Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Formulate and investigate a simple mathematical model for the design of a table mat.

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. . . .

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?

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Investigate what happens when you add house numbers along a street in different ways.

An activity making various patterns with 2 x 1 rectangular tiles.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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?

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?

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

What do these two triangles have in common? How are they related?

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?

What is the largest cuboid you can wrap in an A3 sheet of paper?

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?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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?

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?

Here are many ideas for you to investigate - all linked with the number 2000.

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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!

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?

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?

Why does the tower look a different size in each of these pictures?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

How many models can you find which obey these rules?

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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?

How many different sets of numbers with at least four members can you find in the numbers in this box?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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. . . .

In how many ways can you stack these rods, following the rules?

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

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?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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?