Desmos

In Year 4 we've been getting pretty good at using coordinates. 4G showed what they could do with them on desmos.com:

Rod

Annie

Noémie

And there's more from Marie, James, Samyak, Lucia, Aditi, Gracia, Justus, Alonso and Gabby.

You could do one at home if you like. Samyak did. Here it is:

Here's a slideshow of some of our work:

Jumping frogs

We've been playing the game of Frogs.

The frogs can move into a space either by sliding to the next lilly pad or by jumping over the one frog next to them. You can play the game on the app below:

Full Screen and tablet version

We found the minimum number of moves necessary. We used desmos.com to make a graph of this. 

We looked at the points for 1, 2 and 3 frogs of each colour, and then estimated where the one for 4 frogs would be.

Samyak spotten a pattern in the numbers:

"You add odd numbers!"

Click on the image below to see the graph on desmos.com.

How old?

Today we remembered the time Mr Gregg asked, “There are 25 chairs and 5 tables in the classroom. How old is the teacher?”

It made Gracia ask this question to Mr Gregg:

Solitaire

We've been looking at the game of solitaire. 

You can get all different shaped boards.

Lots of us managed to get it down to just one counter left. Gabby was a bit of an expert!

Have a game online!

Towers of Hanoi

We've been investigating the Towers of Hanoi puzzle. Usually this is done with disks.

But we used Cuisenaire rods.

We started with just three rods.
The aim is to move a whole pile of rods, but in a certain way. Bigger rods can never be on top of smaller ones. You can only move the top rod in the pile. You can never put a big rod on top of a small one. You can only have one pile in a circle.


The challenge was, not just to do the puzzle, but to be able to find a way to write down what we had done. We found lots of different ways:

Then we moved onto four rods:

Some of us shared our ways with the whole class.

It was interesting to look at the pattern in the minimum number of moves necessary for different sized piles of rods at the start:

Here's a slideshow:

PS The next day Rod brought in his own Towers of Hanoi:

 We also returned to that doubling series (called "powers of two" - but we don't need to remember that, do we). Some of us kept on doubling for quite a while...

And we went the other way too: halving. We halved a circle: ½  ¼  ⅛...

Three Cats Three Dogs

There are 3 cats and 3 dogs, arranged like this:


Neighbouring pairs can swap.

How many swaps to sort them?

 

We used counters to investigate.

Cuisenaire rod equations

We've been using letters instead of numbers. All thee Cuisenaire rods have different letter names:

So, looking at some good examples from Annie, seven lots of g is the same length as seven lots of r plus seven lots of w. Or in letters:

7g = 7r + 7w

The two lines are the same length, so the two rows of rods are equal.

We made our own pairs of lines of rods.

 

Later on 4G tried a pair of squares like this.

4B built on top of theirs like this.

 

And we even tried cubes!

 

Here is James P's cube and the algebra to go with it:

 

 

Have a look at a slideshow of our work.