1. Pattern starter Answers

2. 1. Making mountains a) Use sticks to make 1 and 2 mountains. Complete the diagram for 3 mountains. 1 mountain 2 mountains 3 mountains

3. b) How many extra sticks are added each time you make the next design? four sticks c) Discuss how many sticks you would need to make 10 mountains and how you work this out. 42 sticks. 9 4 6 42

4. 2. Making factories a) Use tiles to make first and second factories. Complete the diagram for third factory. first factory second factory third factory

5. b) How many extra blue tiles and how many extra red tiles are added each time you make the next design? One extra blue tile and 4 extra red tiles. Five extra tiles. c) Discuss how many tiles you would need to make the 10th factory and how you work this out. 52 tiles. 9 5 7 42

6. 3) Rose garden a) Below were designs of rose gardens surrounded by green tiles. Use tiles to make first and second rose gardens. Complete the diagram for third rose garden. 1 st rose garden 2 nd rose garden 3 rd rose garden R R R

7. b) How many extra tiles are added each time you make the next design? four extra tiles c) Discuss how many tiles you would need to make the 10th rose garden and how you work this out. 44 tiles. 9 4 8 44

8. Pattern starter 2

9. 1. Making mountains (continue) c) Fill in the table below for the number of sticks used. Number of mountainsNumber of sticksDirect rules (partitioning) 166 210 6 + 4 = 6 + 4 1 314 6 + 4 + 4 = 6 + 4 2 418 6 + 4 3 522 6 + 4 4 1042 6 + 4 9 31126 6 + 4 30 1 million 6 + 4 (1 million – 1) 6 + 4 ( - 1)

10. d) Use your table and the diagrams to find a rule for the number of sticks needed for any number of mountains. Write down the rule. Number of sticks = 4 (number of mountains -1) + 6 e) Use your rule to find the number of sticks needed to make i) 12 mountains50 sticks ii) 29 mountains 118 sticks iii) 99 mountains? 398 sticks f) If Jane has 102 sticks, how many mountains can she make? How did you work that out? 25 mountains.

11. 2. Making factories(continue) c) Fill in the table below for the number of sticks used. Number of mountainsNumber of sticksDirect rules (partitioning) 177 212 7 + 1 5 317 7 + 2 5 422 7 + 3 5 527 7 + 4 5 1052 7 + 9 5 31157 7 + 30 5 1 million 7 + (1million – 1) 5 7 + ( - 1) 5

12. d) Use your table and the diagrams to find a rule for the number of tiles needed for any number of factories. Write down the rule. Number of tiles = 7 + (factory number – 1) 5 e) Use your rule to find the number of tiles needed to make i) 12 th factory 62 tiles ii) 29 th factory 147 tiles iii) 99 th factory? 497 tiles f) If Taine has 102 tiles, what size factories can he make? 20 th factory

13. 3. Rose gardens(continue) c) Fill in the table below for the number of tiles used. Size of rose gardensNumber of tilesDirect rules (partitioning) 188 = 4 + 4 212 2 4 + 4 316 3 4 + 4 420 4 4 + 4 524 5 4 + 4 1044 10 4 + 4 31128 31 4 + 4 1 million 1 million 4 + 4 4 + 4

14. d) Use your table and the diagrams to find a rule for the number of tiles needed for the size of rose gardens. Number of tiles = rose number 4 + 4 e) Use your rule to find the number of tiles needed to make i) 12 th rose garden 52 tiles ii) 29 th rose garden 120 tiles iii) 99 th rose garden? 400 tiles f) If Tara has 92 tiles, what size rose garden can she make? 12 th garden