They're also only this year encountering irrational numbers, or decimals that continue so far, so that's an added challenge.

The model was square and side of square. I think one student was a bit confused, and while the others were beavering away with calculators, I got the cuisenaire rods out and we made squares and talked about what the square root was.

Hi Paula!

I think this could be quite an easy-to-grasp way of first encountering Pythagoras' Theorem...

and another

another

Today I told them about Pythagoras' Theorem. They all made a slant square on apps.mathlearningcenter.org/geoboard/, then added a right angle triangle to it, then put squares on the two other sides of the triangle. @mlcmath.bsky.social

We followed up by playing Square It! @nrichmaths.bsky.social
nrich.maths.org/square-it/

One of my students, M, asked what a square root is. So we gave over the lesson to that.

fraction bars with equal fractions

That's timely. We've just been using Polypad for fraction bars today.

Four squares divided up differently into parts, with annotations of students' responses to the queston Which one doesn't belong?

Which one doesn't belong? today with Grade 4.
We also talked about the fractions in each square. There was some debate about the yellow part in the bottom left. Some thought it was not ¼, but there was a proof it was.

Today we talked about different representations of the same growing pattern.

A king once ordered that a prisoner be killed. When the prisoner knew he was about to die, he became very upset. He shouted angry words in his own language, which the king did not understand. The king asked his helpers,“What is that man saying?” One kind and wise helper said, “He is saying that good people stay calm and forgive.” When the king heard this, his anger went away. He chose to forgive the prisoner and let him live. But another helper said, “That is not true! The prisoner was insulting you and saying bad things.” The king replied, “I like the kind lie better than the cruel truth. The lie saved a life, but the truth would have led to a death.”

Here is the fable, simplified for the students. It needed a couple of read-throughs. I asked the students what they thought the moral of the story might be.

around the image of the story, the students have annotated their thoughts

Lots of thoughtful observations

Chained Prisoners are Brought Before a King, a scene from the Gulistan of Sa'di | The Art Institute of Chicago c. 1550

It's this image, which I think is probably of the first story
www.artic.edu/artworks/131...

What do you see? What do you think? What do you wonder?
G4 students respond to a 16th century image of a 12th century fable by Sa'di of Shiraz.

Yes... of course... 🚲=🐟
I like this graph

Another pair's pattern involved doubling the previous term in the pattern and adding two. They kept going for ages, and also went back and fixed it when it went wrong.

These two (and some other pairs) were keen to go way beyond the points represented in the physical pattern

Entering the numbers in the pattern into a table in @desmos.com graphing

Over several desks students have created a growing pattern of connecting cubes. On the left the pattern has just one green cube, with each step towards the right, there's one more green cube.

Grade 4: Creating a growing pattern with multilink cubes

I think it was something like this one:

Today's Which One Doesn't Belong? with pairs of shapes
#wodb

Cuisenaire rods in a staircase formation, missing the brown rod. Alongside a picture in a book with a similar staircase with the same rod missing.

Making progress towards the picture on the book.

Me: Are you sure that staircase is right?

4yo: Yep, I’m making the picture in the book.

@simon-gregg.bsky.social

Yangma Tetrahedrons and the origami box that seems like its too small to hold them

Been teaching a flurry of polyhedron-related classes to artists, revisiting some favorite forms, like chiral boxes with deep diagonal pockets that @simon-gregg.bsky.social pointed me towards years ago, and the Liu Hiu solids via Jen Silverman www.jensilvermath.com/presentation... #mathart #mtobs

At least it was in some students' range of possibilities!

A glass pots with a large number of pebbles in it.

This was our estimation thing today - how many pebbles?
I let everyone feel the pot of pebbles first, as well as seeing the picture. None of us, including me, estimated a big enough number.
Lesson - There are more than you think - (?)

Student: 'We need to check it.'

Some more big factor trees, created in pairs, using a calculator where useful.

The finished factor three