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Growing Patterns Concept

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The figures as shown below are made up of identical tiles. Fig. 1 Fig. 2 Fig. 3 (a) Following the pattern, how many tiles is Fig. 10 made up of ? (b) Which figure will you form if you are required to use as many of the 300 tiles given to you as possible ? Example

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Solution (a)The figures as shown follow this pattern : 4, 7 ( 4 + 3 ), 10 ( 7 + 3 ),.. No. of tiles in Fig. 2 = 4 + 1 x 3 No. of tiles in Fig. 3 = 4 + 2 x 3 Therefore, the number of tiles in Fig. 10 = 4 + 9 x 3 = 31 (b) Note that number of tiles in Fig. 100 is 4 + 99 x 3 = 301 ( which just exceeds 300 ). Therefore, the figure that can be formed using as many of the 300 tiles given as possible is Fig.99

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Question 1 How many different ways can you arrange 7 chairs, each of a different colour, in a row? Step 1 Start with 2 chairs, A and B. ABBA There are 2 ways.

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Step 2 Add 1 more chair, C. Find the number of ways to arrange 3 chairs. There are 6 ways. ABCBCACAB BACCBAACB

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Step 3 Add 1 more chair, D. Find the number of ways to arrange 4 chairs. There are 24 ways. ABCBACDBACBDABDC

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Look at the numbers below. Can you see a pattern? Step 1: Number of ways = 1 x 2 = 2 Step 2: Number of ways = 1 x 2 x 3 = 6 Step 3: Number of ways = 1 x 2 x 3 x 4 = 24 Now calculate the number of different ways to arrange 7 chairs in a row. There are ________ ways to arrange 7 chairs in a row.

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Question 2 Figure Number 123 Number of Circles 13 (1 + 2) 4 (1 + 2 + 3) Fig 1 Fig 2Fig 3

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a) Calculate the number of circles in Fig 7. There are _______ circles in Fig 7. b) Calculate the number of circles in Fig 88. There are _______ circles in Fig 88. c) Which figure has 276 circles? Figure _______ has 276 circles.

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Question 3 Figure Number 123 Number of Circles Fig 1 Fig 2Fig 3

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a) Calculate the number of circles in Fig 9. There are _______ circles in Fig 9. b) Calculate the number of circles in Fig 50. There are _______ circles in Fig 50. c) Which figure has 130 circles? Figure _______ has 130 circles.

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Question 4 Figure Number123 Number of sides48 Perimeter (cm)816 Area (cm 2 )412 Fig 1 Fig 2Fig 3 The following figures are made up of squares. Each side of the square is 2 cm.

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a) Calculate the perimeter of Fig 6. The perimeter of Fig 6 is ______cm. b) Calculate the area of Fig 12. The area of Fig 12 is _______ cm 2. c) Which figure has an area of 840 cm 2 ? Figure _______ has an area of cm 2.

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Question 5 How many squares are there altogether in the following figure? Hint: There are more than 4 squares. DimensionNumber of Squares 1 x 14 2 x 21 Total5

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How many squares are there altogether in the figure below? Hint: There are more than 9 squares. DimensionNumber of Squares 1 x 19 2 x 24 3 X 31 Total14

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Can you see a pattern? For a 2 by 2 square, the total number of squares is 1 x 1 + 2 x 2 = 5 For a 3 by 3 square, the total number of squares is 1 x 1 + 2 x 2 + 3 x 3 = 14

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How many squares are there altogether in the figure below? Hint: There are more than 25 squares. There are _______ squares altogether in the figure.

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Thats all for today… Thank you. A.L.2007

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