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Junior Focus Group Developing Early Number Sense 8 March 2011. Number Sense. Having a good intuition about numbers and their relationships. Develops gradually as a result of exploring numbers, visualising numbers, forming relationships Grows more complex as children learn more.

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Junior focus group developing early number sense 8 march 2011

Junior Focus Group

Developing Early Number Sense

8 March 2011

Number sense
Number Sense

  • Having a good intuition about numbers and their relationships.

  • Develops gradually as a result of exploring numbers, visualising numbers, forming relationships

  • Grows more complex as children learn more.

Key mathematical ideas
Key Mathematical Ideas

Early number sense

  • Counting tells how many are in a set. Ordinality leads to Cardinality

  • Numbers are related to each other through a variety of number relationships more than, less than, connection to ten

  • Number concepts are intimately tied to the world around us. Application to real settings marks the beginning of making mathematical sense of the world.

    Van de Walle , Karp & Williams

    Elementary & Middle School Mathematics: Teaching Developmentally

    Allyn & Bacon 2010

Early number sense develops when
Early number sense develops when


  • make connections

  • Are able to instantly recognise patterns

  • See relationships related to more, less, after, before,

  • Are able to anchor numbers to five and ten

Tens frames
Tens Frames

  • Crazy Mixed up Numbers – Read the activity page 46

  • A diagnostic task – give your children a blank piece of paper and ask them to draw a tens frame and show a number on it

  • In groups – discuss useful activities for tens frames for children at your level


  • The ability to recognise and name small quantities without counting – links directly to cardinality

  • Use dot cards, dot plates, tens frames, slavonic abacus to provide opportunities every day for children to practise

Dot plates
Dot Plates

  • Hold up a dot plate for 2-3 seconds, ask “How many? How did you see it?

  • Discuss other uses for dot plates – share and record.

  • More, less, same

Counting principles
Counting Principles

Gelman and Gallistel (1978) argue there are five

basic counting principles:

  • One-to-one correspondence – each item is labeled with one number name

  • Stable order – ordinality – objects to be counted are ordered in the same sequence

  • Cardinality – the last number name tells you how many

  • Abstraction – objects of any kind can be counted

  • Order irrelevance – objects can be counted in any order provided that ordinality and one-to-one adhered to

    Counting is a multifaceted skill – needs to be given time

    and attention!

The counting sequence
The counting sequence

  • Learning the counting sequence is essential and will precede what counting one to one achieves.

  • It is a rote process that is needed to lighten mental load.

  • Knowing the word sequence pattern comes before understanding why the pattern occurs.

Counting one to one
Counting one to one

  • A critical piece of understanding is that ordinality – position in a sequence – is intimately linked to cardinality – the number in a set.

  • In order to make the crucial linkage children need to be able to:

    • Say the number words in the right order starting at one

    • Point at objects one-by-one

    • Co-ordinate saying the correct words with identifying the objects one-by-one

  • Need to spend time on this, do not expect it will happen quickly

Counting from ten to twenty
Counting from ten to twenty

  • In English the number words from ten to twenty have no regular pattern from a child’s point of view.

  • Learning to count from ten to twenty there is a heavier load:

    • Eleven bears no relationship to ten and one

    • Twelve is not linked to ten and two

    • Thirteen is not decoded by knowing “thir” means three and “teen” means ten

    • Fourteen is not decoded by it means four and ten, which logically should be ten and four

  • Learning to count from one to nineteen is a rote process

Counting to a hundred
Counting to a hundred

  • The next number after nineteen is twenty

  • It’s difficult for children to understand that “twen” means two and “ty” means tens.

  • Then the numbers follow the rote by ones count – to twenty-nine…

  • Understanding the meaning of thirty, not twenty-ten, is a place value issue.

  • Therefore counting to one hundred needs to be rote first and place value understanding must be given time to develop.

Counting on
Counting on

  • Counting on is useful to solve addition problems. But it is complex. To do 19 + 4 children need to:

    • Start the count at 20, not 19

    • Say the next four numbers after nineteen and then stop

    • Understand the last number they say is the answer.

    • Have a reliable way to check four numbers have been said

  • Place Value is the critical understanding here.

What do we need to do with counting
What do we need to do with counting?

  • Talk with children about the counting process.

  • Help them to make links with one more and one less.

  • Connect number words with objects

  • Make sets and count, reorganise the same set, do we need to count.

  • Watch how children operate – it tells us a lot about what they know.

A thought to leave you with
A thought to leave you with

…listen to children’s mathematical explanations rather than listen for particular responses.

Fiona Walls

in Handling Number


Teaching Primary School Mathematics and Statistics

Evidence-based Practice

Averill & Harvey (Eds)

NZCER 2010


  • Other strand information – NZC/National Standards link.

  • Key Mathematical Ideas