Labour logic

A neater, more standard, variant, perhaps

I've just read the paper more closely. It seems they did reverse the number line for half their subjects. They also varied the way they expressed the quantities, as here. In general children did better than adults (not because they understand fractions better!).

Here's an interesting task! [based on Opfer & DeVries, 2008]

Notice the two centres of enlargement:

I pride myself on my bread-slicing skills, except I so often create an overhang.

Many thanks, Matt. I wonder whether you remember your similar nice scaling response (below) to a fraction task that I posted a couple of years ago? I discussed it at the recent BSRLM conference.

Another variant.

Look at the pattern. Intriguing or obvious?!

Which could expand to this....?

No swimming, just sheep (uninvited)

Or this. [Which is easier?]

What sort of answers might one get here?

Annoying ad campaign from Amazon

In #MathsToday (Y5) tried to use the standard algorithm to subtract 11:05 hours from 15:00 hours. [We'd already solved it informally.] What happens when we have to 'borrow' 1 from the hours column? Does this give us 10 lots of 10-minutes or 6?

And another....

Variation on a theme (the task probably already exists...)

A quite lengthy proof. (Not sure how it connects to the hexagons!)

Gulp! What jolly pastime is this?

Sorry, rather cryptic. It twice uses symmetry, as outlined here:

Wow, that was a long, winding journey!

- and a couple more, one more obscure, one more obvious.

And here the perimeters are equal too!

Had another look last night at this stimulating book from 1997. "Students build mathematical understandings by reflecting and communicating" about challenging problems. Isn't it time we consigned Teaching for Mastery to history, alongside Gibb, Gove and Cummings, the ideologues who promoted it.

@brewdogofficial.bsky.social Cold beer? As opposed to Warm piss? Is this the worst beer in the world? Brewed for 12 year olds, perhaps? Sugar water with a bit of Ovaltine. Yuk.

Sainsbury's v Asda tissues - similar value? £1 v 80p 226 v 180 sheets 9.3 v 6.9 m²

van Aubel's theorem, the movie:

van Aubel's theorem:

Van Aubel's Theorem (mentioned in Paul's report): the purple lines are equal and at right angles. The diagram, based on an article by Yutaka Nishiyama, provides the skeleton of a proof (nicer than Paul's proof based on vectors (in my view!)).

Inspection (or 'cover up') is nice - but why not something more challenging, such as this?