1. Maths Mastery A PRESENTATION FOR PARENTS JANUARY 2017

2. 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!

3. 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.

5. 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.

7. v

8. 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

9. Written v mental calculation! Developing a toolbox of strategies.
Mastery is knowing the most efficient methods to use
How would you solve these? • • • • • • • • • • • •

10. 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

11. 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

12. 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.

13. 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

14. Resources and Representations of Mathematics
Resources to help build concepts

15. 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

16. 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?

17. Using manipulatives to support addition and subtraction written methods

18. Part-Part-Whole Model

19. Part-Part-Whole Models

20. Part-Part-Whole Models

24. 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?

29. 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

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

31. Finding unknowns ? 3 7 20 ? 10 3 ? 10 ?

32. Developing depth/simplicity/clarity7 2 5 7
1.9
5.1 C a b
7.4
1.7
5.7

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

36. 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.

38. 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

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

44. 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?

45. 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

46. 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.

47. 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.