Expected level of development
Australian Curriculum Mathematics V9: AC9M1A01, AC9M1A02
Numeracy Progression: Number patterns and algebraic thinking: P2&3, Counting processes: P6
At this level, students continue to appreciate and observe how patterns are present throughout mathematics. They recognise, continue and create patterns with shapes and objects as well as number patterns formed by skip-counting.
Students learn to interpret and generalise existing ‘repeating patterns’ created with materials, sounds, movements and drawings. They recognise the ‘unit of repeat’ – the core element of a pattern that repeats without change. For example, in the sequence ‘ABCDABCD’, ‘ABCD’ is the repeating unit.
Students also explore ‘growing patterns’ and understand that these have elements that increase or decrease in a consistent manner. Use visual representations to support this. Start by using blocks, or dots on tens frames, to model skip-counting patterns (e.g. 2, 4, 6, 8 … and 5, 10, 15, 20 …). Ensure regular opportunities for skip-counting practice, initially by twos, fives and tens. Practise in everyday contexts such as determining how much money by skip-counting collections of coins.
Play games from various cultures that involve number patterns and include a focus on the presence of patterns in artworks, craft, dance, music and songs.
Teaching and learning summary:
- Explore patterns with classroom talks, songs, rhymes, stories, sounds, number charts and physical materials.
- Foster curiosity about patterns and help students see them reflected in their world.
- recognise, continue and create repeating patterns
- identify the repeating unit/element and how many times it is repeated
- continue growing number patterns where the difference between each term is the same number
- describe the rule for a growing pattern.
Some students may:
- be unable to identify the repeating chunk in a pattern that has an incomplete third term in the pattern. For example, in the pattern ‘square-circle-square-square-circle-square’, they see the whole six parts as a chunk to repeat rather than identify ‘square-circle-square’ as the repeating unit. To address this, provide repeated opportunities to look for and circle the repeating unit. Model and scaffold how to do this.
- not yet grasp that skip-counting patterns are additive patterns. They may be able to skip-count fluently by twos, fives or tens starting from zero, but are unable to start from a multiple of the number without dropping back to zero. For example, when asked to count by fives starting from 15, they begin at zero.
- cannot yet skip-count from a non-multiple of the number. For example, when asked to start at 13 and count by twos students will say ‘I can’t’ or slip into a familiar sequence. They might say ‘13, 15, 17, 19, 20, 22 …’ The 2, 4, 6, 8 pattern of the even numbers is much more familiar than the odd numbers. To address this, ensure that students are confident counting to and from any multiple of the number before moving onto non-multiple starting points. Provide repeated opportunities to explore sequences on hundred charts and for oral counting with the various patterns.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
- We are exploring and learning about different patterns.
Why are we learning about this?
- Patterns are at the heart of mathematics. Understanding patterns supports other mathematical understandings.
What to do
- Notice and discuss repeating patterns in the way we live, for example, days of the week, months of the year, the seasons, or routines such as getting ready for school or setting the table.
- Explore patterns using rhythm. You could take turns creating a clapping pattern and then asking the other person to copy it.
- Draw, create and describe different repeating patterns, for example, triangle-square-circle-triangle-square-circle. Then use the pattern in a creative way, such as a border on a greeting card.
- Identify and explain visual patterns on clothing, wrapping paper, buildings, crockery, cards and furniture. Create a scrapbook to refer back to for ideas during arts and crafts.
- Collect objects to create patterns with, such as gumnuts, twigs, shells or container lids. Make and continue repeating patterns using your found items, for example, gumnut-twig-twig-gumnut-twig-twig, or red-blue-red-red-blue-red.
- Play games that involve recognising the patterns on dice and dominoes.
- Notice and enjoy patterns found in stories, poetry and songs. Listen to and/or create songs with growing number patterns, including skip-counting.
- identify and describe the ‘unit of repeat’ in a repeating pattern
- describe what happens in growing patterns, including skip-counting patterns
- continue different repeating and growing patterns.
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A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.Go to resource
Concrete, Representational, Abstract (CRA model)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.Go to resource
Culturally responsive pedagogy
Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.Go to resource
Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.Go to resource
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.Go to resource
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
Use these tasks to explore repeating and growing patterns.Go to resource
Use manipulatives to explore patterns through these kinaesthetic, visualisation and language-based activities.Go to resource
Multiplication and division
Use the tasks on pages 9 to 14 to explore skip-counting by 2s, 5s and 10s.Go to resource
Use visual representations to explore growing patterns and invite students to observe and make predictions.Go to resource
Once students are familiar with dominoes, use this challenge to recognise, describe and extend number sequences.Go to resource
Big steps in growing
Use these activities to investigate skip-counting by 10s in various contexts.Go to resource
Use this interactive to arrange train carriages according to numbers on their sides.Go to resource
Create counting patterns and play music with them by programming the keyboard which represents a number line.Go to resource
By the end of Year 1, students use numbers, symbols and objects to create skip-counting and repeating patterns, identifying the repeating unit.
Patterns and Algebra
Use the tasks ‘Number patterns that increase or decrease’ (pp. 22–29) to gauge student understanding.Go to resource
Mathematics Year 1: ACARA
Use work sample 1, Number: Skip counting and work sample 8 ‘Number: Growing patterns’ to learn what students know about key concepts.Go to resource