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What can you see? What do you notice? What questions can you ask?

More and More Buckets

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

It's a Fence!

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

What Shape?

Age 7 to 14
Challenge Level

We had some very thoughtful comments from William, Tilly, Neve, Holly, Poppy, Caitlin, Saba, Erin, Alice, Esme, Lauren, Charlie, Ollie, Jamie, Jack, Jay and Annie from St.Helen's C of E Primary School, Abbotsham.

Here is what Tilly, Neve, Holly and Poppy said:

First we played the game and ended up with asking five questions, which is what all of our scores were (strangely!).
After three games we realised some of the questions turned over most of the cards like: Is it a shape? or Does it have a right angle? but we didn't dicuss them until the end.

Some of the shapes are easier to find because a square has four right angles and is regular (it also has other properties).  In contrast we discovered that irregular shapes are much harder to find as they took up more questions.

Then we discused tactics (questions) how we could conqueror this game.  Here are some good and bad questions that could be used to help win this game in the fewest questions:

Best questions:                      
Is it a regular shape?             
Does it have right angles?         
Is it a shape?                     
Is it an angle?

Bad questions:
Is it a strange shape?
Does it have a right angle?
Is it an angle?

We have put some of the questions in both sections because they turn over cards, but not that many.

Caitlin, Saba, Erin and William said:

If you ask a good question you can remove lots of cards and it gets you closer to the correct shape or angle.
Observe the cards set on the table and think about the different questions that could eliminate as many cards as possible, such as 'does this shape have four or fewer sides?', because this can get rid of lots of cards: squares, rectangles, circles and triangles.
When you are down to a few cards left think about a question that relates to most of the cards turned up, so it leaves you with only very few so you can easily guess the right card.
Listen carefully to all questions asked so that you can relate to the cards left turned up and eliminate any cards, also so you don't repeat a question and waste your 12 guesses.

Alice, Esme and Lauren give us some good advice:

To begin with we just asked random questions, then we began to start asking sensible ones that made more sense. Our least amount of moves that we managed to find the shape with was four, and the most was 12.
We found it quite irritating when we asked too many questions and we were out.
Our team worked ok together, but some answers we didn't agree on which caused a bit of an argument, such as 'Is the shape irregular?'.
We also found that by asking if the shape was irregular, it got rid of most of the cards and narrowed it down to just a few. This made it easier to find which shape they had chosen. 
We really enjoyed this challenging task even though our team wasn't perfect. 
'Is it an angle?'  this got rid of fewer cards but was still useful.
Asking what the shape was directly lost us a lot of questions but came in handy at the end.

Ollie, Jamie and Jack wrote:

What we found easy:

After playing for a while we got used to all the cards and we would know what card was missing so we got the shape after one or two goes but sometimes when we chose a hard shape we took a lot longer.

What we found hard:

When we first started we found it hard because we were not used to playing with those cards  and we had not memorised the cards yet.
Also some of the cards like 'Square with corner cut out' and 'Isosceles right angle triangle' we were not used to so when we first saw those shapes we thought they were a bit obscure and odd.

Some of our questions:

The first question was usally 'Is it a shape?' or 'Is it a angle?' then we would ask if it is a triangle or if it is over 90 degrees.
Then a random question if we haven't guessed the shape yet, something like 'Has it got
fewer sides than a hexagon?'.  (That was one of Jack's questions).
Also Jamie said 'Has it got a line of symmetry?' but the shape was a hexagon so we
said 'It hasn't got ONE line of symmetry?' then he did realise that it must have more.

The tricky shapes:

The hardest shape was the 'Isosceles right angled triangle' because of its odd name - we all thought that it should have been 'a right angled triangle' or just an 'isosceles triangle' so because of its odd name when we picked it we never guessed the name.

The easy shapes:

The easiest shape was a square because of it being so common and a lot of people know the square also the rectangle because of it also being so common and used a lot in maths.
As well as them the other common shapes were easy like an equilateral triangle and a right angle.

Annie suggests:

The best questions to ask and get you through the game faster are: 'Is it a shape?' that gets rid of lots of cards.
Then another one is, 'Has it got fewer than four sides?' or 'Has it got more than three vertices?'.
'Has it got parallel sides?' and 'Has it got a line of symmetry?'are all good questions to ask so you can guess in the least number of questions.

Thank you all for your comments and suggestions.  I am sure they will be useful to others who want to have a go at this activity.