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?
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