# Targeting Early Numeracy

### A quality teaching process

## A bit about TEN...

- Originally a targeted intervention program
- Was shaped into a whole class quality teaching process in numeracy
- Grew out of the Best Start Kindergarten Assessment program
- It is not an in-the-box program
- Useful data + regular monitoring = quality teaching and improvement

## Structure

## What have teachers noticed?

- It's what teachers already do - it helps us work as a team to refine and improve
- Teacher understanding has developed
- Assists familiarity with the new Mathematics syllabus
- Links between stages are more obvious
- Students can explain their thinking
- Students have a deeper understanding of mathematical strategies
- Professional dialogue/discussions
- Application in different roles, in different ways
- Transition strategies
- Awareness of progress and goal setting
- Students selecting learning partners/making responsible choices
- Strong willingness to participate
- Manageable with time
- Growing independence
- Influence in other KLAs
- Confidence, pride and success!

## Why have we seen improvements?

- Continuum
- Syllabus
- Dedicated meeting time (regular)
- Daily
- Consistent language and expectations
- Team planning
- Reflections
- Ongoing assessment and monitoring
- Flexible grouping
- Professional dialogue
- Working mathematically outcomes
- Strong purpose, learning intentions and success criteria
- Differentiation
- Same concept through a variety of resources

## What do we teach?

**EARLY STAGE 1**

__Whole Number__

**MAe-4NA** counts to 30, and orders, reads and represents numbers in the range 0 to 20

__Addition and Subtraction__

**MAe-5NA** combines, separates and compares collections of objects, describes using everyday language, and records using informal methods

NUMBER RELATIONSHIPS

· Describe the number before as 'one less than'

· Describe the number after as 'one more than' a given number

· Compare numbers and groups of objects eg. more than, less than, the same as

· Order numbers and groups of objects

· Use the term 'is the same as' to express equality of groups

· Compare two groups of objects to determine 'how many more' or ‘how many less’

· Read and use the ordinal names to at least 'tenth'

NUMBER SENSE

· Use 5 as a reference in forming numbers from 6 to 10, eg 'Six is one more than five'

· Use 10 as a reference in forming numbers from 11 to 20, eg 'Thirteen is 1 group of ten and 3 ones'

· Create and recognise combinations for numbers to at least 10, eg 'How many more make 10?'

· Reads and represents numbers in the range 0-20

· Read numbers to at least 20, including zero, and represent these using objects (such as fingers), pictures, words and numerals

· Recognise numbers in a variety of contexts eg. Charts, telephone, computer keyboard

SUBITISING

· Subitise small collections of objects displayed in **traditional** arrangements eg. dot patterns on dice or dominoes

· Subitise small collections of objects displayed in **random** arrangements instantly recognise (subitise) different arrangements for the same number, eg different representations of five

· Recognise that the way objects are arranged affects how easy it is to subitise

COUNTING

· Estimate the number of objects in a group of up to 20 objects, and count to check

· Count with one-to-one correspondence and

· Recognise that the last number name represents the total number in the collection when counting

· Count forwards to 30 from a given number

· Count backwards from a given number in the range 0 to 20

· Apply counting strategies to solve simple everyday problems and justify answers

OPERATIONS – ADDITION AND SUBTRACTION

· Describe the action of combining, separating and comparing using everyday language

· Use visual representations of numbers to assist with addition and subtraction, eg ten frames

· Record addition and subtraction informally using drawings, words and numerals

· Use concrete materials or fingers to model and solve simple addition and subtraction problems

· Combine two or more groups of objects to model addition

· Count forwards by ones to add

· Model subtraction by separating and taking away part of a group of objects

· Count backwards by ones to subtract

**STAGE 1**

__Whole Number __

**MA1-4NA** applies place value, informally, to count, order, read and represent two- and three-digit numbers

__Addition and Subtraction__

**MA1-5NA **uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers

- Number lines and charts
- Commutative properties (4+5=5+4, where = means ‘same as’)
- Addition and subtraction facts/number combinations up to 20
- Inverse operations (4+5=9 so 9-5=4 etc.)
- Doubles
- Near doubles
- Count on and back
- Partition/Split (37+45 = 30+40+7+5 = …)
- Bridge to tens (7+5 so 7+3=10 and 2 more)
- Jump strategy

## Strategies

## The quality teaching framework

## Emergent Counters

A student who is an emergent counter may have **some knowledge of numbers and counting** but **cannot correctly match the sequence of counting words with objects** where each object is allocated a number in turn, with the final number word corresponding to the total.

## Perceptual Counters

A student who is a perceptual counter can **count items that he or she can perceive** (see, hear or touch). A perceptual counter will demonstrate the **one-to-one** principle, generating terms in the sequence of number words as needed and matching one number word to one item, without skipping or double-counting items.

## Figurative Counters

The figurative counting stage is characterised by students using a figurative representation of numbers. That is, students reconstruct numbers relying on **imagined** or **figural** items. The students match the sequence of counting words to figural items rather than perceptual ones. **Counting from the number one** appears to be necessary for the student to give meaning to the numbers.

## Counting On and Back Counters

The counting-on-and-back stage involves students using the names of numbers as being equivalent to completed counts. That is, to find the total of six and three a student can take six as the result of a count that has already occurred and say: “Six, … seven, eight, nine, … nine!”. The essential feature of this strategy is that the student counts on from “six”. This way of counting on to find the total is sometimes described as **counting up from a number**. To successfully count up from a number the student needs a way of **keeping track **of the number of counts to **know when to stop**.

## Facile (or Flexible) Counters

The flexible or facile counting stage is characterised by using **number properties** combined with **number facts**. Typically, flexible strategies can be described as using ‘this’ to work out ‘that’. A student may determine that 7 + 6 is 13 because double 6 is 12 (or double 7 is 14) and 7 + 6 is 1 more (or 1 less than double 7). Flexible strategies make use of the properties of numbers** **and do not employ counting by ones.

## A LEARNING PLAN

## Let's have a go!

Consider the progression of strategies, the links between groups/concepts and connections between the syllabus and continuum to the task.