RIC-0563 Developing algebraic thinking

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SHAPES Teachers notes Pentagon The equations for Pentagon can be solved so that the remaining equations each have a sum of two digits on both sides of the equal sign. j a + b + c = c + d + e = e + f + g = g + h + i = i + j + a b j a + b = d + e, c + d = f + g, e + f = h + i c i d h g + h = j + a b + c = i + j e f g 9 0 0 1 9 8 7 6 2 3 4 2 5 7 5 3 8 4 6 1 Box Sum The final problem in this section is Box Sum. It has appeared in many different puzzle books, usually with no mathematical background information. Since the sum of each face of the cube must be the same, there are six <strong>algebraic</strong> expressions that are equal. Subtracting like terms from various equations provides several relationships among the digits. b f a e g c d h a + b + c + d = a + b + f + e = a + d + h + e = d + h + g + c = b + c + g + f = e + f + g + h c + d = f + e, b + f = d + h, a + e = c + g b + c = e + h, a + b = g + h, a + d + f + g All six of the equations show that the sum of the two digits on one edge of the cube is the same as the sum of the two digits on the edge diagonally across on the opposite face. 8 5 8 7 4 8 3 2 6 1 7 4 2 3 6 To start, select an edge and two digits. Now, select two other digits that give the same sum. With these initial selections, the remaining tiles become easier to place. 4 9 1 1 6 9 5 3 2 86 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ® ISBN 978-1-74126-088-5
SHAPES Triangle 6 Place any 6 of the digits 0 to 9 in the squares so that the sum of each line is the same. What is the greatest possible sum you can find? Record your results in the Triangle 6 provided. What is the least possible sum you can find? Record your results in the Triangle 6 provided. R.I.C. Publications ® www.ricgroup.com.au DEVELOPING ALGEBRAIC THINKING 87 ISBN 978-1-74126-088-5
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Developing algebraic thinking Writt
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DEVELOPING ALGEBRAIC THINKING Forew
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PROBLEM-SOLVING AND NUMBER TILES Te
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PROBLEM-SOLVING AND NUMBER TILES Te
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Place value picks R.I.C. Publicatio
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PLACE VALUE PICKS Teachers notes Pl
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PLACE VALUE PICKS Teacher’s notes
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PLACE VALUE PICKS 2 Using 9 number
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Same sums R.I.C. Publications ® ww
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SAME SUMS Teachers notes The follow
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SAME SUMS Same sums 1 Use the numbe
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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
Page 59 and 60: Locker numbers R.I.C. Publications
Page 61 and 62: LOCKER NUMBERS Teachers notes Probl
Page 63 and 64: LOCKER NUMBERS Teachers notes Probl
Page 65 and 66: LOCKER NUMBERS 2 Use the number til
Page 67 and 68: Exciting exponents R.I.C. Publicati
Page 69 and 70: EXCITING EXPONENTS Teachers notes E
Page 71 and 72: EXCITING EXPONENTS 2 Place all 10 n
Page 73 and 74: EXCITING EXPONENTS 4 Place all 10 n
Page 75 and 76: Plus and times R.I.C. Publications
Page 77 and 78: PLUS AND TIMES Teachers notes Plus
Page 79 and 80: PLUS 5 Place any 5 of the digits 0
Page 81 and 82: TIMES Place any 5 of the digits 0 t
Page 83 and 84: Shapes R.I.C. Publications ® www.r
Page 85: SHAPES Teachers notes Triangle 10 T
Page 89 and 90: SHAPES Triangle 10 Place all 10 of
Page 91 and 92: SHAPES Pentagon Use all 10 number t
Page 93 and 94: 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
Page 99 and 100: PENTOMINO PUZZLES Use 5 number tile
Page 101 and 102: Alphabet algebra a b e c d h f g R.
Page 103 and 104: ALPHABET ALGEBRA Teachers notes Alp
Page 109 and 110: ALPHABET ALGEBRA B Use all 10 numbe
Page 111 and 112: ALPHABET ALGEBRA D Use any 8 number
Page 113 and 114: ALPHABET ALGEBRA F Use all 10 numbe
Page 115 and 116: ALPHABET ALGEBRA H Use any 7 number
Page 117 and 118: ALPHABET ALGEBRA J Use any 8 number
Page 119 and 120: ALPHABET ALGEBRA L Use any 8 number
Page 121 and 122: ALPHABET ALGEBRA N Use any 9 number
Page 123 and 124: ALPHABET ALGEBRA P Use all 10 numbe
Page 125 and 126: ALPHABET ALGEBRA R Use all 10 numbe
Page 127 and 128: ALPHABET ALGEBRA T Use any 8 number
Page 129 and 130: 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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