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Age 7-11

Positives:
- interesting project related to a real life study from 1986 years ago
- celebrates 900 years since original domesday book - could be taught cross curricularly with a link to history/geography/English
- opportunity for children to create their own study as a class
- good differentiated reasoning questions
- possibilities for group work/group discussion
- lots of opportunities to make this a practical project that last over the course of a couple of lessons

Potential issues:
- the data may seem quite daunting for children who are lower ability/less confident
- the data isn’t presented in a way that is the clearest or how children may have seen data represented before - may cause some misconceptions

https://nrich.maths.org/7554

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Age - 7 to 11.
Positives:
Good opportunity for group work or individual problem solving.
Introducing making shapes with different resources.
Can be extended/simplified to meet the needs of the class.
Has some links to science in the way of predicting results and recording findings.
Practicing of their timestable.

Potential Issues:
Children might struggle to see all of the squares, particularly ones in the middle.
They might lose track of how many sticks they have used.

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Age 5-7
Positives:
A game that can be played on their own or in pairs or even three's it encourages mathematical language and discussion, sharing of ideas to create patterns. Positional language, next to, top bottom.
- Counting of spots to focus on number leading on to subitizing .number bonds, ways to make 10, ways to make ... etc
-can use the coloured dots for pattern
- easy to extend the challenge into different games.
- It's a step up from counting individual concrete items

Negatives
_ dominoes are quite small, may want to print larger ones for children until they are confident at using them and recognising the dots
-if younger children are not secure in counting to 12 and remembering that one dot represents one number then they may find this activity to hard and will need role modelling. They may need physical blocks to show the groups of numbers on the dice.
Domino Patterns (maths.org)

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Age 7- 11
Positives:
-Concrete way of exploring number patterns
-Encourages boys to look at patterns
-No 'right' answer
- Encourages mathematical vocabulary- what number sequences can be used? Which sequences don't return to the start? Why?
- Easy to differentiate & develop
- Cross curricular links- computing, art & design.

Negatives:
- No right answer
- Frustration when the pattern doesn't go back to the start

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How about making designs like the ones above?

It's just a matter of getting a group of numbers together that repeat and then using a simple drawing rule, then colouring the pattern in.

A good way to start is to take a number sequence that you like, for example square numbers or the $3$ times table.
Just keep the ones (units) of those numbers, for example $1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4$ etc. or $3, 6, 9, 2, 5, 8, 1, 4, 7, 0, 3, 6$ etc.
You may notice that with these, and perhaps your own sequences, they go to a $0$ and then repeat.

For this challenge, you just need the numbers that go as far as just before the zero, for example $1, 4, 9, 6, 5, 6, 4, 1$ or $3, 6, 9, 2, 5, 8, 1, 4, 7$.

Now to draw ...

Using squared paper and starting somewhere in the middle, take each of the numbers in turn to tell you how long to draw the line and turn a right angle to the left after you've drawn each line.

This may help you to see what to do, using the example of square numbers and starting with the red $1$. I've coloured each new line with a different colour:

After the final $1$ you start again as shown below:

and so on until you get back to the beginning.
Some squences that you choose may not come back to the start but just keep stepping away!

So now it's your turn ...
Choose your sequence.
Pick out the ones (units) until you find it repeating.
Draw the lines carefully on squared paper turning in the same direction each time by a right angle.
See what you get and colour it in if you like.

You may like to change a rule or two after a while. (For example, you could change the turn to $60^\circ$ instead of $90^\circ$.)

Please send us your pictures.

A very kind teacher Mr Morrison from NSW Australia posted us a Scratch program to use for the same activity you can find it at https://scratch.mit.edu/projects/122888029/ ​

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How about making designs like the ones above? It's just a matter of getting a group of numbers together that repeat and then using a simple drawing rule, then colouring the pattern in. A good way to start is to take a number sequence that you like, for example square numbers or the $3$ times table.

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Age 7-11
Positives:
- can look into different perimeter  of different shapes and gradually build up how the length or width
- can work on area of different shapes with how many equal squares there are in the different shapes.
- can let the pupils explore and give the pupils a chance to look at maths in a different way

Potential issues:
- could become complicated when more pebbles are added
- the children may and the pebbles inside for the shapes inside of the amount of square for the area.

