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# Grade 8 - patterns investigation - Rene Rix - model answers

Module by: Pinelands High School. E-mail the author

Summary: Model answers for patterns investigation

#### Activity 1.1:

 t (number of triangles) 1 2 3 4 6 n 20 m(number of matches) 3 6 9 12 18 3n 60

#### Activity 1.2:

 t(number of triangles) 45 200 m(number of matches) 135 600

#### Activity 2.1

 s(number of squares) 1 2 3 4 6 n 20 m(number of matches) 4 8 12 16 24 4n 80

#### Activity 2.3

1. 1) m = 4s
2. 2)
s = m 4 s = m 4 s = m over 4
(1)

#### Activity 2.4

 s(number of square) 36 120 m(number of matches) 144 480

#### Activity 3.1

 m(number of matches) 1 2 3 4 6 n 20 b(number of blobs) 0 1 2 3 5 n-1 19

b = m - 1

m = b + 1

#### Activity 3.4

 m(number of matches) 55 54 b(number of blocks) 128 127

### Task four: More matchstick triangles

#### Activity 4.1

 t(number of triangles) 1 2 3 4 6 n 20 m(number of matches) 3 5 7 9 13 2n+1 41

#### Activity 4.2

 t(number of triangles) 70 126 m(number of matches) 141 253

### Task five: More matchstick squares

#### Activity 5.1

 s(number of squares) 1 2 3 4 6 n 20 m(number of matches) 4 7 10 13 19 3n+1 61

#### Activity 5.3

1) m = 3s + 1

2) s=m13s=m13s = {m - 1} over 3

#### Activity 5.4

 s(number of square) 234 154 m(number of matches) 703 463

#### Activity 6.1

 m(number of matches) 1 2 3 4 6 n 20 b(number of blobs) 6 11 16 21 31 5n+1 201

#### Activity 6.3

m = 5h + 1

h = m 1 5 h = m 1 5 h = {m - 1} over 5
(2)

#### Activity 6.4

 h(number of houses) 120 91 m(number of matches) 601 456

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