# Noah

## Problem

*You might like to take a look at the poster for this task.*

Noah saw 12 legs walk by into the ark.

How many creatures could he have seen?

How many different answers can you find?

Can you explain how you found out these answers?

## Getting Started

How many legs do they each have?

What's the greatest number of creatures he could have seen?

What's the smallest number of creatures he could have seen?

## Student Solutions

The year 2 children in Laurel Class at Colman Infant School Norfolk worked on this problem and the teacher sent in the following:-

We decided to personalise the problem to fit in with our recent trip to Hickling Broad nature reserve In Norfolk. The children were amused by the idea that Noah might have visited Hickling and were all eager to getstarted.

As a class we looked at how there could be 2 creatures with 12 legs. We quickly established that there could either be 2 ladybirds or a spider and a mouse. We decided that this meant there would probably be more than one way of having three, four or five creatures etc. From then on the children worked with a partner. Some children worked on 12 legs and others on a more ambitious 18. They began by
drawing pictures of the animals and making a zig-zag book. This was a way into the problem that made sense to everyone. All the children worked enthusiastically. Having pictures also meant that the children didn't use the same combination of animals twice as is often the case when ust using numbers. (E.g. 6+4+2=12 and 2+6+4=12)

The idea was to work systematically to find as many different ideas as possible. Some children began to realise that they could use one answer to inform another. For example, if you had 1 Iadybird, 1 mouse and 1 duck you could work out 4 creatures by exchanging a mouse for 2 ducks or a duck for 2 snails.

Later in the week the children looked at their booklets and realised that there were still a lot more answers to find. They were encouraged to work in a more abstract way but could still refer to their numbers as spiders, ladybirds, mice, ducks or snails. This is where they really began to work systematically. They were keen to find as many answers as possible.

Thank you all at Laurel, sounds good

Rhea from Bablake Junior School sent in the following

There are lots of different answers for this. NRICH have put up a very open ended question!

Firstly, lets pretend that all the animals that Noah saw were all 4 legged animals. This would mean that Noah saw 3 animals. You do this by dividing 12 by 4, which is 3.

Secondly, lets pretend that all the animals saw were all 2 legged animals. This would mean that Noah saw 6 animals. You find this out by dividing 12 by 2, which is 6.

Thirdly, lets pretend that all the animals were 3 legged animals. You do this by dividing 12 by 3, which is 4.

Fourthly, lets pretend that that half of the animals Noah saw were 2 legged animals, and the other half were 3 legged animals. To find out the half that were 2 legged, you need to find out what half of 12 is, which is 6. You then have to divide 6 by 2, which is 3! 3 of the animals Noah saw where 2 legged animals. Then, you need to find out how many animals were 3

legged. You do this by dividing 6 (half of twelve: 12 divided by 2) by 3, which is 2. 2 of the animals Noah saw were 3 legged animals.

This is all I have got time for, so make sure you come up with some more solutions for NRICH! Hope you understood 4 of my solutions, thank you for reading this! Bye!

She entered a second submission saying:-

Well, I just entered a solution but I forgot to give examples of some animals Noah could have seen.

For a two legged, maybe birds, like: robins, pigeons, blackbirds, finches, blue tits, doves or swans.

For 4 legged: lion, dogs, cats, tiger, hedgehog, fox, wolf and more. These are examples, but there could be a lot more! Read my other solution on how to work on the 4 legged and two legged animals. It will be very helpful, hopefully you will read it and even make a solution your self! Good luck, hope you have fun on NRICH!

Olivia also from Bablake Junior sent in this solution:-

There are definitely lots of different ways to solve this! Lets start and pretend that all the animals Noah saw were 1 legged animals. In this very easy case, all you need to do is divide 12 by 1, which is of course 12. This means that if all the animals Noah saw were 1 legged animals, there would be 12 of them. I'm sorry about this, but maybe you know some 1 legged
animals? Now lets pretend that all the animals Noah saw were 2 legged animals. In

this case, all you need to do is divide 12 by 2, which is 6. If all the animals Noah saw were 2 legged animals, there would be 6 of them. Now lets think what types of animals they might be. Probably birds- robins, blackbirds, pigeons- maybe even humans- there are lots more!

