Pattern starterAnswers

1. Making mountains

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

• • •

1 mountain 2 mountains 3 mountains

• 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

2. Making factories

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

first factory second factory third factory

   

   

       

• b) How many extra blue tiles and how many extra red tiles are added each time you make the next design?

• 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

• 3. Dot patterns • a) Below were dot patterns. Use counters to

make first and second patterns. Draw the diagram for the third pattern.

•

• • first pattern second pattern third pattern

• b) How many extra dots are added each time you make the next design?

• four dots• c) Discuss how many dots you would need to

make the 10th pattern and how you work this out.

• 41 dots. 9 4 5 41

4) 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.

1st rose garden 2nd rose garden 3rd rose garden

R

R

R

• 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

Pattern starter 2

1. Making mountains (continue)

• c) Fill in the table below for the number of sticks used.

Number of mountains Number of sticks Direct rules (partitioning)

1 6 6

2 10 6 + 4 = 6 + 4 1

3 14 6 + 4 + 4 = 6 + 4 2

4 18 6 + 4 3

5 22 6 + 4 4

10 42 6 + 4 9

31 126 6 + 4 30

1 million 6 + 4 (1 million – 1) 6 + 4 (1 million – 1)

6 + 4 ( - 1) 6 + 4 ( - 1)

• 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 mountains 50 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.

2. Making factories(continue)• c) Fill in the table below for the number of sticks used.

Number of mountains Number of sticks Direct rules (partitioning)

1 7 7

2 12 7 + 1 5

3 17 7 + 2 5

4 22 7 + 3 5

5 27 7 + 4 5

10 52 7 + 9 5

31 157 7 + 30 5

1 million 7 + (1million – 1) 5 7 + (1million – 1) 5

7 + ( - 1) 5 7 + ( - 1) 5

• 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) 12th factory 62 tiles• ii) 29th factory 147 tiles• iii) 99th factory? 497 tiles• • f) If Taine has 102 tiles, what size factories can he

make? 20th factory

• 3. Dot patterns(continue)• c) Fill in the table below for the number of dot used.

Pattern number Number of dots Direct rules (partitioning)

1st 5 5

2nd 9 4 + 1 5

3rd 13 4 + 2 5

4th 17 4 + 3 5

5th 21 4 + 4 5

10th 49 4 + 9 5

31th 154 4 + 30 5

1 millionth 4 + (1 millionth – 1) 5 4 + (1 millionth – 1) 5

4 + ( - 1) 5 4 + ( - 1) 5

• d) Use your table and the diagrams to find a rule for the number of dots needed for the size of the pattern.

• Number of dots = 4 (pattern number -1) + 5• e) Use your rule to find the number of dots needed

to make • i) 12th pattern 49 dots

ii) 29th pattern 117 dotsiii) 99th pattern? 397 dots

• f) If Tara has 93 dots, what size pattern can she make? 23th pattern

4. Rose gardens(continue)• c) Fill in the table below for the number of tiles used.

Size of rose gardens Number of tiles Direct rules (partitioning)

1 8 8 = 4 + 4

2 12 2 4 + 4

3 16 3 4 + 4

4 20 4 4 + 4

5 24 5 4 + 4

10 44 10 4 + 4

31 128 31 4 + 4

1 million 1 million 4 + 4 1 million 4 + 4

4 + 4 4 + 4

• 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) 12th rose garden 52 tiles• ii) 29th rose garden 120 tiles• iii) 99th rose garden? 400 tiles• • f) If Tara has 92 tiles, what size rose garden can

she make? 12th garden