*For all the rich maths tasks and probing questions in this series, and for the pedagogy behind the concept, please visit the Probing Maths Questions Index page.*

So, it’s the start of October, which can mean only one thing… the 2nd Probing Questions activity is now live đź™‚

Following on from the brilliantÂ set of probing questions that teachers came up with for the Factors and Multiples Game last month, I have chosen another of my favourite tasks for you to have a think about this time around.

This was the task I spoke about briefly in the BBC Radio 4 program, “The Educators”. My Year 8s love it. And it goes something like this.,..

Choose 3 Numbers

- Choose three numbers and find all the totals when added in pairs.
- E.g. if the numbers are 13, 7 and 18, the totals will be 20, 25 and 31.
- Give these three totals to someone else and see if they can work out what your original three numbers were

And that is it.

I love this activity, because on the surface it looks so simple. And it is the kind of task that everyone can access as there is nothing stopping you limiting the numbers the students can choose to 1 to 10.

But once the students have played the game a few times, that is when the probing questions, and the associated deep thinking, kick in.

Here are a few questions that I have used in the past to get the students thinking:

- How can you work out someoneâ€™s original numbers from their totals?
- Does this technique also work with negative numbers?
- Can you tell if one of their numbers is a negative from their 3 totals?
- If you know two of the totals and one of the numbers, can you work out the missing values?
- Can you think of a set of 3 numbers that give two totals that are the same
- Can you make three totals that are consecutive numbers?
- Can you make any 3 totals?
- Can you come up with a strategy for finding the original numbers if we multiply the totals instead of adding?

I have also put together the following Excel file that you can use to create examples, or your students can use to test out hypotheses:

As I described in the previous post, and the first one, I like to start everyone off on the same task, and then ask these different questions to different students, ensuring as best I can that each student is engaged and challenged. It is not a perfect strategy, but in my opinion it beats handing out a series of different worksheets any day,

So, now it is over to you. What probing questions can you think of for this activity? They can be simple or complicated. They can take 10 seconds to answer, 10 hours, or maybe they do not have an answer. The can stayÂ within the parameters of the original task, or change the rules completely.

So, please share your thoughts in the Comments below, and if you could spread the word about my Probing QuestionÂ initiative, I would be eternally grateful đź™‚

What happens with four numbers?

What if you knew two pair totals and the total of all three?

What if you know the differences of the pairs instead of the sums?

Given I invented this task some time ago on a train journey and later published it on my website I would’ve thought protocol would be to acknowledge the author!

Hi Mike

I am so sorry! I was told about this activity by a teacher who claimed they had invented it! I’ve since found the activity on your blog. Please accept my apologies, and when I write up the post with the full collection of pruning questions at the end of the month, please be assured I’ll give you the credit you deserve.

Many apologies

Craig