Patterns
Algebra
Embedded Files
Definition
Definition
A pattern is an arrangement of numbers, lines or shapes that follows a rule. A relationship is a particular kind of pattern that connects pairs of numbers, objects or measures according to some sort of rule. (Siemon et al., 2015)
Figuring out how a pattern works brings predictability and allows the making of generalisations. Students can become increasingly able to identify a pattern as something that is a discernible regularity in a group of numbers or shapes. As they are 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. (National Numeracy Learning Progression)
Teaching and learning activities
Teaching and learning activities
The resources below provide targeted teaching strategies to support student improvement in this skill.
Each downloadable lesson activity includes:
learning intentions
a list of required resources
a step-by-step lesson sequence
printable classroom materials
Select the download all icon to download all available activities or select each activity separately.
Understanding patternsIdentify and generate patterns using numbers, symbols and objects, as well as continue the patterns.
Creating patterns in the real worldUsing patterns to determine number of tables and chairs when organising an event.
Download all (ZIP)Download the resource pack containing all activities.
PLAN2 Areas of focus
PLAN2 Areas of focus
An Areas of focus template has been created in PLAN2 to support targeted teaching of Text structure in your learning area.
Search for the DoE template titled ‘DoE HSCMinStd Writing: Text structure’ in the Areas of focus template library tab within the Plan menu, and customise it for your students’ needs.
For more information about using PLAN2 Areas of focus templates with this resource, visit the Using this resource with PLAN2 page.
Relevance to the numeracy test marking
Relevance to the numeracy test marking
The feedback for a Level 3 performance in the HSC minimum standard online numeracy test states:
Individuals performing at this level typically select appropriate strategies from a variety of everyday mathematical processes in familiar and some less familiar contexts. They interpret and comprehend mathematical information in written material, diagrams, charts and tables.
Students are able to explain any simple relationship or pattern.
Connections with ACSF Level 3 descriptors
Connections with ACSF Level 3 descriptors
The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how simple relationships or patterns are assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.
Numeracy Indicator 3.09: Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts
Focus area: Explicitness of mathematical information
Level 3 performance features:
interprets and comprehends a range of everyday mathematical information that is embedded in familiar and routine texts
Numeracy Indicator 3.10: Selects from and uses a variety of developing mathematical and problem solving strategies in a range of familiar and some less familiar contexts
Focus area: Problem solving processes including estimating and reflecting
Level 3 performance features:
select appropriate methods of solution from a limited range of mathematical processes
Focus area: Mathematical methods and use of tools
Level 3 performance features:
uses a blend of personal ‘in-the-head’ methods and formal pen and paper methods to calculate and uses calculator/technological processes and tools to undertake the problem solving process
Numeracy Indicator 3.11: Uses a combination of both informal and formal oral and written mathematical language and representation to communicate mathematically
Focus area: Oral mathematical language
Level 3 performance features:
uses a combination of both informal and formal oral mathematical and general language to present and discuss the mathematical and problem solving process and result
Connections with Numeracy Learning Progression:
Connections with Numeracy Learning Progression:
The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to patterns are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.
Element: Number sense and algebra
Sub-element: Number patterns and algebraic thinking (NPA)
NPA2 — Identifying and creating patterns
NPA2 — Identifying and creating patterns
continues a pattern involving shapes or objects
determines a missing element within a pattern involving shapes or objects
NPA3 — Continuing and generalising patterns
NPA3 — Continuing and generalising patterns
represents growing patterns where the difference between each successive term is constant using concrete materials, then summarising the pattern numerically (e.g. constructs a pattern using concrete materials such as toothpicks, then summarises the number of toothpicks used as 4, 7, 10, 13 ...)
describes rules for continuing growing patterns where the difference between each successive term is the same (e.g. to determine the next number in the pattern 3, 6, 9, 12 … you add 3; for 20, 15, 10 … the rule is described as each term is generated by subtracting five from the previous term )
NPA5 — Generalising patterns
NPA5 — Generalising patterns
creates and interprets tables used to summarise patterns (e.g. the cost of hiring a bike based on the cost per hour)
identifies a single operation rule in numerical patterns and records it in words (e.g. European dress size = Australian dress size + 30)
relates the position number of shapes within a pattern to the rule for the sequence (e.g. number of counters = shape number + 2)
predicts a higher term of a pattern using the pattern’s rule
Page updated
Google Sites
Report abuse