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Have a think about these questions, or you might like to make up some of your own:

1. What number should be where the head of the seagull is?

2. What number should be where the mouth of the crab is?

3. How far up is it from the head of the shrimp to the mouth of the shark?

4. How far from the surface is the eel's mouth?

5. How high above the sea level is the seagull's beak?

6. How much higher is the seagull's beak than the seahorse's mouth?

How did you arrive at your answers? Did you write anything down to help you?

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Sea Level printable sheet
What can you see in this picture? You can click on it to make it bigger if you would like a closer look.

There are black markings all the way up the lighthouse right to the very top, and on the rock that the lighthouse is built on, going down to the sea bed. These markings are 1 metre apart.

We will call sea level '0' and then we could think of the lines as representing positive numbers going upwards and negative numbers going down to the sea bed.

In this task, we are going to look at where the mouths of each of the different animals are. This will allow us to see how deep they are compared to each other, or what distance apart they are.

For example, the seahorse's mouth is 1 metre deeper than the mouth of the blue and yellow fish.

Have a think about these questions, or you might like to make up some of your own:

1. What number should be where the head of the seagull is?

2. What number should be where the mouth of the crab is?

3. How far up is it from the head of the shrimp to the mouth of the shark?

4. How far from the surface is the eel's mouth?

5. How high above the sea level is the seagull's beak?

6. How much higher is the seagull's beak than the seahorse's mouth?

How did you arrive at your answers? Did you write anything down to help you?

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The picture shows a lighthouse and some underwater creatures. Can you work out the distances between some of the different creatures?

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exploring patterns and noticing structures

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These pictures show squares split into halves. Can you find other ways?

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Here's a sort of code you may have seen before:

If you exchanged each letter of your name for a number, what would the code be?

Mine is Lynne so my code is 1 4 1 1 1 . The numbers add up to 8 which is not much!!

What is your name worth using this code?

Try some other names - what names are worth the most and which are worth the least?

Are longer names always worth more?

Can you work out why certain letters are worth a lot and why others are only worth one?

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Letters have different values in Scrabble - how are they decided upon? And would the values be the same for other languages?

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Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?

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Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair.

Now try it with four pairs of socks. Is there more than one way to do it?

Click here for a poster of this problem.

Printable NRICH Roadshow resource.

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Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Now try it with four pairs of socks. Is there more than one way to do it? Click here for a poster of this problem. Printable NRICH Roadshow resource.

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What Was in the Box?

A number in a little box is put into a wonderful big box that adds something to the number and then a new number comes out at the end:

The first time this happens, 10 is put into the little box, so what happened in the big box to get the answer in the picture above?

Now three more boxes with new numbers in, go into the wonderful box one at a time. It still does the same as before.

So, what were these three new numbers that went in and do you have a better idea of what has been going on - remember it was the same for all four numbers that went in.

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Imagine four new boxes now (with new numbers in) and the wonderful box does a new and different add or take away this time. For one of these boxes the number 10 was put in. The numbers that come out are these:

What could have happened? How did you work these out?
Discuss with others and see if there were different ways that you found the answers.

Why do this problem?

Of course this problem is rather like a function machine, but it can be more interesting and is easily extended to challenge a wide range of pupils. It could be used to introduce children to the idea of addition and subtraction, and offers great opportunities for learners to record in different ways.

Possible approach

Introduce the class to just one number going in and give them one outcome to start with so that they understand the process. Then, gradually increase the number of numbers going in until you reach four, as in the problem. Your own examples can be adjusted in complexity according to the level of your pupils.

Once learners have had some time to work on the first part of the problem in pairs, ask them to share their ways of working with the whole group. Look out for those who give good reasons for choosing particular methods.

You may also like to draw attention to different methods of recording that you observe. Some children may have drawn pictures whereas others may have created calculations.

Key questions

What might have gone on in the box to get this number answer?

Could that have produced the other answers too?

