1. Mathematics at the Bridges Federation

2. C.P.A. : What is this approach?
C : Concrete P : Pictorial A : Abstract
Zoe
What’s this approach?
C-P-A : All children need to experience the CONCRETE and PICTORIAL to fully understand the ABSTRACT concept (not just KNOW the answer). E.G. Can someone bring me three things? Can someone represent this as a picture? Can someone show this in an abstract form?

3. Counting:
ACTIVITY: What skills do children need to know to understand the concept of counting to 10?
FEEDBACK:
What is number sense?
Zohra
What’s involved with counting?
What skills do the children need to know to understand the concept of counting to 10?
ACTIVITY: What is number sense?
Feedback:
Counting forwards and backwards, recognition between word and numeral, start at any no. & count back/ forwards, organised and systematic, anything can be counted, cardinality.
What’s the most challenging? The abstract, just numerals and symbols!
Research and development 

4. Subitizing
Subitising is a term that was coined by Piaget and defined the ability to instantaneously recognise the number of objects in a small group without the need to count them. An example often used to explain this, is to think of a die – we immediately recognise the number of dots without having to count each one individually. Subtising is an essential part of developing number sense in early years children by helping them to relate numbers to actual items or groups of items. This is known as number conservation. It is not uncommon that young children learn to count by rote but do not really understand the meaning behind what they are doing. By looking at groups of items, children can start to develop an understanding of how a number is made up: for example, seven dots could be a set of three dots and a set of four dots, or a set of six dots and one dot. This understanding of part-part-whole relationships helps children to separate and combine numbers and accelerates understanding of addition and subtraction. Consider each of the following arrangements of dots. What mental strategies are likely to be prompted by each card? What order would you place them in according to level of difficulty?
Zohra

5. Counting things that move Counting things you can’t see.
Cardinality
Counting things that move
Counting things you can’t see.
How many days are in the week?
How many people are absent?
Comparing
Link counting to no. size
comparison language
shared thinking
Zoe
The ability to explain and share your thinking RATHER than just the answer is MASTERY.
We must model the language from the beginning of school so explaining their thinking and reasoning becomes natural.
e.g. Can you show me four fingers? How do you know it is 4? Can you show me 4 on your fingers in a different why? IS that still four?
MAGIC Sentences: I know …..... Because
SHARE and EMBRACE all opinions to EMBRACE the MASTERY CLASSROOM

6. Ordinality & SEEING NUMBERS WITHIN
Working within 5, 10 etc. Seeing numbers within numbers

7. Part/Whole – How many ways?
Understanding the part/whole relationship is crucial for understanding number and
for applying in addition, subtraction. Encourage children to work systematically.
Katie

8. Demonstrating deeper understanding
Children need to link counting with the size of numbers
(which involves understanding cardinality)
‘Which is bigger, 5 or 4?’
Why do you know that?
How can you prove that?
Can you prove it with…..
Objects? Numicon? A numberline? Pictures? Diagrams? Numbers? An equation?
Katie
Keys for developing number sense.
What number sense skills are there?
bridging
subitizing
concept of cardinality (last no. is no. of objects)
1 number = 1 object
High Stable Order (Stable order knows no.s up to 10)- Structures for mathematical thinking and all future counting & place value.

9. Early Number Sense: What do children need?
1. An awareness of the relationship between number and quantity 2. An understanding of number symbols, vocabulary and meaning 3. The ability to engage in systematic counting, including notions of cardinality and ordinality 4. An awareness of magnitude and comparisons between different magnitudes 5. An understanding of different representations of number 6. Competence with simple mathematical operations 7. An awareness of number patterns including recognising missing numbers.
Zohra
(Relationship between no. & quantity/ symbols, vocab & meaning/ systematic counting with cardinality & ordinality/comparisons/ representations of number/ competence with simple mathematical operations/ awareness of number patterns & missing numbers).
EYFS
Purposeful Maths
Child’s interest leads the investigation
Rich language and modeled talk to share thinking
Open ended questioning:
Children need to leave EYFS with a mastery of counting and an understanding of the part/ whole structures.

10. Show and explain their thinking/ their answer in different ways.
Unitizing:
15 separate objects
A group of 1 ten and 5 ones
KAtie
Unitising is a key idea in the development of place value.
At what point do we unitise? 10
Our Place Value system works in base 10
Ten ones become one ten; ten tens or a hundred ones become one 100..
CONCRETE: What does this look like? (unifix cubes)
PICTORIAL: What does this look like?
ABSTRACT: What does this look like?
How do you know this? Can you do it in other ways?
Can you unitize things? Books? Buttons? People? Etc.
Show and explain their thinking/ their answer in different ways.

11. Use the resources to explain What’s happening:
13+4=10+___?
With manipulatives
Activity