# National Numeracy Learning Progression

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## Number patterns and algebraic thinking description

Figuring out how a pattern works brings predictability and allows the making of generalisations. This sub-element describes how a student becomes increasingly able to identify a pattern as something that is a discernible regularity in a group of numbers or shapes. As students become increasingly able to connect patterns with the structure of numbers, they create a foundation for algebraic thinking (that is, thinking about generalised quantities). For example number patterns are evident in house numbers on opposite sides of streets. Algebra enables the ‘generalisation’ of patterns from one situation to another.

Algebraic thinking is also used to capture the relationship between quantities such as F=ma or force equals mass multiplied by acceleration.

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 of the sub-element name followed by ascending numbers. The abbreviation for this sub-element is NPA. 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.

### NPA1

Identifying patterns

• recognises simple patterns in everyday contexts
• copies simple patterns

### NPA2

Identifying and creating patterns

• identifies standard patterns (dice or domino) without counting individual items
• creates repeating patterns with numbers and shapes (circle, square, circle, square or 1,2,3   1,2,3   1,2,3)

### NPA3

Identifying repeating patterns

• identifies the pattern unit within a simple repeating pattern (continues a simple pattern)
• identifies standard patterns up to 10 (patterns in ten frames, finger patterns, playing cards)
• finds the missing element in a pattern involving shapes or objects

### NPA4

Continuing number patterns

• continues patterns where the difference between each term is the same number
(2, 4, 6, 8, 10 …)
• describes rules for continuing patterns where the difference between each term is the same number (to find the next number in the pattern 3, 6, 9, 12 … you add 3)
• sequences numbers to identify a pattern or rule

Introducing number sentences

• recognises the equals sign as meaning ‘is equivalent to’ or ‘is the same as’ not just ‘makes’ (recognises that 5 + 3 = 6 + 2)
• finds missing values in a number sentence (5 + ? = 6 + 2)

### NPA5

Generalising patterns

• identifies elements, including missing elements, in a one-operation number pattern

Number sentences

• uses equivalent number sentences involving addition or subtraction to find an unknown (527 + 96 = ? is the same as 527 + 100 – 4 = ?)
• applies knowledge of factors associated with the row and column structure of arrays to explain the commutative property of multiplication (3 x 4 = 4 x 3)

### NPA6

Generalising patterns

• identifies a single operation rule in numerical patterns and records it as a numerical expression (2, 4, 6, 8, 10 … is n + 2, or 2, 6, 18, 54 … is 3n)
• predicts a higher term of a pattern using the pattern’s rule

Number properties

• creates and interprets number sentences demonstrating the inverse relationship between multiplication and division
• balances number sentences involving one or more operations following conventions of order of operations (5 x 2 + 4 = 4 x 2 + ?, 5 + 2 x 3 = 11)
• recognises that any number multiplied by 0 equals 0 which means that one of the factors is 0 (3 x ? = 0)

### NPA7

Representing unknowns

• uses words or symbols (including letters) to express relationships involving unknown values
• finds the value of formulae or algebraic expressions by substituting
• creates algebraic expressions from word problems involving one operation

### NPA8

Algebraic expressions

• creates and identifies algebraic expressions from word problems involving two operations and one unknown
• recognises equivalent algebraic expressions

### NPA9

Algebraic relationships

• interprets and uses formulae and algebraic representations that describe relationships in various contexts (Body Mass Index – BMI)
• creates an algebraic expression in two unknowns to represent a formula or relationship (Anna has 6 times as many stickers as Carol)