The mathematical investigation workspace is a place to record your own conjecture, the cases you try, and any counterexamples. It then shows whether your conjecture is supported or disproved, and what is still missing before it counts as proved.
It does not do the thinking for you. The reasoning and the general argument stay yours.
How do you use it?
- Write your conjecture and your assumptions and conditions.
- Under Cases tried, add each case: what you varied, what happened, and whether the conjecture holds. Press Add case.
- Use Remove on any row you want to delete.
- In My general argument, write in your own words why it must always work.
- Read the status panel. Press Download record for a text copy, or Reset to example to go back to the demonstration.
How do you read the result?
The status panel first counts your cases, for example “5 cases: 5 hold, 0 fail”.
If any case fails, it says Disproved. One counterexample is enough, and you are asked to refine the conjecture.
If every case holds, it says Supported, but NOT proved. If you have not written an argument, it tells you the claim is still a conjecture. If you have, it reminds you that the tool cannot check it, so you ask whether each step follows and whether it covers every case.
Below are prompts for varying systematically and for checking a proof.
Example walk-through
The sample conjecture is: the sum of the first n odd numbers is n², where n is a positive whole number. Five cases are already entered, such as n = 3: 1 + 3 + 5 = 9. All hold, so the status is “Supported by 5 cases, but NOT proved”.
Add n = 6 with the result 1 + 3 + 5 + 7 + 9 + 11 = 36, and mark it as holding. That is six cases, and the claim is still unproved.
To prove it, write a general argument. The nth odd number is 2n − 1.
Write the sum S forwards and backwards, then add the two lines.
Each of the n pairs adds to 2n, so 2S = n × 2n and S = n². That argument covers every n, not just the cases you tried.
Now try a different conjecture, “n² + n + 41 is prime”. It gives primes for n = 1 to 39, but for n = 40 it gives 1681 = 41 × 41.
Add that case as fails. The status changes to Disproved after one counterexample, even though 39 cases worked.
What are the assumptions and limits?
- The tool records and organises. It does not create cases, find counterexamples or judge proofs.
- Cases are only your own entries. Fitted data is never treated as proof.
- Check the 0607 assessment requirements for investigation tasks separately, including what needs to be shown and how work is authored.
- The record is kept only on this device in your browser.
Which lessons explain the ideas behind it?
- Generate systematic cases for a pattern shows how to choose cases.
- Move from observed cases to a conjecture covers stating the pattern.
- Test a counterexample to a conjecture explains the n² + n + 41 type of check.
- Explain a general rule with algebra builds the general argument.
- State limits of a pattern-based conclusion covers what cases can and cannot show.
- Use second differences to investigate a quadratic rule is one worked investigation method.
The wider topic is International Mathematics investigations, with a mixed practice set. The 0607 code and route guide and the page on how 0580 and 0607 differ help you confirm which course you follow.
For a teacher to go through your own investigation tasks, see online one-to-one Mathematics tuition. Other tools are in the learning tools directory.