Now lets pretend that all the animals Noah saw were 3 legged animals (I know there might not be 3 legged animals, but lets pretend there is!) Now all you have to do is divide 12 by 3 which is 4. If all the animals Noah saw were 3 legged animals, there would be 4 of them. Now lets think what type of animals they might be. I'm sorry about this, but I don't know any 3 legged
animals, maybe you do? Now lets pretend that all the animals Noah saw were 4 legged animals. In this case, all you need to do is divide 12 by 4, which is definitely 3. So,

if all the animals Noah saw were 4 legged animals, there would be 3 of those animals. Different types of 4 legged animals are dogs, cats, hedgehogs, horses, pigs, cows and lots, lots more! Now lets pretend that all the animals Noah saw were 6 legged animals. (I

know these are probably not real, but lets just pretend, okay?) All you have to do now is divide 12 by 6, which is 2. If all the animal Noah saw were 6 legged animals, there would be 2 of them. They are all the basic solutions, but see if you can mix 2 legged animals and 4 legged animals. There are loads of answers but these are the basics. Hope I've helped, thank you for
reading this! Hope you have fun on NRICH!

The teacher of Year 1 at Bute House Prep School sent in the following:-

Year 1 had a lot of fun investigating how many animals could have gone into the Ark if Noah had counted 12 legs. They thought of their own line of inquiry within this problem and so some looked at whether they could have every number of animal from 1-12 with 12 legs, others looked at how many ways they could have groups of animals with the same number of legs
making 12, while others investigated how they could best record their findings

systematically. Here are a few of their discoveries :-)

Amelia and Olivia found a number of ways of counting 2,3 and 6 animals, although they realised they couldn't have a rabbit and a fly as this wouldn't be enough legs

Annabelle and Julia found solutions for 3, 4 and 6 animals.

Claudia explored which combinations of the same number of legs would work to add to 12.

Beatrix and Mariana decided that a snail had one leg, a bird 2, a horse 4, an insect 6 and a spider 8 and worked from there. They found solutions for 2,3,4,5,6,11 and 12 animals.

Sophie realised that if you used snails it was possible to make up lots of animal numbers eg 4 birds and 4 snails = 8 animals with 12 legs. 6 snails and 3 birds would be 9 animals and 12 legs.

The girls thought 1 animal would be impossible!

Children at Thorpe Primary in Peterborough created a display of their work. Thank you to their teacher Mr Condon for sending in these photos of the display:

Thank you all for these very detailed accounts of your work. maybe some would go further and consider a larger number of legs seen by Noah. What is there would be only two types of animals and the same numbers of each, which Rhea used.

## Teachers' Resources

### Why do this problem?

Cross curricular links can be made by using the story of Noah and the ark as an introduction. Considering creatures with one 'leg' such as slugs and snails, no legs such as snakes and all the other possibilities is great fun and provokes interesting responses from the children. You may be surprised by their ingenuity.

### Possible approach

- Ask for suggestions and encourage the children to come to the board and draw their animals. Count the number of creatures each child draws and discuss who has drawn the least, the most, the same as ... etc.
- Give the children playdough and 12 equal lengths of straw each so that they can make the creatures - and put them into groups of 12 legs for a display.
- Let each child draw a picture, write the number sentence below it (eg $6 \: + \:4 \; + \; 2 \; = \; 12$) and make them all into a class zig-zag book - Our Story of Twelve.
- Give each group of children a different number of legs to investigate and ask them to make their own group zig-zag book.

### Key questions

### Possible extension

What if there were more legs... 18, 24, 19 ... or fewer?