Primary Mathematics Teaching for Mastery Specialist Teacher Programme Jason Darley Ceris Morris Gill Holmes Julie Gallimore

If 16 x 16 = 256 What is 17 x 17 ? 256 + 16 + 17 = 289

If structure was part of teaching throughout 6 + 2 = 8 then 6 + 2 + 1 would equal 9

If structure was part of teaching throughout 2 + 5 = 7 and 7 – 5 = 2

How do you solve + 13 = 15 + 23

Using structure rather than calculation + 13 = 15 + 23

Using variation + 13 = 15 + 23 + 25 = 45 + 24 67 + = 87 + 12 13 + 27 = + 17

Bar Model

We observe that children from quite early ages are able to appreciate structure to a greater extent than some authors have imagined. Initiating students to appreciate structure implies, of course, that their appreciation of it needs to be cultivated in order to deepen and to become more mature. John Mason, Appreciating structure for all

Fluency

Fluency involves: Quick recall of facts and procedures The flexibility and fluidity to move between different contexts and representations of mathematics. The ability to recognise relationships and make connections in mathematics 15

How fluent are you at solving these? 8 + 4 = + 5 68 - = 59 – 38 48 x 2.5 = x 25 39 ÷ 3 = 3.9 ÷ Consider the strategies you used 16

Memorisation of Facts: Effective strategies Make Connections between facts – related facts are easier to learn than unrelated ones. Understand Why – e.g. why any number x 0 is 0 and any number x 1 is itself Reasoning about Answers – can 3 + 4 cannot equal 6 since 3 + 3 = 6 Making Time for Practice Develop Flexibility 17

Making Connections Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. (National Curriculum p3) 18

Representation and Structure Fact Families 3 8 5 + = Identification of relationships and making Connections supports depth and sustainable learning and paves the way for later learning + = - = - = 19

Finding Time for Practice of number facts Identify times in the day 10 minute maths Transition periods Start/End lessons Utilise other times in the day 20

Assess Fluency Consider the assessment information that this question provides 21 Gina Kling and Jennifer M. Bay-Williams (2014)

Assess Flexibility 22

Assess use of appropriate strategy 23 Gina Kling and Jennifer M. Bay-Williams (2014)