Possible extension

Pupils who have gone onto multiplication and division and may be moved onto further thinking by going to What's in the Box?.

Possible support

For just one number going in you can use counters and a cloth. Show the counters and then cover them with the cloth. Secretly add the required extra number of counters under the cover before revealing them to the pupil. Then a number of probing questions can be asked: How many counters now? What must have happened under the cover?

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A number in a little box is put into a wonderful big box that adds something to the number and then a new number comes out at the end: The first time this happens, 10 is put into the little box, so what happened in the big box to get the answer in the picture above?

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Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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There are three baskets, a brown one, a red one and a pink one, holding a total of ten eggs.

The Brown basket has one more egg in it than the Red basket.

The Red basket has three fewer eggs than the Pink basket.

How many eggs are in each basket?

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There are three baskets, a brown one, a red one and a pink one, holding a total of ten eggs. The Brown basket has one more egg in it than the Red basket. The Red basket has three fewer eggs than the Pink basket. How many eggs are in each basket?

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This activity focuses on similarities and differences between shapes.

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This challenge is about chocolate. You have to imagine (if necessary!) that everyone involved in this challenge enjoys chocolate and wants to have as much as possible.

There's a room in your school that has three tables in it with plenty of space for chairs to go round. Table $1$ has one block of chocolate on it, table $2$ has two blocks of chocolate on it and, guess what, table $3$ has three blocks of chocolate on it.

Now ... outside the room is a class of children. Thirty of them all lined up ready to go in and eat the chocolate. These children are allowed to come in one at a time and can enter when the person in front of them has sat down. When a child enters the room they ask themself this question:

"If the chocolate on the table I sit at is to be shared out equally when I sit down, which would be the best table to sit at?"

However, the chocolate is not shared out until all the children are in the room so as each one enters they have to ask themselves the same question.

It is fairly easy for the first few children to decide where to sit, but the question gets harder to answer, e.g.

It maybe that when child $9$ comes into the room they see:

$2$ people at table $1$

$3$ people at table $2$

$3$ people at table $3$

So, child $9$ might think:

"If I go to:

table $1$ there will be $3$ people altogether, so one block of chocolate would be shared among three and I'll get one third.

table $2$ there will be $4$ people altogether, so two blocks of chocolate would be shared among four and I'll get one half.

table $3$, there will be $4$ people altogether, so three blocks of chocolate would be shared among four and I'll get three quarters.
Three quarters is the biggest share, so I'll go to table $3$."
Go ahead and find out how much each child receives as they go to the "best table for them". As you write, draw and suggest ideas, try to keep a note of the different ideas, even if you get rid of some along the way.

THEN when a number of you have done this, talk to each other about what you have done, for example:

A. Compare different methods and say which you think was best.

B. Explain why it was the best.

C. If you were to do another similar challenge, how would you go about it?

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This challenge is about chocolate. You have to imagine (if necessary!) that everyone involved in this challenge enjoys chocolate and wants to have as much as possible. There's a room in your school that has three tables in it with plenty of space for chairs to go round.

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Using the picture of the fraction wall, can you find equivalent fractions?

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The aim of this game is to match pairs of cards.

Click on a card in the interactivity below to turn it over. Then click on another one. If the two cards match, they will stay face-up. If the two cards do not match, they will return to being face-down.

The game ends when all the cards have been matched in pairs.

How do you know when a card matches another card?
Can you remember where particular cards are to help you match the pairs?

We would love to hear about the strategies you use as you play the game.

You may like to explore these alternative versions of the interactivity:

Play with a scoring system - you start with 100 points, lose 10 points whenever you turn over cards that don't match, and add 50 points whenever they do match.

Play against the clock - can you beat your personal best?

Play with face-up cards - the cards are all face-up at the start so you can focus on the maths rather than the memory aspect of the game.

Here is the set of cards for this game which you can print off to play away from the computer if you wish.

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Can you find different ways of showing the same fraction? Try this matching game and see.

