WeekSession Content Standards 1 Seminar Induction Developing Maths Concepts: the four operations Q14, 15, 17 2 Seminar Learning to calculate mentallyQ14, Q15, Q23 3 Seminar Learning to calculate mentally Lead lecture – assignment guidance Q14, Q15 Q17 4 Seminar Learning to calculate mentallyQ14, Q15 Q17 5 Seminar Progression from mental to written methodsQ14, Q15, Q25 6 Seminar Progression from mental to written methodsQ1, 2, 4, 6, 7 Q14, Q15, Q25 7 Seminar Progression from mental to written methods Assignment due date Q14, Q15, Q25 (a) (b)

Learning Intentions Mathematics Module To develop an understanding of the structure, notation and language of each of the four operations To develop an understanding of the structure, notation and language of each of the four operations To identify appropriate representations and contexts to model each operation To identify appropriate representations and contexts to model each operation Study Skills Module To develop strategies for organising your studies effectively To develop strategies for organising your studies effectively

Martin Hughes working with Patrick (4yrs, 1 month) MH:How many is two and one more? P:Four MH:How many is two lollipops and one more? P: Three MH: How many is two giraffes and one more? P: Three Hughes, M. (1986) Children and Number: Difficulties in Learning Mathematics, Oxford, Basil London

Early addition strategies Count all Count all Count on from first number Count on from first number Count on from larger number Count on from larger number Use a known fact Use a known fact Can these strategies be used to add more than two numbers?

a) There were 9 books in a pile, the teacher took three of them. How many were left? b) If my friend is 9 and his brother is 3, how much older is he? c) There were 9 soldiers, 3 were ill. How many were not ill? d) The price of a sweet in a shop was 9p. The shop thought this was dear and took 3p off. e) John was 3 and 6 years later he was 9 adapted from examples in Haylock and Cockburn (2003) – see link in handbook and reading log

Conceptualising multiplication Repeated addition Repeated addition Scaling Scaling

24 eggs are shared between 6 people. How many do they each get? 24 eggs are packed in boxes of 6 How many boxes are needed?

Early conceptual understanding of division Sharing Sharing Grouping Grouping

Links between the four operations Addition Addition Subtraction MultiplicationDivision

Independent study task Working with your study group, do the mental arithmetic audit (see LN). This audit is not a test. Its aim is to support you in exploring your own and others approaches to calculation. The best way to explore and develop learning is by talking about it, so this audit is designed to be done collaboratively with a fellow student/s and will encourage you to discuss the mathematics you are doing. With every calculation you encounter, ask yourselves, ‘Could this be done efficiently with mental arithmetic?’, before you resort to any other methods of calculation. Make a few notes about what you learn, notice and discuss as you work on it together.

WeekSession Content Standards Suggested timeline for your maths assignment 1 Seminar Induction Developing Maths Concepts: the four operations Q14, 15, 17Consider the mathematical ideas which underpin mental calculation 2 Seminar Learning to calculate mentallyQ14, Q15, Q23Define mental calculation and consider why it is important 3 Seminar Learning to calculate mentally Lead lecture – assignment guidance Q14, Q15 Q17Identify three mental calculation strategies and explore their relative efficiency/ versatility using calculation examples 4 Seminar Learning to calculate mentallyQ14, Q15 Q17Explore the knowledge skills and understanding needed to make use of each of your chosen strategies Plan the content of your guidance paper 5 Seminar Progression from mental to written methodsQ14, Q15, Q25Consider how jottings support your chosen strategies Start to draft your guidance paper 6 Seminar Progression from mental to written methodsQ1, 2, 4, 6, 7 Q14, Q15, Q25 Final draft and proof read 7 Seminar Progression from mental to written methods Assignment due date Q14, Q15, Q25 (a) (b)