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Imagine that you're walking along a sandy beach collecting pebbles. You start off with four pebbles and you place them on the sand as the corners of a square. The area inside your pebbles is just 1 square.

By adding another 2 pebbles you double the area to 2 squares, like this:

The rule is that you keep the pebbles that you already have, not moving them to any new positions, and add as few new pebbles as necessary to double the previous area.

So, to continue, we add another three pebbles to get an area of 4:

You could have doubled the area by doing this instead:

But this would not be allowed because we are adding as few pebbles as possible each time.

The sixth arrangement of pebbles would look like this:

Now it's time for you to have a go.

What do you notice about the arrangements? What questions could you ask about them?

You might like to explore:

How many extra pebbles are added each time? This starts off as 2, 3, 6...

How many are there around the edges? This starts off as 4, 6, 8...

How big is the area? This starts off as 1, 2, 4...

How many pebbles are there inside each arrangement? This starts off as 0, 0, 1, 3, 9...

Don't forget the all-important question to ask - "I wonder what would happen if I ...?''
More Pebbles is a three-dimensional version of this task, which you might like to have a go at afterwards.
You may also like

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exploring patterns and noticing structures

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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Suggested age group 7-11
Positives:
Focuses on relations between numbers and engages reasoning. For example I focused on division facts with 6 and it quickly became apparent that to not have a remainder it would have to be an even number and a multiple of 3, which I could check by adding the digits. This made sense as 6 is just double 3 so therefore must both be even and a multiple of 3.

Potential Issues:
The challenge requires a lot of confidence in division which is often a tricky calculation. It also offers very limited guidance with how to explore the facts, and it is possible that pupils would be stuck on just focusing on odds/evens.

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Age: 5-11
Positives:
- Easy game which children can complete in pairs, which will encourage discussion and sharing of skills.
- Good for practicing number bonds and working out the differences between numbers.
- Good for fluency skills and reasoning skills, if working in a team children can explain why they are picking certain numbers in order to cross off as many as possible.
- Simple to differentiate for different ages, and levels of challenge.

Potential issues:
- May seem a little bit complicated  for children to understand initially, will need demonstrating for younger children.
https://nrich.maths.org/strike-it-out

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Age: 7-11

Positives:
-Pupils can work in pairs which will encourage discussion.
-Additional rows can be added to increase challenge for higher ability pupils.
-Practising number bonds, halving/doubling and looking for patterns/trends.
- It could be useful for pupils to practise highlighting key information in questions (useful for solving word problems).

Potential issues:
-children many not read through all of the information and miss important information.
- pupils may struggle to understand the pattern for the green shirts.

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These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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Age: 5-11

Positives:
- Develops a sense of team working (as they could work in teams).
-Shows that there is not always just ONE way to find an answer.
-Puts more emphasis on their working out and their investigation rather than the actual answer which might result in less Maths anxiety because the actual height of the tree is not what is important here (as long as this piece of information is shared correctly).
-Encourages trial and error-keep on trying.
-Easily adaptable to look at different objects withing the environment/providing multiple objects (different sized objects could require different measurements-different areas within Maths).
-As knowledge around Maths increase there will be different answers/ideas being built upon. What answers you get in year one will be different to the ones in year four.
-Question phrasing put the student at the center of the learning, as it states 'YOU' and makes it more child-lead than teacher-led.
-Develops independent working from the teacher.
-Allows for a lot of creativity and exploring.- Fun and engaging.
-Multiple resources could be used/introduced here by either the class or the teacher.
-Creates discussion such as where to start measuring from and where to stop measuring such as from the base of the trunk to the top of the trunk or to the highest branch or do you start from the roots of the tree.
-Allows for open questioning and questions which would show the depth of a learner's understanding.

Potential issues:
-If done in the classroom around an object the class can not see this might be quite hard for SEND learners who need more visual aids. Could also be more tricky for learners who believe they would need an actual answer on the size of the tree (this could be altered to give further support to help these students).
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A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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Ages 7-11

Positives:
- Develops working systematically
- Encourages trial and error
- Interactive option (or physical manipulatives if possible) - develops a CPA approach (manipulatives can be replaced with visuals / drawings)
- Easily adaptable (using different sized rods)
- Could be completed in pairs / groups to encourage mathematical discussion
- Develops pattern spotting and thinking
- Can be extended past using cuisenaire rods to thinking about using numbers (how many ways can you make 10 using 2 and 1)

Potential Issues:
- Without use of concrete resources or interactive materials, understanding of equal amounts could suffer (ie. without being able to visualise that 10 whites = 1 orange)

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I've been playing around with cuisenaire rods, this is what I came to.
There are five different ways for us to make the pink rod using just red and white rods.