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The large rectangle above is divided into a series of smaller quadrilaterals and triangles. Each of the shapes is a fractional part of the large rectangle.

Can you untangle what fractional part is represented by each of the ten numbered shapes?

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The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

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How will you record the triangles you've made? You might like to print off this sheet to use.
You could try drawing triangles which have a side made by joining two pegs next to each other. How many different triangles can you make in this way?
How will you know when you've got them all?

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How many different triangles can you make on a circular pegboard that has nine pegs?

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The class were making number patterns and then making graphs of them.

Several children had plotted graphs of the "times tables". They made good-looking straight lines.

Tom had started on the six times table but had then decided to do something more interesting. He had made the triangular numbers with counters last year. That was a better idea, he thought.

So he started to put them on the same graph paper as the unfinished six times table.

"It's not a very good straight line," he remarked to Andy who was sitting next to him.
"I think it's going to cross the six times line," answered Tom, "But you'll have to make a lot more of both of them. I'm going to try square numbers, I bet the tables one will cross that!"

Does the graph of the triangular numbers cross that of the six times table?
And if it does, where?

Does the graph of square numbers cross those of the times tables?
And if it does, where?

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The class were making number patterns and then making graphs of them. Several children had plotted graphs of the "times tables". They made good-looking straight lines. Tom had started on the six times table but had then decided to do something more interesting. He had made the triangular numbers with counters last year.

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Building Blocks

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

What do they look like from different positions? Please send us photographs or pictures of your models.

Working from 2D representations to 3D can be quite problematic at this level, and this problem gives children experience of doing just that, as well as then possibly transferring back to 2D. The activity provides a great opportunity to develop children's familiarity with positional language, for example behind, in front, to the left, to the right, above/on top, below/underneath etc.

For this activity, you'll need plenty of multilink cubes. Display the picture on the screen of the interactive whiteboard, or project it onto an ordinary board. You could start with one of the shapes, for example the yellow one, and ask children to describe it. Encourage them to talk about the number of cubes used and their relative positions. Some learners might say it looks like an 'L' shape.

Ask children to make the yellow shape, individually or in pairs, and they can compare the shapes to check they're the same. Depending on your class' experiences, you could then challenge them to draw their shape on isometric paper , sketch their shape on plain paper, or just put their shape on the table in front of them so that it looks different from the picture in the problem.

The other shapes could be tackled in similar ways and you could take some photographs of the results for display alongside a print-out of the problem itself.

How many cubes will you need for that shape?

Can you describe how they are joined together?

Some pupils might like to try The Third Dimension problem which is much more challenging and requires drawing on isometric paper.

It may be useful to have each of the shapes made up yourself prior to the lesson so that you could show them to the group. Children are likely to find it easier to replicate a shape if they can see a 'real' version rather than just a picture.

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Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

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Christina from Marborough Primary, London has given this one some thought and made the sensible suggestion of trying to find all the symmetrical patterns with one coloured square, then with two squares, then three, then four. That's just what Tom has done below.

Tom was very careful in trying to make sure that he found them all. First, he looked for patterns with no coloured squares. Of course, there's only one of those:

Then he looked for patterns with one coloured square. Here are the patterns he found:

Next he looked for patterns with two coloured squares. He had to be a bit more careful here, to make sure that he didn't miss any. First of all, he coloured in the top left square. Then he wondered whether he could find any patterns with this square coloured where the line of symmetry was vertical. He found this one:

but that was the only one. Then he looked for patterns with this square coloured where the line of symmetry was horizontal, but he came up with the same one again (rotated, of course). Then he looked for ones where the line of symmetry was diagonal. Here are the two patterns he found:

These were the only symmetrical patterns with a corner square shaded. Next he shaded the top centre square and looked for patterns with a vertical line of symmetry. Here's what he found:

He noticed that he wouldn't get any new patterns by looking for ones with horizontal lines of symmetry, so he looked for patterns with a diagonal line of symmetry. This is the only one he found:

He used a similar system to find the symmetrical patterns with three or four shaded squares. Here's what he found:

Finally, Tom noticed that really these told him all of the symmetrical patterns, because he could imagine a coloured grid where the white squares were the ones that had been shaded, and these would give the patterns with five, six, seven, eight or nine shaded squares.

