The Amazing Splitting Plant
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Age
5 to 7
Challenge level
The splitting plant grows in a special way.
In the first week, the stem splits into two branches.
In the second week, each of these two branches split into another
two branches - making four branches altogether.
This keeps happening every week, until at the end of the sixth week
each branch grows a flower.
How many flowers will the plant have?
Image
How many branches will there be after three weeks? Four
weeks ...?
How will you keep track of the number of branches?
It might help to draw a picture or jot some things down.
How will you keep track of the number of branches?
It might help to draw a picture or jot some things down.
We had quite a few submitted solutions to this activity and we start with Jaheim from Woodside Primary Academy in England who sent in this to show what he did:
How does it work?
Well because each of the stalks are splitting into two you have to times by two i.e: 1 changes to 2 2 changes to 4. Join in with my solution and see if you understand.
The number in the beginning is one as there is only the stem.
In the first week the one stem in the beginning has now split to become two stalks so the current number has changed from 1 to 2.
In the second week the two stalks split again so that the branch out in their own directions. The number has changed from 2 to 4.
In the third week the number has changed from 4 to 8.
In the fourth week the number has changed form 8 to 16.
In the fith week the number has changed from 16 to 32.
In the last week the number has changed from 32 to 64 and so the plant will have 64 flowers (that's a lot of flowers!).
I hope you understand.
Yes I do understand Jaheim, thank you.
Now we turn to Nathan from Carr Head Primary School:
This is a table of how I worked it out
| Week | Flowers |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
| 6 | 64 |
The amount of flowers doubles every week so if the stem splits into two branches in the 1st week then it doubles, in the 2nd to make four branches then it doubles again and again until it gets to the 6th week and it has 64 branches and every branch grows a flower so there would be 64 flowers.
From Michael at Cloverdale Catholic School in Canada we had;
If the branches grow two more every week, then you are going to end up with twice the amount of flowers.
First week: The plant splits into 2 branches.
Second week: The branches split into two, and so on, and so on.
The method I used was adding the first number again (or multiplying by 2):
The plant split into two branches, so that's 1 (the stem) + 1.
The next week, the branches grow two EACH, so 2 + 2, and so on.
The following pattern is shown below:
2 4 8 16 32 64
Every time the branches grow two more branches, the branch count doubles.
So if the stem grew three branches, then the branch count would triple (e.g. 3+3+3):
3 9 27 81 243 etc.
If you just want an easier way to find out (if you are in upper grades), you might have used exponents, or multiplying repeatedly.
Let's say, on the third week. You could have put down two to the power of 3, which is 16, or 2 with a little three at the top-right corner of the 2.
Then, at the sixth week, all the branches grow one flower. So, we used multiplication to find out that the branches are 64. Thus, the plant grew 64 flowers.
Image
Thank you to everyone who submitted their ideas. Most saw that the numbers doubled and wrote down their answers, but I've shown here some of those who described how they went about working it out, and how they recorded their answers.
The Amazing Splitting Plant
The splitting plant grows in a special way.
In the first week, the stem splits into two branches.
In the second week, each of these two branches split into another two branches - making four branches altogether.
This keeps happening every week, until at the end of the sixth week each branch grows a flower.
How many flowers will the plant have?
Image
Why do this problem?
This activity offers a situation that is not too complex to understand and yet opens out many possible explorations. It would be a good chance to focus on the different ways children have represented their solutions.
Possible approach
You could present the problem orally to the class, rather like telling a story. Ask them how many branches there would be by the end of the second week. You could then invite them to talk in pairs about the number of branches at the end of the third week. Giving learners mini-whiteboards might help at this stage. How did they work out the answer? Having got this far, leave them to work
on the problem in their pairs.
In the plenary, you could draw attention to the different ways of representing the problem you have seen. Some children may have drawn pictures of the plant, others may have just drawn lines. There may be some children who have simply noted down numbers. Invite several pairs to talk about their own representation and then you could have a group discussion about the advantages of each
way.
You may want to make a note of the numbers of branches at the end of each week and to ask the children what they notice. Can they explain why this pattern occurs? Could they predict how many branches there would be after seven weeks (if there weren't any flowers) without drawing a picture?
Key questions
How many branches will there be after three weeks? Four weeks ...?
How will you keep track of the number of branches?
What kinds of things have you noticed?
Possible extension
Once children have solved the problem as it stands, the activity may be opened out and extended. For example:
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] is:
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 plant branches in different ways, maybe in 3s, 4s, 5s etc. For example the fours and fives units would look like:
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The pupils can then be asked to explore what the patterns show and look at others for 6s 7s etc.
Further extension ideas are described on this sheet.
Possible support
You may want to talk to individual pupils about what is happening to the plant at each stage so they understand the context better.