Week Seven: Pre-algebra, early algebra, patterns to develop algebraic thinking

Big Ideas	Algebra starts in the foundation year as Samuel Johnson in 1700’s stated back then that students need to learn algebraic thinking to prevent cluttered thinking. Having prior knowledge of pre-algebra is fundamental for students in higher years of education as learning to recognise patterns and coming to an understanding concepts of variable and function as they outline the elements of algebra and patterning.   Beginning algebra processes involve and lead to more sophisticated: •          Patterns involving geometry or geometrical shapes; •          Patterns involving numbers; and •          Other areas of mathematics such as Algebra which is simply the abstract level of number reasoning. Concepts related to algebra: Patterns & Functions Equivalence and equations Patterns, sequences and generalisations Skills applying to geometry and number patterns: (Reys,2012) Recognizing the pattern (What’s happening?) Describing the pattern (What’s repeating?) Repeating or copying the pattern (need to be able to see the relationships to do this) Growing or extending or continuing the pattern Replacing missing elements of the pattern Translating the pattern Determining Relationships of  numbers: The key to finding a number pattern in a linear sequence is to look for a relationship b                                                 1, 3, 5, 7 …                                                 5, 10, 15, 20…                                                 1, 4, 9, 16 …                                                 1, 3, 6, 10, 15…                                                 1, 2, 4, 7, 11, 16… But to find the nth number in a sequence, you need to find the relationship between the Step number and the number! Tessellations: Shapes that fit together with no gaps
Demonstrate concept skills and strategies	Concept: algebra is a statement of a relationship, it’s an abstraction of number understanding.         2+3=5 is an addition number is an number understanding 2+_=5 a simplistic form of algebra         Algebraic equation is statement of that relationship Skills: able to find the missing element, to grow a pattern, to make a pattern, to be able to state the relationship between the elements of a pattern. Thinking strategies:
Demonstrate Language model
Demonstrate/ describe teaching strategies	Learning algebra starts in foundation and extends throughout school, teaching strategies need to be fun and not scare students algebra. Such as the link before starts students off recognising the pattern and sorting out differencing elements of the shapes and seeing the relationship http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/SSCongruentSimilar.swf (2016).
Describe misconception	The equals sign is not about here comes the answer, equals describes a point of balance. Using scales in the classroom, digital scales game or worksheet that has a picture of scales demonstrates and demonstrates that equals means point of balance.  http://www.mathplayground.com/AlgebraScales_Main.swf
ACARA	Mathematics / Foundation Year / Number and Algebra / Patterns and algebra / ACMNA005 Content Description Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings Elaborations ·         observing natural patterns in the world around us ·         creating and describing patterns using materials, sounds, movements or drawings (Australian Curriculum and Assessment Reporting Authority [ACARA], 2014)
Resources and ideas	Gives students personal experience playing with tessellations and how didn’t shapes that are not common can tessellation can tessellate. http://www.mathcats.com/explore/tessellations/tesspeople.html
Concise synthesis textbook	In the Australian Curriculum in strand of number and algebra students in primary and early years are to recognise patterns and understand concepts of variable and function  (ACARA, 2014).  Algebra in primary school can be seen in Primary school mathematics essential parts consist of problems, patterns and relations. Building algebraic concepts and thinking stems from the relation of: properties of numbers and functions and equality relation (Reys,2012).
References	Australian Curriculum and Assessment Reporting Authority. (2014). Foundation to Year 10 Curriculum: Language, Language for Interaction (ACELA1428). Retrieved from http://www.australiancurriculum.edu.au/english/Curriculum/F10?y=F&y=7&y=8&y=9&y=10&s=LA&s=LT&s=LY&layout=1           (2016). Sheppardsoftware.com. Retrieved 29 May 2016, from http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/SSCongruentSimilar.swf          Model Algebra. Mathplayground.com. Retrieved 29 May 2016, from http://www.mathplayground.com/AlgebraScales_Main.swf          Reys, R. (2012). Helping students learn mathematics (pp. 139-163). Milton, QLD: WILEY. Tess people in Math Cats' Tessellation Town!. (2016). Mathcats.com. Retrieved 29 May 2016, from http://www.mathcats.com/explore/tessellations/tesspeople.html