So Tom found 62 symmetrical patterns in all.

Children from Kellett School in Hong Kong, noticed that Tom had missed out one of the patterns. Here is the image they sent:

So that makes a total of 64 possible solutions.

Thank you for your all your ideas everyone.

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How many symmetric designs can you make on this grid? Can you find them all?

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You may also like

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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md angles polygons and geom proof - stage 3

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There are a number of coins on a table.

One quarter of the coins show heads.

If I turn over two coins, then one third show heads.

How many coins are there altogether?

Once you have thought about how you would begin to solve this problem, click below to see how other children began to work on it:

Freddie said:

I got some coins to try out ways to make it work.

Vasanthi and Francis said:

We noticed that there were more heads after turning over two coins.

Hussam and Suzy said:

First we thought of what number could have a quarter and a third which are whole numbers.

Did you start the problem in the same way as any of these children?
What do you think about each method?

Now continue to work towards a solution to the problem. You could choose to use Freddie's, or Vasanthi and Francis', or Hussam and Suzy's method.

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There are a number of coins on a table. One quarter of the coins show heads. If I turn over two coins, then one third show heads. How many coins are there altogether?

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How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?

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Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?

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I was looking at the number plate of a car parked outside my house - S208VBJ.

Using my special code S208VBJ adds to $65$.

They all also add to $65$ using my code!

Using the code you treat every character, that is a digit or a letter, as separate.

Numbers are simply added together so that, in the first number plate $208$ is $2 + 0 + 8 = 10$.

Letters are translated into numbers in an organised and systematic way. That means that if you know the value of F and H you not only know the value of G, but can easily work out all the rest of the alphabet.

Can you crack my code and use it to find out what both of these number plates add up to?

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I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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Break it Up!

You have a stick of seven interlocking cubes (or a tower of seven Lego blocks). You cannot change the order of the cubes.

You break off a bit of it leaving it in two pieces.

Here is one of the ways in which you can do it:

Here is another way you can do it:
In how many different ways can it be done? Now try with a stick of eight cubes: What about with a stick of six cubes?

What do you notice?
Now predict how many ways there will be with five cubes.

Try it! Were you right?

How many ways with 20 cubes?
Will your noticing always be true? Can you create an argument that would convince mathematicians?
Why do this problem?

This problem encourages learners to connect geometrical and numerical ideas, which will help them to generalise and prove. The task makes a very good introduction to algebraic thinking, however, it also has a very accessible starting point so everyone can begin.

Possible approach
This problem featured in an NRICH Primary webinar in March 2022.
You could start by giving everyone in the group some interlocking cubes (or Lego blocks) and asking them to make a stick (or tower) of seven. Ask them to break their stick into two pieces and hold one piece in each hand. Ask how they have done this and record the various ways on the board. (Try to be guided by the group in terms of how you record. Perhaps learners would like you to sketch the two resulting sticks; perhaps they are happy for numbers to be recorded; some may wish to include an addition sign...) Then enquire if there are any other ways that it could have been done. How will they know that they have found all the different ways?

At this point, it might be useful to record each different solution on a different piece of paper, as you can then move them around the board (or table, or floor) to impose some sort of order on them. (Alternatively, you could gather the sticks/towers themselves.) This will help reveal which, if any, have been omitted. This is the basis of working systematically.

Some learners may suggest that 2+5 is the same as 5+2. Numerically they are identical, but the context is also important. In this case, because we are using seven differently coloured cubes or Lego blocks, splitting into 2 and 5 will look different from 5 and 2.

