Crack the pattern
You will inspect 1, 1, 2, 3, 5 and explain a possible next number. The difference between entries keeps changing, so adding the same amount each time will not fit.
- Maths
- Explorer
- About 10 minutes
Grown-up needed: yes for setup, checking and any preparation of paper or small items
What you need
- Paper
- A pencil
- A one-minute timer if wanted
The rule
Explain how you found it.
How to do it
- Write 1, 1, 2, 3, 5 and leave a final gap.
- Circle the first two entries together.
- Add each neighbouring pair and compare with the following entry.
- Write the next entry predicted by that rule.
- Explain the pairing to a partner using your own words.
Why it works
In this sequence, adding the previous two entries produces the next one. One plus one gives two, one plus two gives three, and two plus three gives five. Continuing that rule gives three plus five, which is eight. Some plant arrangements involve related number patterns, but your paper sequence does not prove a rule for every sunflower. It simply gives you a relation you can check and extend one step at a time.
Make it harder
- Write three more entries.
- Start with 2 and 3 instead.
- Compare the changes between entries in both starting sequences.
Ask Taz
- Why do we add two earlier entries instead of one?
- Why does the gap between entries keep increasing?
- Why does a number pattern not prove every plant follows it?
For grown-ups
Ask your child to show a pair that creates each result, rather than praise a quick answer alone. The one-minute suggestion is optional and should not obscure the explanation. Ask at dinner: “How would a different starting pair change the sequence while keeping the same rule?”
Taz is an AI and can be wrong, so stay close by. Read how safety works on Taz.
Show us yours
Film your hands and what you made, not your face or name. Ask a grown-up before posting anywhere else.
Questions parents ask
How much preparation does this need?
Use the household items above and begin with one small example. A grown-up can prepare the space or checking sheet while the child chooses the prediction. The time is an estimate and includes a little room to repeat.
What if we get different answers?
Compare the rule, the method and what each person recorded. A difference can reveal a changed assumption or an ordinary variation, so check before deciding someone must be wrong.
Does the child have to share online?
No. Discuss the work at home first. Public sharing is optional and needs the grown-up permission and privacy wording above.
More to try
See all Taz Challenges, or look through the science labs. One place for every why. Ask for early access at aitaz.com
Try it in 3D: Fibonacci spiral.