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Starter Question 1. Write the next two numbers in the sequence: 12, 13, 15, 18, 22, 27 2. Calculate the area of a rectangle with length 4m and breadth 8m Area of a rectangle = l x b =4x8 = 32 m2 3. Write the ratio of boys to girls in the class 4. Which is longer 0.5cm or 6mm? 0.5 cm = 0.5 x 10 = 5 mm longer Complicated Linear Patterns A pattern is made using matchsticks: 1 triangle 2 triangles 3 triangles 3 matches 5 matches 7 matches Number of Triangles (T) Number of matches (M) 1 2 3 4 5 3 5 7 9 11 Complicated Linear Patterns Number of Triangles (T) Number of matches (M) 1 2 3 4 5 3 5 7 9 11 +2 +2 +2 +2 For every new triangle => the number of matchsticks rises by 2 Complicated Linear Patterns Step 1: In symbols we can begin to write M = 2 x T BUT look at the table: Number of Triangles (T) Number of matches (M) 1 2 3 4 5 3 5 7 9 11 M = 2 x T M=5, T=2 2 x 2 = 5 Complicated Linear Patterns Step 1: In symbols we can begin to write: M = 2 x T Step 2: We need a correction number to make the pattern work T = 2, M = 5 2 x 2 = 5 2 x 2 ++ ?1 = 5 Complicated Linear Patterns Formula M=2xT+1 Check: Number of Triangles (T) Number of matches (M) 1 2 3 4 5 3 5 7 9 11 Complicated Linear Patterns Formula M=2xT+1 Q) If there are 20 triangles how many matches are there? M=2xT+1 T=20 M = 2 x 20 + 1 M = 41 Complicated Linear Patterns 2 posts 3 posts 4 posts 1 support 2 supports 3 supports Number of Posts (P) Number of supports (S) 2 3 4 5 6 1 2 3 4 5 Simple Linear Patterns Number of Posts (P) Number of Supports (S) 2 3 4 5 6 1 2 3 4 5 +1 Step 1: 1 x P S = ? Step 2: 1 S = 1 x P -? +1 +1 +1 Simple Linear Patterns Number of Posts (P) Number of Supports (S) 2 3 4 5 6 1 2 3 4 5 +1 Formula S=1xP-1 S=P-1 +1 +1 +1 Simple Linear Patterns Formula S=P–1 Q) If there are 156 posts how many supports are there? S=P-1 P=156 S = 156 - 1 S = 155