After this introduction, learners could work in pairs on finding the number of ways that sticks of six and eight cubes can be broken into two pieces. Look out for pairs who record their findings clearly, keeping track of what they have tried, and using their recording to help them know whether they have found all possibilities. You could share some of these recordings in a mini plenary if appropriate. Try to encourage learners to use any resources they choose.

After a suitable length of time, gather everyone together again. Encourage learners to explain how they knew they had found all the ways in each case. Make a note on the board of the number of ways for six cubes, seven cubes and eight cubes. What do they notice? Can they use what they notice to predict the number of ways of breaking up twelve cubes into two pieces, for example? Work together as a whole group to find the ways practically, to verify their conjecture.

Is the number of ways of breaking a stick of cubes into two pieces always going to be one less than the number of cubes? Explain that mathematicians aren't usually satisfied with finding a few examples, they want to build a convincing argument that something is always true. Can the class help create such an argument?

Key questions

How are you going to record what you have done?
How do you know you have found all the ways of breaking it into two pieces?
Can you see a connection between the total number of cubes and the number of ways you can break the stick into two pieces?
How many ways do you think you can break 20 cubes?
How could you express that "for any number"?
How would you convince a mathematician that this is always going to be true?

Possible support

Learners might find it helpful to use interlocking cubes or Lego blocks and to record on squared paper with coloured pencils/pens.

Possible extension

If all the cubes are the same colour, a split of 4 and 2 will look the same as a split of 2 and 4. Challenge learners to consider how many ways there are of splitting 6 cubes now. Can they predict how may ways there will be with any number of cubes?

Then they could try a different problem in which generalisation is required such as Sticky Triangles.

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In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

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Strike it Out

Watch the video below which shows two people playing the first few turns of a game.

What do you notice?
What do you want to ask?

If you can't access YouTube, here is a direct link to the video.

Watch the video a second time.

Can you work out how to play the game?
What do you think the rules might be?
How might someone win the game?

If you are unable to view the video, you could click through this powerpoint presentation, which also demonstrates how to play. Alternatively, the rules of the game are hidden below.

The aim of the game:
The player who stops their opponent from being able to go wins the game.

The first player chooses two numbers on the line and crosses them out. Then they circle the sum or difference of the two numbers and they write down the calculation.

For example, the first player's turn could look like this:

The second player must start by crossing off the number that Player 1 has just circled. They then choose another number to cross out and then circle a third number which is the sum or difference of the two crossed-off numbers. Player 2 also writes down their calculation.

For example, once the second player has had a turn, the game could look like this:

Play continues in this way with each player starting with the number that has just been circled.

Once a number has been used in a calculation, it cannot be used again.

The game ends when one player cannot make a calculation. The other player is the winner.

It's your turn!
Try playing the game against someone else a few times to get a feel for it.
Do you have any good ways of winning?

Now it's time to work together with a partner, rather than against them.
Try to create a string of calculations that uses as many numbers as possible on the 0-20 number line.
Is it possible to create a string of number sentences that uses all the numbers on the 0-20 number line? Why or why not? How would you convince a mathematician?

Once you've had a good think about it, you may like to look at this proof that has been scrambled up.
Can you rearrange it into its original order?

If you would prefer to work away from a screen, you could print off, cut up and rearrange the statements. (This sheet includes three copies of each statement.)

What about the 1-20 number line? Is it possible to create a string of number sentences that uses all the numbers on the 1-20 number line? Why or why not? How would you convince a mathematician?

Again, once you have thought about it, you may like to look at this proof that has been scrambled up.
Can you rearrange it into its original order?

If you would prefer to work away from a screen, you could print off, cut up and rearrange the statements. (This sheet includes two copies of each statement.)

Why play this game?

This game offers an engaging context for practising addition and subtraction, but it also requires some strategic thinking. The collaborative version provides a fantastic opportunity for learners to reason mathematically, and to experience proof.

