RIC-0563 Developing algebraic thinking

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2 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ®
DEVELOPING ALGEBRAIC THINKING Foreword Over the past few years, many mathematics educators have directed their interests towards the development of algebraic thinking in students. As more and more schools move towards algebra for all, teachers need to be able to provide their students with the knowledge and skills necessary for success in a mathematics class where the focus on algebra is considerably different from the traditional course of study. What is algebraic thinking? Although there does not appear to be one agreed-upon definition, several common threads appear in the related literature. • Exploring and conjecturing about patterns • Formalising patterns • Verbalising relationships • Making generalisations • Symbolising relationships • Working with functions • Making connections between real-world situations and algebraic statements Together, all of these interrelated components form a framework for algebraic thinking. This type of thinking ‘embodies the construction and representation of patterns and regularities, deliberate generalisation, and most important, active exploration and conjecture (Chambers, 1994, 85).’ Problem-solving and problem-solving strategies permeate the activities. Contents Teachers notes ............................................................. 2–8 Place value picks ........................................................ 9–22 Same sums ............................................................... 23–34 Primes and composites ........................................... 35–44 Divisibility rules ....................................................... 45–58 Locker numbers ....................................................... 59–66 Exciting components ............................................... 67–74 Plus and times .......................................................... 75–82 Shapes ...................................................................... 83–92 Pentomino puzzles ................................................. 93–100 Alphabet algebra ................................................. 101–132 Numbered tiles ............................................................ 133 R.I.C. Publications ® www.ricgroup.com.au DEVELOPING ALGEBRAIC THINKING 3 ISBN 978-1-74126-088-5
Page 1: Developing algebraic thinking Writt
Page 5 and 6: PROBLEM-SOLVING AND NUMBER TILES Te
Page 7 and 8: PROBLEM-SOLVING AND NUMBER TILES Te
Page 9 and 10: Place value picks R.I.C. Publicatio
Page 11 and 12: PLACE VALUE PICKS Teachers notes Pl
Page 13 and 14: PLACE VALUE PICKS Teacher’s notes
Page 15 and 16: PLACE VALUE PICKS 2 Using 9 number
Page 23 and 24: Same sums R.I.C. Publications ® ww
Page 25 and 26: SAME SUMS Teachers notes The follow
Page 27 and 28: SAME SUMS Same sums 1 Use the numbe
Page 33 and 34: SAME SUMS Consecutive Sums 11 Use t
Page 35 and 36: Primes and composites R.I.C. Public
Page 37 and 38: PRIMES AND COMPOSITES Teachers note
Page 39 and 40: LOTS OF PRIMES, LOTS OF COMPOSITES
Page 41 and 42: MORE PRIMES Use all 10 number tiles
Page 43 and 44: ALL PRIMES Use all 10 number tiles
Page 45 and 46: Divisibility rules R.I.C. Publicati
Page 47 and 48: DIVISIBILITY RULES Teachers notes D
Page 49 and 50: DIVISIBILITY RULES Teachers notes D
Page 51 and 52: DIVISIBILITY RULES Divisibility rul
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DIVISIBILITY RULES Divisibility rul
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Page 59 and 60:
Locker numbers R.I.C. Publications
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LOCKER NUMBERS Teachers notes Probl
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LOCKER NUMBERS Teachers notes Probl
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LOCKER NUMBERS 2 Use the number til
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Exciting exponents R.I.C. Publicati
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EXCITING EXPONENTS Teachers notes E
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EXCITING EXPONENTS 2 Place all 10 n
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EXCITING EXPONENTS 4 Place all 10 n
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Plus and times R.I.C. Publications
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PLUS AND TIMES Teachers notes Plus
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PLUS 5 Place any 5 of the digits 0
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TIMES Place any 5 of the digits 0 t
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Shapes R.I.C. Publications ® www.r
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SHAPES Teachers notes Triangle 10 T
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SHAPES Triangle 6 Place any 6 of th
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SHAPES Triangle 10 Place all 10 of
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SHAPES Pentagon Use all 10 number t
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Pentomino puzzles R.I.C. Publicatio
Page 95 and 96:
PENTOMINO PUZZLES Teachers notes Gr
Page 97 and 98:
PENTOMINO PUZZLES Use 5 number tile
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PENTOMINO PUZZLES Use 5 number tile
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Alphabet algebra a b e c d h f g R.
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ALPHABET ALGEBRA Teachers notes Alp
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ALPHABET ALGEBRA B Use all 10 numbe
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ALPHABET ALGEBRA D Use any 8 number
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ALPHABET ALGEBRA F Use all 10 numbe
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ALPHABET ALGEBRA H Use any 7 number
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ALPHABET ALGEBRA J Use any 8 number
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ALPHABET ALGEBRA L Use any 8 number
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ALPHABET ALGEBRA N Use any 9 number
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ALPHABET ALGEBRA P Use all 10 numbe
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ALPHABET ALGEBRA R Use all 10 numbe
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ALPHABET ALGEBRA T Use any 8 number
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ALPHABET ALGEBRA V Use any 7 number
Page 131 and 132:
ALPHABET ALGEBRA X Use any 9 number
Page 133 and 134:
ALPHABET ALGEBRA Z Use all 10 numbe
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RIC-0563 Developing algebraic thinking

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