THE BIG IDEAS IN NUMBER

At Hackham East Primary we are always striving to create learning environments where both students and staff have and are supported to develop a ‘Growth Mindset’.   We create learning environments that foster ‘Life Long’ learners where both students and staff understand that a key part of learning is making mistakes, being in the ‘Learning Pit’ and working through learning that is new, challenging and sometimes uncomfortable. 

In Mathematics, we focus on building student’s automaticity in the Big Ideas in Number. Over the last 3 years, Staff have become competent with and are successfully implementing the Big Ideas pertinent to their year level and students’ abilities in their class, with the support of our Maths Mentor and Year 5/6 Teacher, Mrs Fiona Dealtry.  This differentiated approach targets every student within each class ensuring that all students mathematics needs are being met so individual progress can be achieved.

Number underpins the numeracy general capability. It’s used across learning areas and in our everyday personal and professional activities. Number sense includes knowing the principles of counting and that: subitising tells us how many, an arrangement of a collection won’t change, and that the quantity of different arrangements are useful in solving problems. Number sense includes thinking and questioning the ways numbers are used in different contexts. It allows students to create mental objects that can be manipulated flexibly with understanding and confidence.

Di Siemon, Chief Academic responsible for The Big Ideas in Number framework, suggests that the concepts of ‘trusting the count’, ‘place value’, ‘multiplicative thinking’, ‘partitioning’, ‘proportional reasoning’, and ‘generalising’ are the checkpoints in number sense each student is required to pass through before progressing further in mathematics.

The Big Ideas in Number are categorised into the following stages at a Junior Primary and Primary year level: 

1. Trusting the Count is understanding that 2 is always 2, 5 is always 5 and not having to count through 1 to 1 correspondence.  It is having deep number sense, understanding a given number in a variety of ways. For example, seven is 3 + 4, 1 less than 6, 2 more than 5.
2. Place Value is understanding that the placement of a digit in a numeral determines the value of that digit. For example, the 3 in 327 represents 300, whereas the 3 in 32 represents 30. 
3. Multiplicative Thinking is understanding that two numbers multiplied can be represented in a variety of ways. For example 5 x 6 could be five groups of 6, 6 groups of 5, an array of 5 rows and 6 columns, a space which is 5 units long and 6 units wide.
4. Partitioning is the ability to divide objects into equal parts or fractions. Students who understand partitioning/division/fractions can work within groups to divide wholes into equal parts. The content areas progress from fractions to division to decimals and then percentages

The Big Ideas in Number provide stepping stones or stages for learning maths and allows students to build the foundations in mathematical concepts. Students need to understand the concepts at each stage before moving on to learning concepts at the next stage. Conceptual Understanding Numeracy involves students recognising and understanding the role of mathematics in the world.

Due to the consistent approach across the school, buy in from all teachers and ongoing professional development for staff, several of our Primary Students have made exponential growth and are currently working within the 5th Big Idea – Proportional Reasoning, and the 6th Big Idea - Generalisation which are generally consolidated in High School.  Continual practise and revision of the Big Ideas in Number is how we will continue to build confidence in our children’s maths ability. 

Our staff are committed to ongoing professional learning and a focus on assessing and teaching the ‘Big Ideas in Number.’ This will support our students to build solid foundations in the critical ‘Big Ideas in Number’ relevant to their year level and level of progression to build fluency, confidence and positive dispositions towards maths learning and problem solving.

Scott Megson

Deputy Principal