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Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
How many tiles do we need to tile these patios?
This article for teachers suggests ideas for activities built around 10 and 2010.
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
What do these two triangles have in common? How are they related?
I cut this square into two different shapes. What can you say about the relationship between them?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?
Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.
If the answer's 2010, what could the question be?
Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.
Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Bernard Bagnall describes how to get more out of some favourite NRICH investigations.
Investigate what happens when you add house numbers along a street in different ways.
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Here are many ideas for you to investigate - all linked with the number 2000.
Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Explore one of these five pictures.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
What is the largest cuboid you can wrap in an A3 sheet of paper?
An investigation that gives you the opportunity to make and justify predictions.
Investigate the number of faces you can see when you arrange three cubes in different ways.
A follow-up activity to Tiles in the Garden.
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.