Maths Mastery A PRESENTATION FOR PARENTS JANUARY 2017

Starter for chocolate On each table, there is one bar of chocolate. Each bar is the same size. Choose your seat carefully to ensure you get the biggest possible share of the chocolate! Once seated, you must not send people away who want to join you!

Mastery and the National Curriculum • become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems overtime, so that pupils are able to recall and apply their knowledge rapidly and accurately to problems • reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language • can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Children must master the curriculum for their year group, so that they have firm foundations to build on the following year.

SINGAPORE AND SHANGHAI CURRICULUM IS BASED UPON: An emphasis on problem solving and comprehension, allowing students to relate what they learn and to connect knowledge Careful scaffolding of core competencies of : visualisation, as a platform for comprehension mental strategies, to develop decision making abilities pattern recognition, to support the ability to make connections and generalize Emphasis on the foundations for learning and not on the content itself so students learn to think mathematically as opposed to merely reciting formulas or procedures.

v

Some expectations have not changed. Some well known mental calculation strategies • Partition and recombine • Doubles and near doubles • Use number pairs to 10 and 100 • Adding near multiples of ten and adjusting • Using patterns of similar calculations • Using known number facts • Bridging though ten, hundred, tenth • x4 by doubling and doubling again • ÷4 by halving and halving again • x5 by x10 and halving • ÷5 by ÷10 and doubling

Written v mental calculation! Developing a toolbox of strategies. Mastery is knowing the most efficient methods to use How would you solve these? • 225 + 142 • 125 + 127 • 25 + 49 • 167 + 133 • 145 +127 • 3537 + 2946 • 167 - 145 • 267 -259 • 478 - 199 • 300 - 150 • 468 - 237 • 3241 - 2167

Strategy toolbox: Written v mental calculation! Mastery is knowing the most efficient methods to use How would you solve these? • 24 x 50 • 52 x 4 • 26 x 15 • 148 x 5 • 136 x 9 • 245 x 1.6 • 123÷ 3 • 165÷ 10 • 325÷ 25 • 408÷ 17 • 728÷ 5 • 753÷ 6

What is maths mastery? What does it mean to master something? I know how to do it It becomes automatic and I don’t need to think about it- for example driving a car I’m really good at doing it – painting a room, or a picture I can show someone else how to do it. What is Maths Mastery? Achievable for all Deep and sustainable learning The ability to build on something that has already been sufficiently mastered The ability to reason about a concept and make connections Being fluent Mastery involves the development of three forms of knowledge: 1. Factual – I know that 2. Procedural – I know how 3. Conceptual – I know why

The children don’t need to just know if the answer is correct, they need to know why. Manipulatives and visual representations ‘open the door’ to conceptual understanding and should be used with all children. This will then lead to the procedural fluency and the mastery that the new National Curriculum requires. Teaching rules alone does not give children the conceptual understanding that they need.

Mathematical Thinking Number Facts Table Facts Fluency/flexibility Making Connections Procedural Conceptual Chains of Reasoning Problem Solving Access Pattern Representation & Structure Mathematical Thinking Fluency Variation Coherence Small steps are easier to take

Resources and Representations of Mathematics Resources to help build concepts

Concrete Pictorial Abstract (CPA) These stages are continuous Some children may need all stages Some children may go through all stages quickly Vary through topics  Therefore, it is important that a variety of representations are available for children to use at all times. Sometimes children will need to touch and manipulate, but at other times simply seeing or imagining the representation will be enough. Using objects that can be moved, grouped and rearranged to help them make sense of a problem (plastic fruit, counters, cubes etc.) Meaningful pictures/ drawing them Numbers or symbols

The importance of understanding place value Using the resources n your table , how many ways can you represent the numbers 7, 17 and 27? How is the representation of each number different in terms of how you ‘understand’ the number? How does this lead to supporting children with calculation?

Using manipulatives to support addition and subtraction written methods

Part-Part-Whole Model

Part-Part-Whole Models

Part-Part-Whole Models

I know that 18 bottles of lemonade at 29p each cost £5.22 altogether. How can I use this to calculate the cost of… 19 bottles? 18 bottes at 28p each? 18 bottes at 44p?

The bar model… • It is a mathematical representation of a word problem • It is a representation that reveals the structure of a word problem • A way of ‘acting’ out a problem • It is not a calculating tool

The relationship between addition and subtraction a = b + c a = c + b a – b = c a – c = b Part / whole relationships

Finding unknowns ? 3 7 20 ? 10 3 ? 10 ?

Developing depth/simplicity/clarity 7 2 5 7 1.9 5.1 C a b 7.4 1.7 5.7

Subtraction: Comparison Peter has 5 pencils and 3 erasers. How many more pencils than erasers does he have?

Multiplication, Division, Fractions, and Ratio All of these concepts involve proportional and multiplicative relationships and the bar model is particularly valuable for representing these types of problems and for making the connections between these concepts visible and accessible.

Multiplication Peter has 4 books Harry has five times as many books as Peter. How many books has Harry? How might you represent the problem? 4 Discuss the representation, including how it represents multiple addition and scaling for multiplication The squares on the second line might be pushed together to form one bar You might also discuss that multiplication always starts at zero (i.e. we don’t start with the original 4 and add 5 more to it, although altogether there are 6 times 4 since Peter has one times, and Harry has 5 times 4 4 4 4 4

Division Mr Smith had a piece of wood that measured 36 cm. He cut it into 6 equal pieces. How long was each piece?

GCSE higher paper 2012! Ralph posts 40 letters, some of which are first class, and some are second. He posts four times as many second class letters as first. How many of each class of letter does he post?

How have we changed Maths at NVPS? We haven’t! We have adapted our practice in line with the new curriculum Developed ‘Maths Principles’ for working towards and teaching a Mastery curriculum… Maths Hub Membership Lots of training- teachers, teaching assistants, pupils… Increased time spent focussing on maths More Maths = better standards! Daily maths lessons and 3 timetabled ‘Maths Meetings’ per week Planning and assessment Long term plans/map indicates time slots for each topic Medium term plans indicate the key year group standards, apparatus, visuals, vocabulary , key questions and reasoning and assessment links Daily plans are responsive

Maths principles… Practical resources All lessons feature: Practical resources Problem solving and reasoning opportunities that challenge all children in order to deepen understanding and develop mathematical thinking Planned opportunities for peer, pair and group talk using correct terminology Recording that is purposeful Draw downs that are timely and effective Flexible groupings, fluid seating and the use of near ability and mixed ability pairing Lessons will sometimes, but not always, follow a structure that develops the use of a practical example, through to a visual task then to questions that involve the abstract Lessons linked to real life and familiar contexts Teachers will model, question and continually assess pupil progress Classes work through the same concepts at the same time.

So, how can all this help you to help your child at home? Develop fluency- make it fast and furious! Use practical contexts at every opportunity Ask children to explain their thinking Ask them to tell you what they already know about the topic Draw diagrams and pictures Enjoy maths with them Feel Ok to say you don’t know- let’s see if we can sort it out Above all, DON’T tell them you don’t like maths or were never any good at it! At New Valley we teach the children that everyone has the potential to be good at maths. It’s proven.