# National Numeracy Learning Progression

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This sub-element describes how a student becomes increasingly able to choose and use additive computational strategies for different purposes. The transition from counting by one to more flexible methods of dealing with quantity, where numbers are treated as the sums of their parts, is a critical hurdle to be addressed in students becoming fluent users of number. Rather than only focusing on the speed of producing correct answers, an emphasis on attending to the relation of given numbers to sums and differences is needed for flexibility. This supports the development of additive strategies such as adding the same to both numbers to reach an easier calculation (47 – 38 = 49 – 40).

The capacity to make reasonable adjustments to numbers is essential in estimating. Estimating is not a basic skill as it requires students to be able to conceptualise and mentally manipulate numbers. The estimation process involves selecting numbers to simplify mental manipulation.

Additive strategies apply equally to subtraction, as can be seen in ‘Giving change’ in the Understanding money sub-element.

Some students will communicate using augmentative and alternative communication strategies to demonstrate their numeracy skills. This may include digital technologies, sign language, braille, real objects, photographs and pictographs.

Each sub-element level has been identified by upper-case initials and in some cases lower-case letters of the sub-element name followed by ascending numbers. The abbreviation for this sub-element is AdS. The listing of indicators within each level is non-hierarchical. Subheadings have been included to group related indicators. Where appropriate, examples have been provided in brackets following an indicator.

Emergent strategies

• combines two groups of objects and attempts to find the total
• compares two quantities of up to 10 and states which group has more

Perceptual strategies

• counts items that can be perceived by ones to find the total of two groups with one-to-one matching of number words and objects
• builds and subtracts numbers by using objects or fingers
• makes combinations to form numbers up to 10

Figurative (imagined units)

• solves additive tasks involving two concealed collections of items by visualising, counting from one to determine the total

Counting on (by ones)

• treats a number word as a completed count when solving problems (‘I have 7 apples. I want 10. How many more do I need?’ Treats the 7 as a completed count)
• uses a strategy of count-up-from to calculate addition (to find 6 + 3, responds 6, 7, 8, 9. It's 9)
• uses a strategy of count-up-to to solve missing addends tasks (to solve 6 + ? = 9, responds 6 ... 7, 8, 9. It's 3)

Counting back (by ones)

• uses count-down-from for subtraction tasks (9 – 3 = ?, 9 ... 8, 7, 6. It equals 6)
• uses count-down-to to calculate (9 take away something equals 6, responds 9 ... 8, 7, 6 ... It's 3)
• finds the difference between two numbers less than 20
• counts back to find the difference between two quantities where the difference is no greater than 4

Flexible strategies with combinations to 10

• uses a range of non–count-by-one strategies when adding or subtracting two or more numbers (bridging to 10, near doubles)
• uses part-whole construction of number to partition a whole number into parts (partitions 7 into 5 and 2, 6 and 1, 4 and 3)
• applies inverse relationship of addition and subtraction

Flexible strategies with two-digit numbers

• applies knowledge of 10 as a unit to add and subtract 2 two-digit numbers (jump strategy, split strategy or compensation)
• manipulates tens and ones flexibly for addition and subtraction (to add 45 and 37, adds the tens on 45 … 55, 65, 75, then partitions the 7 into 5 and 2, adds the 5 to make 80 and 2 more to make 82)
• uses part-whole knowledge of numbers to 20 to calculate two-digit addition and subtraction (when finding 53 – 27, recognises the subtraction within as 13 – 7 and regroups the 53 into 40 and 13 and the 27 into 20 and 7)