Possible approach

Show the video to the group, explaining that there is no sound as such and inviting them to think about what they notice and what they want to ask. (You could click through this powerpoint presentation one 'go' at a time if you cannot access the video.) Having watched it once, give them an opportunity to talk to a partner and then collect some of their questions and 'noticings' on the board. Encourage other members of the class to respond rather than you. Before playing the video a second time, explain that as they're watching, you'd like them to consider what the rules of the game might be. Mediate a discussion following the second viewing so that the class comes to an agreement about the rules of the game and how a player wins.

Give children time to play several games in pairs so they get a feel for it, perhaps on some printable number lines. Share some of their strategies and then ask them whether they think it might be possible to cross off all the numbers in a game. Give them time to work co-operatively with their partner on this challenge before bringing them together again to see what they have found out. You could find out whether, for example, any pairs have used more than half the numbers. More than fifteen numbers? Given enough time, do they think they could find a way to use all the numbers? Some will have realised that it is impossible to cross off zero - encourage them to explain why this is the case. To give them an example of the kind of reasoning that constitutes a proof, you could share this proof sorter with them. It includes all the steps to create a watertight chain of reasoning, but muddled up. The challenge is to put the statements in the correct order. (If you would prefer learners to be working away from a screen, you could print off and cut up copies of the proof sorter statements.)

Learners could then investigate whether it is possible to use all the numbers if the number line goes from 1 to 20 instead. Give them chance to explore this new scenario in pairs. Many will be able to reason that it is still not possible due to there being an even number of numbers in total. Again, you could work on this proof sorter as a class, ordering the statements to help learners get to grips with the idea of proof. (Alternatively, you could print off the proof sorter statements.)

Key questions

Have you found any good ways to beat your opponent?

Can you cross out all the numbers in one game? How do you know?

What is the biggest number of numbers you can cross out?

Possible support

If children are struggling with the calculations, a shorter number line may be appropriate so focusing on a number line to 10 still elicits many of the same ideas about possibilities and outcomes as well as the way in which the operations of addition and subtraction work on a limited set of numbers.

Possible extension

Children can suggest their own 'what if ...?' questions, for example:

What if we could use multiplication/division?

What if we drew a longer number line?

What would happen if we included decimal numbers in our number line?

What if the number line extended beyond zero to negative numbers?

The possibilities are endless but do make sure they try out their new version of the game to check it is a 'good' game.

The Highland Numeracy Team in Scotland kindly shared with us some ideas for adapting Strike it Out. Some variations include the use of concrete materials suited to the version of the game, such as tens frames, Dienes, or place value counters.

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Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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It's a race against the clock to answer 30 questions.

What are you waiting for? Quickly answer the questions below. This is level 1: Addition of single digit numbers. You can earn a trophy if you get at least 25 answers correct and you do this activity online at www.transum.org/go/?to=beat .

Is the clock too fast for you?
Did you make some mistakes?
Would you like to try again?

Start Again

© Transum Mathematics WWW.TRANSUM.ORG

Description of Levels

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Level 1 - Addition of single digit numbers

Level 2 - Subtraction of numbers less than 20

Level 3 - Addition and subtraction of numbers less than 30

Level 4 - Multiplication facts up to twelve times twelve

Level 5 - Division facts in tables up to twelve.

Level 6 - Mixed Multiplication and Division

Level 7 - All four operations, two terms

Level 8 - All four operations, two terms, harder

Level 9 - All four operations, three terms

More on Mental Methods including lesson Starters, visual aids and self-marking exercises.

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Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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It's a race against the clock to answer 30 questions.

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Unlimited, unique questions to make practice engaging.

Fun awards to keep your students motivated!

Intuitive, visual reports to track progress.

Adaptive skills to support and challenge every learner.

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IXL is a maths and English practice tool for educators and families that adapts to a student’s individual level of proficiency and includes achievement awards and progress reports. Non-members are always welcome!

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In Teddy Town, teddies are either red or yellow and they live in red or yellow houses. There are 4 teddies - 2 red and 2 yellow, and 4 houses - 2 red and 2 yellow.

