1. Welcome to our Maths open evening
June 2018
Thank you for coming.

2. Aims for the evening
To give you an overview of the expectations of the curriculum for Maths and how we deliver at North Marston
To help you to understand how we teach your children the four main mathematical operations
To help you support your children with their Maths learning at home

3. “Our Primary Curriculum in maths and science focuses insufficiently on key elements of knowledge and is not demanding enough.”
(DfE, 2014)

4. The National Curriculum for mathematics aims to ensure all pupils:
become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and 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.
If your child is achieving well, rather than moving on to the following year group’s work we will encourage more in depth and investigative work to allow a greater mastery and understanding of concepts and ideas.

5. The National Curriculum for mathematics aims to ensure all pupils:
Fluent recall of mental maths facts e.g. times tables, number bonds etc… and use of informal and formal written methods.
Problem solving – applying these skills to real-life contexts.
To reason mathematically – children need to be able to explain the mathematical concepts with number sense; they must explain how they got the answer and why they are correct.

6. What is Mastery?
What is mastery?
Teaching maths for mastery involves employing approaches that help pupils to develop a deep and secure knowledge and understanding of mathematics at each stage of their learning.
A pupil shows mastery of a concept it they can
• describe it
• represent it in a variety of ways
• explain it to someone else
• make up their own examples
• see connections between it and other facts
• recognise it in new stations
• make use of it in a variety of ways
Key features of teaching to Mastery
• Fewer things (strong focus on number, deepening knowledge, applying skills, develop reasoning)
• Greater depth
• Class working together
• Longer time on topics

7. How do we deliver the Maths Curriculum?
WHITE ROSE HUB
The White Rose Maths is one of many national Government funded hubs. Having listened to teachers they have devised a curriculum plan to support ‘Teaching for Mastery’. This consists of a yearly overview and a termly plan for each year group from Year 1 to Year 6. Each term is split into twelve weeks allowing time for flexibility, revision, consolidation and assessing. A significant amount of time is devoted to developing key number concepts each year.

8. Concrete, pictorial, abstract . . .
Children and adults can find maths difficult because it is abstract. The CPA approach helps children learn new ideas and build on their existing knowledge by introducing abstract concepts in a more familiar and tangible way. Concrete Concrete is the “doing” stage, using concrete objects to model problems. Instead of a teacher demonstrating how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical objects themselves. For example, if a problem is about adding up four baskets of fruit, the children might first handle actual fruit before progressing to handling counters or cubes which are used to represent the fruit. Pictorial Pictorial is the “seeing” stage, using representations of the objects to model problems. This stage encourages children to make a mental connection between the physical object and abstract levels of understanding by drawing or looking at pictures, circles, diagrams or models which represent the objects in the problem. Building or drawing a model makes it easier for children to grasp concepts they traditionally find more difficult, such as fractions, as it helps them visualise the problem and make it more accessible. Abstract Abstract is the “symbolic” stage, where children are able to use abstract symbols to model problems for example +, –, x, ÷

9. Calculation - Addition
Combining two parts to make a whole: part-part-whole model
Starting at the bigger number and counting on (number lines, bead strings, cubes, hundred squares, Base 10)
Regrouping to make 10 (using knowledge of number bonds)
Rounding and adjusting
Adding three single digits
Column method - no exchanging
(Adding the least significant digits first.
Using Base 10 blocks and place value counters. )
Column method - exchanging

10. Informal methods =
= 54
54 – 1 = 53

11. Calculation - Subtraction
Taking away ones
Counting back ((number lines, bead strings, cubes, hundred squares, Base 10)
Find the difference (cubes, bar models)
Make 10 (using knowledge of number bonds)
Rounding and adjusting
Column method - no borrowing and exchanging
(Subtracting least significant digits first.
Using Base 10 blocks and place value counters. )
Column method - borrowing and exchanging

12. Informal methods =
= 14
= 15

13. Formal methods

14. Calculation -Multiplication
Doubling
Counting in multiples
Repeated addition
Partitioning
Arrays
Column method - no borrowing and exchanging
Column method

15. Informal methods Array 4 x 4 = 16 Repeated addition 23 x 7 =
= 161
23 x 7 = 161

16. Calculation - Division
Sharing objects into groups
Division as grouping
Division within arrays
Repeated subtraction
Division with remainders
Short division
Long division

17. Informal methods
Sharing ÷ 4 = 3
Sharing ÷ 4 = 3

18. Formal methods 2 4 1 6 ²4 (6 x 24) (10 x 24) 3 8 Long multiplication2 4 1 6 ²4
(6 x 24)
(10 x 24) 3 8
Formal methods
Learning a new method of calculating does not mean other ways are no longer relevant. By the time children get to year 6 they need to have a repertoire of strategies, including written methods so they can look at a calculation and decide on the best way of doing it. Ask themselves – “Can I do any of this in my head? What do I need to jot down? What’s the best method for tackling this?”

19. Part-part-whole models
Part-part-whole thinking refers to how numbers can be split into parts. It allows children to see the relationship between a number and its component parts.
1.5
0.8

20. Bar models 63 a = b + c ; a = c + b ; a – b = c ; a – c = b
The bar model is used to support children in problem solving. It is not a method, but a way of gaining insight and clarity as to how to solve it.
a = b + c ; a = c + b ; a – b = c ; a – c = b
Ratio problems
A gardener plants tulip bulbs in a flower bed. She plants 3 red bulbs for every 4 white bulbs. She plants 63 bulbs.
How many white bulbs does she plant?
A gardener plants tulip bulbs in a flower bed. She plants 3 red bulbs for every 4 white bulbs. She plants 63 bulbs.
How many white bulbs does she plant?
The Bar Model will allow pupils to see that they need to divide 63 by 7, and then multiply the result by 4 to get the answer. 4 x 9 = 36. 63
red
white

21. Bar models £12.45 Sam Ben Sam + £3.45 Sam and Ben have some money.
Ben has £3.45 more than Sam.
Altogether they have £12.45
How much money does Sam have?
£12.45
Sam
Ben
Sam + £3.45
£ £3.45 = £ £9 ÷ 2=£ Sam has £4.50

22. Bar models Sam and Tom have £67.80 between them.
Sam has £6.20 more than Tom.
How much money does Tom have?

23. Reasoning and Problem Solving
Adding and subtracting decimal numbers

24. Reasoning and Problem Solving
To add and subtract fractions
Can you write an addition sum, adding three fractions, all of which have the same denominator, where the numerator of the total is one less than the denominator?
Bix and Josh share these chocolates. They both
eat an odd number of chocolates.
Complete the number sentence to show what fraction of
The box of chocolates they each could have eaten. =

25. How to help at home Always talk about mathematics in positive ways.
Find mathematics everywhere.
Talk to your child about maths.
Play games.
Support lots of practice at home.
Constantly ask your child “Why?” and “How do you know?”
Provide support when problem solving at home.
Help your child develop automatic recall of basic facts, times tables.