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MaST Mathematics Specialist Teacher

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What is MaST? Recommended by the Williams Review “My key recommendation is the presence of a Mathematics specialist in every primary school, who will champion this challenging subject and act as the nucleus for achieving best pedagogical practice.” (Williams 2008:1)

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3 Main Aims To develop deep subject knowledge and understanding of the curriculum and progression from EYFS up to KS3. To develop a fit-for purpose pedagogy so that they can draw on a wide repertoire of teaching approaches to support children’s learning of mathematics. To develop skills needed to work with colleagues providing effective professional development through classroom based collaborative activities.

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What does the course consist of? 1 Higher Education Day each term. 1 Local authority meeting each term. A Residential Easter School run over two days. In addition to these other tasks include: Readings on subject knowledge and pedagogy. Reflective learning logs An end of unit essay based on the focus of the over lying theme of the year.

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The course runs over 2 years awarding 30 credits per yearly module. After successful completion recommendation is made to the DFE for award of Mathematics Specialist Teacher Status.

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MaST Content of HEI days 1 and 2 Content of LMs 1 and 2

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HEI Day 1 Using and applying Maths Puzzle wall Discuss the key aspects of Maths covered. Not just ‘problem solvers’ but ‘problem posers’ Excellent website

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‘People Mathematics’ 1.Reverse Order … A group of people are given the numbers 1 - N and stand in order in a line. They can swap adjacent pairs The number of swaps is counted until the initial order has been reversed What is the number of swaps required to reverse a line of N people?

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Looking for Patterns Nth Term (the number in this pattern) Number of MovesPatterns 1 st (1 2) 2 nd (1 2 3) 3 rd ( ) 4 th ( )

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What does it mean to be a mathematics champion? Watch a short clip of maths at Weeke Primary School maths-real Comment of the philosophy and ethos of this school Compare it honestly to your own school what do you consider to be the most challenging aspect for you / your school?

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Fractions … misconceptions LM 1 Fractions Discuss errors such as the one below What fraction of the shape is not shaded? Answer given: 1/3 … why? where next?

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Fractions Models and Images

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Part of a whole which is divided into equal parts

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Comparison between a subset and the whole set

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A point on the number line

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Comparing two sets of objects Jo has yellow counters and Claire has pink counters. Claire has ¾ the amount of counters that Jo has.

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Comparing the size of two measurements

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Final thought: Are a range of models and images used for the teaching and learning of fractions in your school? Any limitations in each model?

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6 key aspects of fractions

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Fractions of shapes 1/2

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Fractions of a number 1/3 of 15

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Fractional numbers on a number line….

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Fractions as divisions (powerful…) Links to decimals and percentages.. ¾ is the same as 3 ÷ 4 (3 pizzas shared between 4 friends)..Each person will have one quarter of each pizza – three quarters in total per person…

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LM2 Division Difference between sharing and grouping 1)I share 29 pencils between 6 people. How many pencils does each person get? 2) 29 people are going on a journey. Each car holds 6 people. How many cars are needed? 3) Work out 29 ÷ 6 correct to three decimal places. 4) You collect 29 CD tokens. You can get a CD for every 6 tokens. How many CDs can you get?

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Sliding Box ÷R =

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Tests of divisibility Back to menu

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Divisible by 7? To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number. If you don't know the new number's divisibility, you can apply the rule again Example: If you had 203, you would double the last digit to get six, and subtract that from 20 to get 14. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven.

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Task Using only odd digits make a 3 digit number that is: Divisible by 7 but not by 11 Divisible by 11 but not by 7 Divisible by 11 and 7 Not divisible by either 11 or 7

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Always, sometimes, Never true If a number is divisible by ‘x’ it will be divisible by the factors of ‘x’ The sum of three consecutive numbers is divisible by 3 Does it then follow that: The sum of four consecutive numbers is divisible by 4 The sum of five consecutive numbers is divisible by 5?

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Multiplication

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‘ Restricting our representations of multiplication and division to just repeated addition and subtraction hinders our ability to recognise and explain some of the properties of these operations’ Barmby, P. Bilsborough, L. Harries,T. and Higgins,S.(2009) Primary Mathematics; Teaching for Understanding. Maidenhead: OUP

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The 4 Properties of multiplication Models which help to structure learning of these properties Line of argument

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Discuss the meaning of each of these: Repeated Addition Inverse of Division Commutative Distributive Understanding properties empowers! Properties of multiplication

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Commutative: 8 x 3 = 3 x 8 Distributive: 25 x 7 = (20 x7) + (5x7) (based on place value) 3 x 8 = (2 + 1) x 8 = ( 2 x 8) + ( 1 x 8) (based on number bonds)

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Models The Set Model 2 X 12 = 24

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The Number Line Model 2 X 12 =

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The Arrays Model 2 X 12 = 24

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PropertiesModels SetNumber lineArray Repeated addition Inverse of division Commutative Distributive

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PropertiesModels SetNumber lineArray Repeated addition Inverse of division Commutative Distributive (part)

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PropertiesModels SetNumber lineArray Repeated addition Inverse of division Commutative Distributive (part)

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PropertiesModels SetNumber lineArray Repeated addition Inverse of division Commutative Distributive

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3 X 13 = X Arrays - links to grid method and area

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Grid Method and Fraction Arrays (connections) 1/2 5

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‘ Restricting our representations of multiplication and division to just repeated addition and subtraction hinders our ability to recognise and explain some of the properties of these operations’ Barmby, P. Bilsborough, L. Harries,T. and Higgins,S.(2009) Primary Mathematics; Teaching for Understanding. Maidenhead: OUP Reflection

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