10 x 4 = 40
+ 1 x 2 = 2
x = 0.1
x 9 = 0.09
x 5 = 0.005

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

13. Challenge
Seen in a Y5 lesson in Birmingham

14. Pass the fraction
George

15. 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?