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Mastery Specialist Teachers Katie Crozier Claire Gerrard Jo Harbour Luke Rolls What do we mean by Mastery? • Deep and sustainable learning – for all Depth is the key to avoiding the need to repeat teaching. It doesn’t feel like we’re starting again each term. • The ability to build on something that has already been sufficiently mastered …for this stage of learning - Mastery is a continuum What do we mean by Mastery? • The ability to reason about a concept and make connections • Cuts down on the amount I need to learn eg relating concepts of division, fractions and ratio • Deepens conceptual understanding. •Conceptual and procedural fluency • Move maths from one context to another. Recognise concepts in unfamiliar situations. • Know number facts and tables, have efficient procedures What do we mean by Mastery? • A mastery approach: a set of principles and beliefs. This includes a belief that all pupils are capable of understanding and doing mathematics, given sufficient time. Pupils are neither ‘born with the maths gene’ nor ‘just no good at maths’. With good teaching, appropriate resources, effort and a ‘can do’ attitude all children can achieve in and enjoy mathematics. NCETM https://www.ncetm.org.uk/resources/46689 Teaching for Mastery • Access • Pattern • Making Connections • Chains of Reasoning • Making Connections Representation & Structure Mathematical Thinking Small connected steps are easier to take Coherence Variation • Procedural • Conceptual • Making Connections Fluency • Number Facts • Table Facts • Making Connections What examples of the five big ideas can you spot during this session? Use of stem sentences. 5 5 is the whole. 2 is a part. 3 is a part. 2 3 Use of stem sentences. 5 5 is the whole. 4 is a part. 1 is a part. 4 1 Also use zero. 5 0 5 5 1 ? ? 5 ? ? ? 4 is a part. 2 is a part. 6 is the whole 4 2 1 1 is a part. 7 is a part. 8 is the whole 7 ? 6 3 Use of stem sentences. 3 3 is a part. 3 is a part. 6 is the whole 6 6 ? Use of stem sentences. ? 6 is the whole 1 is a part. 5 is a part. 6 Move from pictorial/ symbolic to abstract. 6 6 1 5 Mastery of the part part whole model! 10 10 10 1 5 2 8 3 9 5 2 3 2 3 4 8 10 Subtraction within a context ? What does the 6 represent? What does the 2 represent? What does the 4 represent? Before Next Now 6-2=4 What does the 6 represent? What does the 5 represent? Before What does the 1 represent? ? Next Now 6-5=1 Year 2 停车场 7+5 7+5 7+5 3 2 7+5 2 5 2+2+2=6 What if there were 9 explorers? 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18 What if there were 9 explorers? 2 × 9 = 18 What if there were 8 explorers? 2 × 8 = 16 What if there were 5 explorers? 2 × 5 = 10 What if there were 0 explorers? 2×0=0 Procedural variation is used to support deeper understanding of a mathematical procedure or process. By asking pupils to compare two successive procedures, where the first is linked to a second, relationships can be observed. Opportunity is given to observe the variant and invariant properties of the procedure - i.e. what stays the same and what changes? (depending on the numbers/ conditions) leading to generalising about the procedure. What is the variation within the questions and between the questions 49 Variation 43 X 3 Which number is the multiplicand? Which number is the multiplier? STEM SENTENCES: The multiplicand is … The multiplier is … 43 X 3 = 129 43 X 3 = 129 44 X 3 What’s the same and what’s different about these two calculations? Can you use your answer from 43 x 3 to work out 44 x 3? 43 43 + 1 44 + 1 44 43 43 X 3 = 129 + 1 44 44 X 3 = 43 x 3 + ? 44 X 3 = ? A full jar of beads holds 58 beads. How many beads are there in 6 full jars? 58 X 6 STEM SENTENCES: 58 The multiplicand is … The multiplier is … 58 58 X 6 = 348 58 58 58 58 A full jar of beads holds 58 beads. In 6 full jars there are 348 beads. 58 X 6 = 348 58 58 58 58 58 58 We’re going to use this answer to find out how many beads there are in 7 full jars. Draw a bar picture to show 58 x 6 Draw a bar picture to show 58 x 7 What’s the same and what’s different about them? 58 58 58 58 58 58 58 58 58 58 58 58 58 X 7 = 58 x 6 + ? 58 58 X 7 = 348 + 58 = 406 Use column multiplication to work out the first multiplication calculation. Adjust your answer from a) to work out the product of b). Think about whether the multiplicand or the multiplier has changed. You could draw bar picture to help you see what is the same about the calculations and what has changed. 1a) A book has 37 pages. How many pages are in 7 books? 1b) How many pages are there in 8 of these books? 2a) 2b) A concert ticket costs £38. How much do 6 tickets cost? The cost of a ticket goes up to £41. How much do 6 tickets cost now? Teaching for Mastery • Access • Pattern • Making Connections • Chains of Reasoning • Making Connections Representation & Structure Mathematical Thinking Small connected steps are easier to take Coherence Variation • Procedural • Conceptual • Making Connections Fluency • Number Facts • Table Facts • Making Connections Katie Crozier – Eynesbury Primary School [email protected] Jo Harbour - Mayfield Primary School [email protected] @joharbour Claire Gerrard – Thorndown Primary School [email protected] Luke Rolls – University Primary School l[email protected]