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

Week Six Number sense, numeration & mental computation, focusing on place value

Week Six Number sense, numeration & mental computation, focusing on place value
Big Ideas	Number Knowledge •           Formal ideas related to numeration and place value, and •          Informal ideas that we call number sense. Mental Computation: 1.       have open tasks; 2.       work with quantities NOT symbols e.g., 22+20 becomes: “double 2 tens and add 2 more 3.       use their own language; develop their own strategies, and Rely on the context for clues. The encouragement of mental computation and not always using the calculator is a main focus when introducing and using the calculator. However there is a time and a place for the calculator and teacher needs to work with the calculator as tool to further extend mathematics while encouraging individual thinking strategies. Number Place value and the importance of 0 and placement of numbers has high importance although this needs to stem off when students are competent in counting.
Demonstrate concept skills and strategies	The Concept of place value is where the number sits in the digit and where that number sits on the number line. The skills for working with place value help guide addition, subtraction, multiplication and division while being able to go up and down and expand the number on the number line. Thinking strategies for place value and addition is putting a number on the number line able to do addition on the place value by jumping up the number on the line.  Showing students clearly as well as reminding students the main points of place value such as the imagine below:
Demonstrate Language model	Children’s language Materials Language Maths Language Symbolic Language Materials Animals, counters, cars, bears, figurines, chickens, pegs, ect. Paddle pop sticks, counters, MABS MABS/ Place Value Chart/ Board MABS Place Value Chart/ Board Language Went away, disappear, more or less, add, addition ‘Can you show me 78 in MABS please?’ Subtract, equals, addition, taken away ‘How many had places has the number been moved?’ Recording No symbol, rudimental recording, children drawing drawings, rudimental recording children drawing, pictures only (including maths materials), record symbolically and show symbolically on number board
Demonstrate/ describe teaching strategies	Place value games are a very good resource for teachers to find out what students are thinking and how much they understand of our number system. Using trading games that have rules about the trading gives students a fun game where they are learning about place value. For young students the game is to be introduced with a small sized collections such as three yellows equals one blue and then move onto base ten value (Reys, 2012).
Describe misconception	Oral counting or rote recitation of counting up to and beyond ten can be done by some students and this can be taken as they understand the place value. This is not so as in most cases they have a confusion or misunderstanding from wrong use or lack of experience of materials with trading. With the student the teacher needs to go back to counting on a number line focusing on where numbers sit on the line (Reys, 2012).
ACARA	(Australian Curriculum and Assessment Reporting Authority [ACARA], 2014)
Resources and ideas	http://www.bbc.co.uk/bitesize/ks1/maths/place_value/play/popup.shtml This game goes from simple to hard, starting with small numbers and using their tenths, hundreds and ones forms. Giving students a change to have fun while gaining an understanding on the units ("BBC - KS1 Bitesize Maths - Safari Units", 2016).
Concise synthesis textbook	Characteristics of Hindu- Arabic numeration system: 1,place value 2, Base ten 3, Use of Zero 4, Additive property Natural of place value can be demonstrated by -Modelling ungrouped and regrouped -Modelling proportional and nonproportional -Grouping and trading   Calculators is a means to both support and extend students mathematical experience’s although this means teachers are to help students understand how to use this technology appropriately. This comes with students understanding that calculators don’t think and that the student is to do all the thinking. This also means students need to understand that using a calculator is not always the fastest way for doing a sum. Mental computation is used with building on thinking strategies used to develop basic facts making a need for students to understand the importance of mental computation and that teachers need to encourage it (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              BBC - KS1 Bitesize Maths - Safari Units : Fullscreen. (2016). Bbc.co.uk. Retrieved 29 May 2016, from http://www.bbc.co.uk/bitesize/ks1/maths/place_value/play/popup.shtml            Reys, R. (2012). Helping students learn mathematics (pp. 139-163). Milton, QLD: WILEY.