The Amazing Splitting Plant


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Let's look at some ways in which the activity may be opened out and extended.
I'm assuming the pupils have got an answer to the Splitting Plants.
1/ If the plant branches in twos each year and we look at the units figure for a few years growth we see year by year that the number of flowers [2 4 8 16 32 64 as in the problem] are:

2 4 8 6 2 4 . . . . . . .

You can ask the pupils to see what they notice about the pattern.


2/ Then you can pretend that the plants can branch in different ways, may be in 3's, 4's, 5's etc. For example the fours and fives units would look like:

4's&5's

The pupils can then be asked to explore what the patterns show and look at others for 6's 7's etc.

3/ Then you can ask the pupils to explore further by introducing the thought "What if you had 10 plants - each branching differently [in 1's, 2's 3's . . . .9's] and you lined them up 1 to 9.
The pupils could then be asked to look at them after two lots of branching and the number of flowers for each plant.

1 4 9 16 25 36 49 64 81

So they could explore these [square] numbers.

Look at units:

1 4 9 6 5 6 9 4

1 Look at digital roots:

1 4 9 7 7 9 4 1 9

Look at the table of differences:

1stTableDiff

4/ Often in opening out activities we move away from the practical situation and get involved with the numbers that are coming out in patterns.

So, they could be asked to look at the numbers you'd get after another year of growth.
But of course three lots of branching means we're cubing the numbers instead of squaring them. Calculators come in useful, even the simple ones of course allow the children to do things like 6 x 6 x 6. This may be one way in which you want to introduce the whole idea of powers.

Four lots of multiplication [to the power 4] of the numbers 1 to 9 would give:

1 16 81 256 625 1296 2401 4096 6561

The units will be:

1 6 1 6 5 6 1 6 1

The digital roots will be:

1 7 9 4 4 9 7 1 9

The table of differences would be:

4's Table of Diff

All of which can be explored.

5/ Referring back to May 1998's activity "Number Squares " use the first 4 figures of the above pattern to start off the square.
sq4start
sq4No.4

Then explore, and then try the powers of 5, 6, 7, etc.

So once you've got some ideas as to how to answer the original question, we look at some answers, and get the pupils to think about "I wonder what would happen if we . . . . . ?" .

In extending this activity producing powers of the number 1 to 9 may be the outcome. Then look at the patterns/sequences in a variety of ways - unit figures, digital roots and lastly special arrangements.