We count white, white, red as different from the white, red, white even though they both use two white rods and one red rod.

Using our Cuisenaire environment, can you work out how many different ways there are, using only the red and white rods, to make up:

The light green rod?

The yellow rod?

The dark green rod?

The black rod?

Without using the interactivity, how many different ways are there to make up the orange rod (equivalent to 10 white rods)?

Can you explain the pattern?

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I've been playing around with cuisenaire rods, this is what I came to. There are five different ways for us to make the pink rod using just red and white rods. We count white, white, red as different from the white, red, white even though they both use two white rods and one red rod.

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Age 5-7

Positives:
- Allows for discussions surrounding why something could sometimes be true. Thereby facilitating mathematical thinking and reasoning.
- Questions could be made practical, allowing for students to develop from concrete to abstract thinking.
- Could be differentiated and altered in difficulty.
- May be a good activity to recap what has been learned over the course of lessons (formative assessment)

Potential Issues:
- Understanding could be dependent on student language/reading skills (Counter this by doing the activity as a class, led by the teacher? or students in groups).

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Are the following statements about number always true, sometimes true or never true?
How do you know?

Can you find examples or counter-examples for each one?

For the 'sometimes' cards can you explain when they are true? Or rewrite them so that they are always true or never true?

When you add two numbers you
can change the order and the
answer will be the same

If you add 10 and take away 1,
it is the same as adding 9

When you add 10 to a number,
the answer is a multiple of 10

When you subtract one number
from another number you can
change the order and the answer
will be the same

What about these statements about shapes?

If you put two squares together
you get a rectangle

All 3D shapes have more than
four faces

When you cut a square in half
you get a triangle

Four sided shapes are called squares

Three sided shapes are called triangles

You could cut out each set of cards from this sheet ( word, pdf) and arrange them in this grid.

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Are the following statements about number always true, sometimes true or never true? How do you know? Can you find examples or counter-examples for each one? For the 'sometimes' cards can you explain when they are true? Or rewrite them so that they are always true or never true?

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1) Explore a range of different age-appropriate sequences and investigations on the NRICH website by clicking on the following  three specific links:

- Patterns, Sequences and Structures - Describing Patterns  and Sequences

•Thinking Mathematically - Investigations

•Thinking Mathematically– Generalising

2) Take one of the N-Rich tasks that you have explored to make a posting.

Put the name of the selected task as the title

Suggested age group

Add comments about the chosen tasks under the two headings: Positives/Potential Issues

Insert the direct web-link to your chosen task

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If you are looking for resources on a particular curriculum topic, we recommend you start by taking a look at our curriculum mapping documents, available on the Primary and Secondary Teacher pages.

or select from the list below

All broad topics

PROBABILITY AND STATISTICS

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If you are looking for resources on a particular curriculum topic, we recommend you start by taking a look at our curriculum mapping documents, available on the Primary and Secondary Teacher pages. or select from the list below

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Age 5-7
Positives:
-Develops knowledge on colour and recognition of colour
-Uses and encourages mathematical vocabulary to be used
-Encourages deeper learning and teaches children 'why'
-Develops CPA approach
-Engages with current issues and key events in the environment
-Fun and interactive
-Can be adapted and varied for different children depending on any specific learning difficulties
-May encourage children who are interested in sport but not mathematics

Potential Issues:
-Does not include irregular shapes
-Does not show variation in size
-Very closed questioning and choice of what the children can do
-Limiting to the children's knowledge on shapes
Webink:

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Five coloured interlocking rings have been the symbol of the Olympics for nearly one hundred years.

What colours can you see?

You can see the way they interlock if you click here.

How would you describe the picture?

Can you design your own symbol using five coloured rings?

Other shapes could be linked in a similar way.
Have a go at linking five squares. Make them interesting colours.

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Five coloured interlocking rings have been the symbol of the Olympics for nearly one hundred years. What colours can you see? You can see the way they interlock if you click here. How would you describe the picture? Can you design your own symbol using five coloured rings?