Solve mathematical puzzles…

We are learning to…

•Test hypotheses;

• Tabulate systematically the information in a problem or puzzle;

• Identify and record the steps or calculations needed to solve it.

Mental/ Oral starter

1 2 3 4 5

3 5

8

Even if we change the order of the numbers on the bottom tier, the number at the top will always be the same.

Main Activity

What plant is this?

Mistletoe is a parasite that grows on other trees.

Mistletoe grows mathematically. Every year, each branch will split in two…

Interesting facts about mistletoe

Year One

Year Two

Year Three

How many new

branches will there be next

year?

Year Four

Year Number of new branches

Year Number of new branches

One 1

Two 2

Three 4

Four 8

Five

Six

Seven

Eight

Task OneHow many new branches will there be in the seventh year?

Which year will be the first year to see over 500 new branches?

Year New branches

1 1

2 2

3 4

4 8

5 16

6 32

7 64

8 128

9 256

10 512

11 1024

12 2048

13 4096

14 8192

15 16384

16 32768

17 65536

18 131072

19 262144

20 524288

Year New branches Total branches

1 1 1

2 2 3

3 4 7

4 8

5 16

6 32

7 64

8 128

9 256

10 512

11 1024

12 2048

13 4096

14 8192

15 16384

16 32768

17 65536

18 131072

19 262144

20 524288

Task TwoHow many branches are there in total?

Year New branches Total branches

1 1 1

2 2 3

3 4 7

4 8 15

5 16 31

6 32 63

7 64 127

8 128 255

9 256 511

10 512 1023

11 1024 2047

12 2048 4095

13 4096 8191

14 8192 16383

15 16384 32767

16 32768 65535

17 65536 131071

18 131072 262143

19 262144 524287

20 524288 1048575

Plenary

What have we learnt?

What strategies did you find useful?