1. NSW Curriculum and Learning Innovation Centre Exploring Early Arithmetical Strategies (EAS) Building capacity with the new syllabuses

2. NSW Curriculum and Learning Innovation Centre Early Arithmetical Strategies (EAS) Early Arithmetical Strategies (EAS) refers to the range of counting strategies that are used to solve addition and subtraction problems. Arithmetical learning develops through two complementary processes, counting and grouping. The transition from count-by-one strategies to grouping strategies underpins the structure of the Early Arithmetical Strategies (EAS) framework.

3. NSW Curriculum and Learning Innovation Centre The Early Arithmetical Strategies (EAS) Stages Emergent Perceptual Figurative Counting- on-and- back EAS Stages describing count-by- one strategies Facile (Flexible) EAS Stage describing grouping strategies

4. NSW Curriculum and Learning Innovation Centre Emergent counting Stage description VideosSyllabus outcomes Key ideas in the syllabus Sample related content The student cannot count visible items. The student either does not know the number words or cannot correctly coordinate number words with items when counting. These videos show students attempting a counting task. Click on an image to view the video Working towards: MAe-4NA Counts to 30, and orders, reads and represents numbers in the range 0 to 20 Working towards: MAe-5NA Combines, separates and compares collections of objects, describes using everyday language, and records using informal methods Working towards: Count forwards to 30 and backwards from a number in the range 0 to 20 Compare, order, read and represent numbers to 10, then 20 Combine two groups of objects to model addition Take part of a group away to model subtraction Connect number names, numerals and quantities to 10 Recognise numbers in a variety of contexts Compare order and make collections to 10 then to 20 Recognise dice and domino patterns

5. NSW Curriculum and Learning Innovation Centre Perceptual counting Stage description VideosSyllabus outcomes Key ideas in the syllabus Sample related content The student is able to count visible items. The student builds numbers by using materials or fingers to represent each number when solving addition and subtraction questions. The materials must always be present during the counting. These videos show students using a perceptual counting strategy. Click on an image to view the video MAe-5NA Combines, separates and compares collections of objects, describes using everyday language, and records using informal methods Combine two or more groups to model addition Take part of a group away to model subtraction Compare two groups to determine ‘how many more’ Record addition and subtraction informally Use concrete materials or fingers to model and solve simple addition and subtraction problems Use visual representations of numbers, e.g. ten frames, to solve addition and subtraction problems Create and recognise combinations of numbers to at least 10

6. NSW Curriculum and Learning Innovation Centre Figurative counting Stage description VideosSyllabus outcomes Key ideas in the syllabus Sample related content The student is able to count concealed items by visualising the items but always starts counting from “one”. The student may sub-vocalise when counting. These videos show students mentally solving an addition question using a figurative counting strategy. Click on an image to view the video MA1-5NA Uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers Use and record a range of mental strategies for addition and subtraction of one- and two- digit numbers Solve word problems involving addition and subtraction Create, record and recognise combinations for numbers from 11 up to and including 20 Model and record number patterns for individual numbers Use the terms add, plus, equals, is equal to, take away, minus and the difference between

7. NSW Curriculum and Learning Innovation Centre Counting-on-and-back Stage description VideosSyllabus outcomes Key ideas in the syllabus Sample related content The student counts-on or counts-back from one of the numbers rather than counting from “one” to solve addition and subtraction problems. The student understands that one of the numbers takes the place of a completed count. This video shows a student counting on to solve addition questions. Click on the image to view the video MA1-5NA Uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers Use and record a range of mental strategies for addition and subtraction of one- and two- digit numbers Solve word problems involving addition and subtraction Make connections between addition and subtraction Use a range of mental strategies to solve addition and subtraction problems involving one- and two-digit numbers including: -counting-on from the larger number to find the total of two numbers -counting-back from a number to find the number remaining -counting-on or counting-back to find the difference between two numbers.

8. NSW Curriculum and Learning Innovation Centre Facile (flexible) number knowledge Stage description VideosSyllabus outcomes Key ideas in the syllabus Sample related content The student uses known facts, number structure and other grouping strategies to solve addition and subtraction problems. This video shows a student using a facile counting strategy. Click on the image to view the video MA1-5NA Uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers MA2-5NA Uses mental and written strategies for addition and subtraction involving two-, three- and four- digit numbers Recognise and recall number combinations that add to numbers up to 20. Model and apply the commutative property and associative property for addition. Use the inverse operation to check addition and subtraction calculations. Use and record a range of mental strategies for addition and subtraction of one-, two-, three- and four- digit numbers. Use a range of mental strategies to solve addition and subtraction problems including: -using doubles or near doubles -combining numbers that add to 10 -bridging to 10 -partitioning numbers to at least 20.

9. NSW Curriculum and Learning Innovation Centre Where to next? Consider assessing each student to determine where he or she is on the Early Arithmetical Strategies aspect. Look at the associated syllabus outcomes as indicated on the numeracy continuum. The syllabus content associated with each outcome will help you to plan a teaching program aimed at progressing each student to the next level along the continuum. Consider Look Plan