Can you match each teddy to a house so that the 4 pairs are all different from each other?

Imagine now that there are 3 different colours of teddies and houses - red, yellow and blue. In Teddy Town there are now 9 teddies and 9 houses. All 9 pairs of houses and teddies are different from each other.

Here is a map showing Teddy Town:

The streets are very special. If you walk along a street from east to west, or west to east, all the houses are a different colour and the teddies living in the houses are a different colour too. The same is true if you walk along the streets in a north-south or south-north direction.

In other words, looking at the map grid, each row and column must have different coloured houses and different coloured teddies.

Can you arrange the houses and teddies on the map grid, making sure that all 9 pairs of houses and teddies are different from each other?

Teddy Town is expanding rapidly as green teddies move to the area and green houses are built. Now there are 16 teddies and 16 houses.

There are 16 different ways to combine the teddies and houses. How could these 16 households be organised on the map now? Remember that in each row and column there must be both different coloured houses and teddies.

Now... yes, you've guessed it. Another colour of teddy bear has moved to Teddy Town. As well as red, yellow, blue and green teddies there are now purple teddies. Of course, this means that purple houses will have to be built. So, now in Teddy Town there are 5 of each colour bear, making 25 teddies in all, and also 25 houses, again 5 of each colour.

Can you make the 25 different combinations of teddy and house now? Arrange these on the street map below in the same way as before:

Teddy Town is becoming very overcrowded! However, there is just enough room for some turquoise teddies to join. Living there now are 36 teddy bears: 6 red, 6 yellow, 6 blue, 6 green, 6 purple and 6 turquoise. There are 36 houses for them to live in: 6 red, 6 yellow, 6 blue, 6 green, 6 purple and 6 turquoise.

Make the 36 combinations of teddies and houses. Do you think it will be possible to put these 36 combinations in the street grid? Maybe it won't be. Have a go!

Now, look back at what you have done and ask yourself some of these questions:

Was it easier to arrange the combinations in some of the grid sizes compared with others?

Why do you think this is?

What was your strategy for solving the arrangement puzzle each time?

What would happen if the two diagonals on the map also had to have different coloured houses and different coloured teddies? Can you solve the problem for each street plan now?

Printable NRICH Roadshow resource.

Acknowledgements

This activity is based on a Bernard's Bag problem from December 1997 called Tea Cups. The idea for the teddies came from Andrew Massey who is an Advisor for Worcestershire County Council. Thank you!

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There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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Fair Feast

Here is a picnic that Petros and Michael are going to share equally.

Can you tell us what each of them will have?

In this problem, the familiar context of sharing provides an opportunity in which to explore fractions in a variety of ways. The task involves finding fractional quantities of whole numbers as well as dividing a unit into equal pieces.
You may be interested in this report, originally published on the NCETM website. It outlines a collaborative project between six primary schools, intended to develop fluency and understanding of fractions through rich mathematical tasks. All participating schools used this Fair Feast task with their learners. (The two appendices can be foundhere and here.)
You may want to create your own 'picnic' consisting of empty boxes and cartons, or the real thing. Alternatively, the problem could be introduced by displaying the photo on the board. No matter how you present the food to be shared, you could contextualise the picnic by telling a 'story' to your class.

Allowing learners to talk, perhaps in pairs, about the solution will give them a chance to articulate what they know about halving. Walking around the room listening to their discussions may be a good assessment opportunity for you.

When you come to talking about the solution as a whole class, it would be helpful to be able to physically share the picnic, if using real food or models. If you're using the photograph, it would be good to be able to annotate it, for example on the interactive whiteboard, so children could come up and group/split the images of the items. Encourage pupils to explain how they know each part of the picnic has been shared equally, listening out for responses which refer to the two parts being exactly the same. You can discuss different ways of describing the share of pizza - two slices, two quarters, one half ...

How many/much of these/this is there altogether?

How would we share that fairly between two?

