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Talking about patterns and algebra

Early Stage 1 to Stage 3 TalkingaboutPatterns & Algebra581 Contents Overview 3 Early Stage 1 6 Stage 1 33 Stage 2 70 Stage 3 107 Enrichment 136 Glossary 154 324 State of New South Wales through the NSW Department of Education and Training, 2010 2 & AlgebraTalkingaboutPatternsAcknowledgeme nts Board of Studies, NSW, for permission to include the outcomes from the Mathematics K 6 syllabus (2002). State of NSW, Department of Education and Training Curriculum K 12 Directorate, 2010. Downloading, copying or printing or materials in this document for personal use or on behalf of another person is permitted. Downloading, copying or printing of material from this document for the purpose of reproduction or publication (in whole or in part) for financial benefit is not permitted without express authorisation. State of New South Wales through the NSW Department of Education and Training, 2010 3 & AlgebraTalkingaboutPatterns Overview ThePatterns and Algebrastrand emphasises two components, Number patterns and Number relationships.

facts for ones, twos, ives and tens. Using the terms ‘more than’ and ‘less than’ to describe inequality. Applying collection-based methods, including the commutative ... students can place counters. In this way, students can be involved in discussing patterns, describing them, identifying

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Transcription of Talking about patterns and algebra

1 Early Stage 1 to Stage 3 TalkingaboutPatterns & Algebra581 Contents Overview 3 Early Stage 1 6 Stage 1 33 Stage 2 70 Stage 3 107 Enrichment 136 Glossary 154 324 State of New South Wales through the NSW Department of Education and Training, 2010 2 & AlgebraTalkingaboutPatternsAcknowledgeme nts Board of Studies, NSW, for permission to include the outcomes from the Mathematics K 6 syllabus (2002). State of NSW, Department of Education and Training Curriculum K 12 Directorate, 2010. Downloading, copying or printing or materials in this document for personal use or on behalf of another person is permitted. Downloading, copying or printing of material from this document for the purpose of reproduction or publication (in whole or in part) for financial benefit is not permitted without express authorisation. State of New South Wales through the NSW Department of Education and Training, 2010 3 & AlgebraTalkingaboutPatterns Overview ThePatterns and Algebrastrand emphasises two components, Number patterns and Number relationships.

2 Each of these components includes three aspects which show a progression from Early Stage One to Stage Four. While these aspects are shown separately, it is not suggested that each one should be taught in isolation. Learning about number patterns involves students in: creating and continuing number patterns describing, discussing and labelling patterns finding specific terms of a about number relationships involves students in: using symbols and operations to show equality andinequality applying collection-based methods to generalise working out unknown elements to complete section provides an overview of the distinctive learning and key concepts within the patterns and algebra strand for each stage. It does not describe the full scope of learning for each stage. Particular attention has been given to emphasising the links between the patterns and algebra and the Number strands.

3 State of New South Wales through the NSW Department of Education and Training, 2010 4 & AlgebraTalkingaboutPatternsFocus: Number patterns Creating number patterns Describing number patterns Finding terms in a number pattern ES1 Creating patternsusing shapes, objects numberpatterns that increaseor decrease. Describing a patternmade of shapes, objectsor pictures in terms ofdistinguishing featuresand of the number of repeating elements. Finding the next termin a number patternthat increases or decreases. S1 Creating patternsusing whole numbersthat increase or decrease. Describing a patterninvolving wholenumbers. Determining a missingelement within an additive pattern. S2 Creating additivepatterns using wholenumbers, fractions and decimals. Describing a patterninvolving wholenumbers, fractions or decimals. Continuing a patternto determine a higheror a lower term when given some consecutiveelements.

4 S3 Creating patternsof multiples usingwhole numbers and bymultiplying or dividingdecimals by single digitnumbers, 10, 100 or 1000. Completing a tableof values for patternsinvolving oneoperation. Describing a pattern inmore than one way. Determining a rule todescribe a pattern andusing it to derive thevalue of a higher term. S4 Completing a tableof values for patternsinvolving more thanone operation. Creating an algebraicequation that describes a pattern. Using an algebraicexpression thatdescribes a pattern tocalculate an element. State of New South Wales through the NSW Department of Education and Training, 2010 5 & AlgebraTalkingaboutPatterns Focus: Number relationships Describing number relationships Generalising about number relationships Finding unknown elements ES1 Using the term is thesame as to unequal groups. Comparing groupsto generalise aboutnumbers.

