Early Years Learning in Mathematics Pattern Number and Geometry
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Connect with Maths Early Years Learning in Mathematics: Pattern, Number and Geometry presentation helps students to build knowledge and make connections between number and pattern in the early years
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Early Years Learning in Mathematics Pattern Number and Geometry
- 1. Implementing the Australian Curriculum Part 2 Sharyn Livy: slivy@mav.vic.edu.au Sharyn Liv slivy@mav.vic.edu.au Number and Algebra - making connections Sandy Treloar sftreloar@gmail.com
- 2. Overview Australian Curriculum Pattern hunt Making and describing patterns Interactive patterns Questions
- 3. Australian Curriculum • Content strands – Number and algebra – Statistics and probability – Measurement and geometry • Proficiency strands – Understanding – Fluency – Reasoning – Problem solving
- 4. Understanding Students: • build a robust knowledge of adaptable and transferable mathematical concepts • make connections between related concepts and progressively apply the familiar to develop new ideas • develop an understanding of the relationship between the ‘why’ and the ‘how’ of mathematics • build understanding when they: connect related ideas; represent concepts in different ways; identify commonalities and differences between aspects of content; describe their thinking mathematically; and interpret mathematical information.
- 5. Early Years Pattern Foundation: Copy, continue and create patterns with objects and drawings (ACMNA005) Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA016) Year 2: Describe patterns with numbers and identify missing elements (ACMNA035) https://www.scootle.edu.au/ec/resolve/view/M015929?accContentId=ACMNA005
- 6. Patterns • We are going on a pattern hunt • Where might we find patterns?
- 7. Patterns
- 8. Foundation students’ brainstorm of their experience of pattern.
- 9. Patterns • Checkerboards • Buildings • Skip counting • Block building • Decorative patterns • Music patterns • Action patterns • Chants and rhymes • Tessellations • Arrays
- 15. Shapes associated with sounds and actions • The concept came from Monster Choir Making Patterns http://www.scootle.edu.au/ec/viewing/L1056/index.html
- 17. Making patterns • Using the coloured counters make a pattern • Share and describe your patterns • Creating, describing, analysing patterns • Describing patterns • Extending patterns http://www.nctm.org/standards/content.aspx?id=24462 http://www.nctm.org/standards/content.aspx?id=33186
- 20. Describing Pattern Repeating patterns Growing patterns
- 22. ALGEBRA, PATTERN & STRUCTURE involves - • Visualising • Representing and • Organising mathematical thinking Tens frame4 & square 3 & triangle One third
- 23. Tessellations and growing patterns http://topdrawer.aamt.edu.au/Patterns/Misun derstandings/Tessellations/Growing- patterns-can-tessellate Visit Teachers Top Drawer for my ideas on teaching pattern www. http://topdrawer.aamt.edu.au/Patterns
- 24. Credits • Thanks to the students from Deer Park North Primary school for sharing their patterns • Websites www.topdrawer.aamt.edu.au www.nctm.org http://www.scootle.edu.au
Editor's Notes
- Introduce each other! Sandy- Sharyn has worked as a Mathematics educational consultant with the Mathematical Association of Victoria and is currently teaching pre-service teachers at Victoria University.Sharyn - Sandy has worked as school based mathematics coach and continues to support primary teachers in their classrooms. Sharyn -Introduce presentation.Sandy - As we make our way through our presentation, we would welcome your comments and questions
- Sharyn - Helping students to build knowledge and make connections between number and pattern in the early years.
- Sharyn -The Australian Curriculum: Mathematics Foundation to Year 10: - provides the skills for students to be confident, creative users and communicators of mathematicsenables students to investigate, represent and interpret situations both at school and in their lives out of schoolfocuses on developing increasingly sophisticated and refined mathematical understanding, fluency, logical reasoning, analytical thought and problem solving.Proficiencies describe the actions in which students can engage whilst learning the content and are incorporated into the content descriptions. Introductory year level statements are included at the beginning of each year level to accentuate where the proficiencies are evident in the content descriptions.
- Sharyn - summary of slideSandy – Ideally we will also be making connections with aspects of the children’sworld through the use of story, real life examplesand stimulus materials.
- Sandy - The Australian Curriculum content descriptors are outlined on this slide. Before students can copy, continue or create patterns, they need to know what pattern is. You can draw on student’s prior knowledge through class discussion to begin to define the word ‘pattern’. There is also a video describing and demonstrating pattern available on Scootle. Asking students to describe their patterns is a good precursor for number work that follows in later years.
- Sharyn _Ask everyone to to comment about what answers they might predict from a group of Foundation or younger students.
- Sandy -These were some ideas presented by a Foundation class before they embarked on a pattern hunt. They also worked on a definition of the word ‘pattern’.
- Sharyn - Other students may come up with more ideas.
- Sandy – These students went outside to explore and discover patterns in their environment.By taking photos a record can be made so that students can later sort, describe and share the patterns they have found.They also act as a stimulus for when students begin to create their own patterns.
- Sharyn - Students asked to make their own patterns using a choice of materials.Sandy –What questions might you ask of students to describe the attributes of their pattern and assess understandings? What colour is the 5th animal?......
- How might students describe this pattern? Are connections being made to other strands or sub-strands of mathematics?
- Sandy –After working with the interactive program Monster Choir Making Patterns, students created shape patterns that were associated with sounds or actions.
- Sandy -These two Foundation students performed elephant and rhino sounds and actions as they moved along the pattern.
- Sharyn -Make patterns with this link horizontal – diagonal – the tenth pattern is green use three colours
- Sharyn - Talk about importance of making then recording
- Sharyn-Many students experience difficulties with algebraic thinking. Some of these difficulties stem from students’ lack of understanding of the structure of arithmetic.Classroom experiences need to involve experiences that assist students to generalise the structure of arithmetic, a change in focus from procedural to conceptual understanding.
- Repeated pattern: copy the pattern, create your own pattern and extend patterns.Growing patterns are patterns in which each section experiences growth
- Two links here number pattern and making patternsIf I have to repeat 2 repeated patterns what is the ratio of yellow to read?Add the digits that make each number. What pattern do you see?How can you check if a number is divisible by 3Extend this thinking to find the rule for checking if a number is divisible by 9If we change the width of our board to 5 rather than 10, which numbers will make diagonal patterns?How are the column patterns and diagonal patterns related to the width of the board?Draw a ratio table: 2:1 4:2 6:3Ratio is repeated pattern