How many different sets of numbers with at least four members can you find in the numbers in this box?
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .
In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which way of flipping over and/or turning this grid will give you the highest total? You'll need to imagine where the numbers will go in this tricky task!
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
Formulate and investigate a simple mathematical model for the design of a table mat.
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
A challenging activity focusing on finding all possible ways of stacking rods.
In how many ways can you stack these rods, following the rules?
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!
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
An investigation that gives you the opportunity to make and justify predictions.
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
If the answer's 2010, what could the question be?
What do these two triangles have in common? How are they related?
Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?
What is the largest cuboid you can wrap in an A3 sheet of paper?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
An activity making various patterns with 2 x 1 rectangular tiles.
Investigate what happens when you add house numbers along a street in different ways.
In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
This article for teachers suggests ideas for activities built around 10 and 2010.
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?
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
Explore one of these five pictures.
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
A follow-up activity to Tiles in the Garden.
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
How many tiles do we need to tile these patios?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Why does the tower look a different size in each of these pictures?
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.