5 Forming groups thathave the same number of elements. S1 Using the equals sign to mean is the same as . Building all additionfacts to 20. Building multiplicationfacts for ones , twos, fives and tens. Using the terms morethan and less than to describe inequality. Applying collection-based methods, including thecommutative property of additionand multiplicationto generalise aboutnumber relationshipswithin Stage One content. Completing numbersentences involving oneoperation within StageOne content. S2 Building allmultiplication facts to10 10. Using symbols to showinequality. Applying collection-based methods, including theassociative propertyof addition and multiplication togeneralise aboutnumber relationshipswithin Stage Two content. Completing numbersentences involving oneoperation within StageTwo content. S3 Describing numberrelationships usingnumber sentences involving more thanone operation.

6 Applying collection-based methods to solve number sentences that do not have a whole number solution. Completing numbersentences that involve more than one operation, fractionsand decimals. S4 Simplifying, expanding, factorising andcomparing algebraicexpressions. Translating betweenwords and linearrelationships createdfrom simple numberpatterns and equations. Solving algebraicequations. & AlgebraTalkingaboutPatterns State of New South Wales through the NSW Department of Education and Training, 2010 6 81 TalkingaboutPatterns& algebra Early Stage 1 5324 Early Stage 1 & AlgebraTalkingaboutPatterns State of New South Wales through the NSW Department of Education and Training, 2010 7 Overview of Early Stage 1 content Recognises, describes, creates and continues repeating patterns and number patterns that increase or decrease. To recognise a pattern, students have to understand what a pattern is, so this is an important early focus.

7 When young children splash blobs of paint on paper and an adult asks what it is, they sometimes reply, It s just a pattern. But is this what we mean in mathematics? There needs to be an explicit focus on the meaning of pattern in mathematics. Toss a few counters of different colours on the floor and ask the students to discuss if you have made a pattern. Then arrange some counters in a pattern (say, a row of three blue, and under them a row of three yellow, then under them a row of three blue, and another row of three yellow) and ask, Is this a pattern? Ask the students what the difference is between the two groups of counters. In terms of patterns and algebra , we are Talking about repeating patterns , and students need to have a clear understanding of this. We can provide some materials that assist in creating patterns , such as a long pegboard with one row of holes, or a strip of card with a row of circles on which students can place counters.

8 In this way, students can be involved in discussing patterns , describing them, identifying the repeating components of patterns and suggesting number labels for patterns . Frequently return to the question, Is this a pattern? to generate discussion. Early Stage 1 & AlgebraTalkingaboutPatterns State of New South Wales through the NSW Department of Education and Training, 2010 8 It is important to model the words repeat, repeated and repeating. For example, have a child use counters to make a three pattern and ask, What parts would you repeat to continue the pattern? Also at this stage, students will develop an understanding of the concept of equality, and learn to form and compare groups to generalise about number. Early Stage 1 & AlgebraTalkingaboutPatterns State of New South Wales through the NSW Department of Education and Training, 2010 9 patterns and algebra - Early Stage 1 Simple patterns is a pattern?

9 11 is a pattern? - BLM 12 and action patterns 13 and action pattern representations15 5. patterns with objects, shapes and pictures16 6. Drawing patterns17 7. Identifying a repeating component of apattern18 8. People patterns19 Naming patterns patterns 20 Number patterns that increase or decrease numbers 22 backwards by sock numbers23 of socks - BLM 24 card counting 25 counting 26 patterns that increase 27 sequences 28 patterns that decrease 29 Early Stage 1 & AlgebraTalkingaboutPatterns State of New South Wales through the NSW Department of Education and Training, 2010 10 Equality equality30 posing31 groups32 Early Stage 1 & AlgebraTalkingaboutPatterns State of New South Wales through the NSW Department of Education and Training, 2010 11 Simple patterns What is a pattern? Key idea Recognise, describe, create and continue repeating patterns Materials Three photocopies of BLM What is a pattern?

10 Cut to make six cards (p. 12) Show the students one of the cards. Ask, Is this a pattern? Allow the students to discuss their ideas, and lead them to understand that this, by itself, is not a pattern. Next, line up the six cards. Ask, Is this a pattern? Lead the students in a discussion to understand that this is a pattern because there is a repeating element. Early Stage 1 & AlgebraTalkingaboutPatterns State of New South Wales through the NSW Department of Education and Training, 2010 12 What is a pattern? BLM -Early Stage 1 & AlgebraTalkingaboutPatterns State of New South Wales through the NSW Department of Education and Training, 2010 13 Sound and action patterns Key idea Recognise, describe, create and continue repeating patterns Materials None Create patterns using a sequence of different sounds or actions, such as: clap, clap, stamp, stamp, clap, clap, stamp, stamp.


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