Jonathan Hall

I’m sure you’ve mentioned this before (many years ago now)
Can you share a few examples if you get chance please - I’d like to see them!

I’m afraid I don’t, I just display the prompt and the rest flows naturally.

I’ll give them hints to point them in the right direction if needed.

Interestingly, I think there are also times when the opposite approach is worthwhile!

The original I used today included other multiples of 8, but I felt it would work better next time with only the "important ones" - I tweaked it before posting - and hence the unfortunate typo.

Ha I spot it.

Why the oops?

A slide that reads: Here are some multiples of eight.​ 0​, 8​, 24​, 48​, 80​, 120​, 169​, 224​ Square any odd number. What do you notice?​

In #MathsToday we made a conjecture from this prompt...then tried to prove it.

Id say the x in the middle is probably “nicer” symbolically - especially (obviously?) when we start finding the product of consecutive numbers.

Ah, thank you for sharing! ☺️

In fact, the first thing I did was to ask them to choose any number and add on the next four and got them all to shout out their totals.

They quickly conjectured it would always be a multiple of 5 and that led nicely to the tiles/proof.

I did it side by side with the formal algebraic proof during the lesson.

I didn’t want to dabble with negative tiles for now, but maybe something to explore later.

Algebra tiles demonstrating that 5 consecutive integers can always form a 5 by "something" rectangle.

We used algebra tiles in #MathsToday to prove that the sum of 5 consecutive integers is always a multiple of 5.

This thread is absolutely perfect for stuff I’m trying in my classroom these days. I’m taking part in a “Developing Mathematical Thinking” project with University of Dundee and we are looking at things like this. Will try out lots of these. Did the 4 digit palindrome one. S-C-G would’ve improved it.

Ok, so I know twin primes are always one more and one less than a multiple of 6

So (6n+1)(6n-1)=36n² - 1

So one less than a multiple of 9…which MUST be where the digital root of 8 comes from.

Am I on the right lines?

This task is a perfect example!

An eminently worthwhile structure.

How about this:

Pick a pair of twin primes bigger than 3. Multiply them together. Find the digital root of your answer (add digits together, repeat until single digit reached).

Try another pair of twin primes (>3).

Make a conjecture?

Prove it?

Ooh, I’ve not come across this one before. I’ve got to the conjecture stage pretty quickly…now to try and figure out why it works.

Thanks for sharing!

I added a couple more of my favourites to this thread earlier today.

February Calendar Problems February is here and if you need a distraction from winter weather ❄️, I have the February 2016 Calendar of Problems from 10 years ago for some wintertime problem solving enjoyment. I have a few mo…

Time for winter #ProblemSolving! Here's the February Calendar of Problems for you and your students.

Tell us your working out here or on the post. ENJOY!
#MTBoS #iTeachMath #RecreationalMath #MathSky #MathsToday #T3Learns

karendcampe.wordpress.com/2026/02/01/f...

A series of growing squares formed from L-shapes of alternate red and yellow counters. A prompt above reads: "If yellow is 1 and red is -1, what would be the value of the 100th pattern in this sequence?"

If yellow is 1 and red is -1, what would be the value of the 100th pattern in this sequence?

S: Find the value of the first few patterns.

C: What do you notice about the odd and evens?

G: Find the total for the nth pattern. Describe how the rule changes if n is odd or even.

A picture of a multiplication square with the prompt: "What's the lowest common multiple of all the numbers in a 10 × 10 multiplication square?"

What's the lowest common multiple of all the numbers in a 10 × 10 multiplication square?

S: Try finding the LCM of all the numbers in the top row.

C: What prime factors are used? And more notably, which primes will never be used?

G: What strategy would you use to find the LCM for any grid size?

Yeah, good point.

I like the idea of the task though, I’ll probably spend some time making a version which is much harder to guess.

I’m going to need Autograph proof Rob.

Oooh, sneaky Sam.

Which one gets to 2000 first?

a) 1, 2, 4, 8, 16, …
b) 100, 200, 300, 400, 500, …
c) 1, 1, 2, 3, 5, …
d) 1, 4, 9, 16, 25, …

I’ve not worked it out yet, but 2000 seems like a decent number to make it close.

Gut instinct? Then calculate.

I normally start with numerical examples first.

bsky.app/profile/stud...

bsky.app/profile/stud...

Definitely better than Coen.

@welcometowillerby.bsky.social

A partially filled hundred square with 3 pairs of coloured tiles.

Which pair of coloured tiles has the greatest total?

How do you know?

In case you missed it yesterday. Quite proud of where this is going.

This will keep me busy for many years to come.