What would happen if the picnic was split between four children instead of two? Are there other numbers of children that it would be easy to split the picnic for?

Some pairs might find it easier to have a print out of the photo to work from. Having items to share physically will make this problem more accessible.

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Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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How can these shapes be cut in half to make two shapes the same
shape and size? Can you find more than one way to do it?

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Noah saw 12 legs walk by into the Ark. How many creatures did he see?

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The Irish primary education system aims to provide a holistic education to enable children to live their lives to the full and to realise their potential as unique individuals.

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PMC - Oide - Welcome to the Primary Mathematics Curriculum Hub

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PMC - Oide - Welcome to the Primary Mathematics Curriculum Hub

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Welcome to our Micro Maths page, designed for passionate teachers seeking dynamic resources.

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Addition and Subtraction Word Challenge Cards 2nd Class

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Addition and Subtraction Word Challenge Cards 2nd Class

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QR CODE

Scan this on mobiles and tablets to quickly open this web page.

Hit the Button is an interactive maths game with quick fire questions on number bonds, times tables, doubling and halving, multiples, division facts and square numbers. The games, which are against the clock, challenge and develop mental maths skills. An untimed, practise mode is available in our Hit the Button app along with lots more extra features.

The activities can be matched to appropriate mathematical ability. Regular use of Hit the Button can help students to sharpen their recall of vital number facts in a fun way and learning multiplication tables need not be boring.

AGE

6-11 Years

SUBJECTS

Maths Times Tables Division Number Bonds Doubles Halves Square Numbers

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Hit the Button - Quick fire maths practise for 6-11 year olds

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Quick fire questions on number bonds, doubles, halves, times tables, division facts and square numbers against the clock. Superb!

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ABCya! * Adventure Man and the Counting Quest

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ABCya! * Adventure Man and the Counting Quest

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Join Adventure Man as he races to find the hidden treasure before his arch nemesis, the sinister Mr. Thief gets to it first!

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Ducky Race Subtraction is an educational multi-player racing game for kids to practice subtraction. How quickly the student correctly answers the subtraction problems determines how quickly the ducky will go. The student with the fastest rate of correct answers will win the race.

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Hit the Button

Quick fire questions on number bonds, doubling, halving, times tables, division facts and square numbers against the clock. Brilliant for improving mental maths and calculation skills, but particularly times tables either up to 10 or up to 12 times.

Subtraction Grids

Can you meet the challenge to see how many subtraction calculations you can do in two minutes? There are different levels and you can choose either one or two missing numbers to make your number sentence correct.

Mental Maths Train

Mental Maths Train is a maths game which focuses on the essential vocabulary of addition, subtraction, multiplication and division. A multiple choice game which can give children confidence in the four arithmetic operations.

Caterpillar Ordering

A flexible game for ordering numbers and for number sequences. Fantastic on an interactive whiteboard. Levels range from ordering and sequencing numbers to 5 up to decimals.

Rocket Rounding

A multiple choice game involving rounding numbers to ten, a hundred and to a whole number. There are two options, one with a number line and the other more difficult level, without one.

Multiples and Factors

A multiple choice game with two game modes. In the first you need to identify the Lowest Common Multiple and in the second the Highest Common Factor. Questions increase in difficulty depending on accuracy

Shape Patterns

Shape Patterns is a shapes sequencing game. Complete the pattern of different coloured 2D shapes. There are three levels of difficulty.

Teddy Numbers

The Teddy Numbers game can help you to learn numbers to 15. Learn the digits and words for the numbers and it game can help you learn to count too.

2D Shape Reveal

An interactive whiteboard resource to help with the teaching and learning of the names and properties of 2D shapes.

Arrow Cards

Build a two or three digit number using the cards. Click the button to see how it is written. This site can help children understand place value. It is suitable for use on an interactive whiteboard.

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Searchable site of thousands of quality teaching resources, interactive resources, homework, exam and revision help. Useful for teachers, pupils and parents.