List

Open Spaces

Circles, Circles
problem

Circles, Circles

Age
5 to 11
Challenge level
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Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Build It Up
problem

Build It Up

Age
7 to 11
Challenge level
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Can you find all the ways to get 15 at the top of this triangle of numbers?
Spirals, Spirals
problem

Spirals, Spirals

Age
7 to 11
Challenge level
filled star empty star empty star
Here are two kinds of spirals for you to explore. What do you notice?
Move those Halves
problem

Move those Halves

Age
7 to 11
Challenge level
filled star filled star empty star
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Roll Over the Dice
problem

Roll Over the Dice

Age
7 to 11
Challenge level
filled star filled star empty star
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
Plants
problem
Favourite

Plants

Age
5 to 14
Challenge level
filled star filled star empty star
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Train Carriages
problem

Train Carriages

Age
5 to 11
Challenge level
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Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
2 Rings
problem
Favourite

2 Rings

Age
5 to 7
Challenge level
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The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
Street Sequences
problem

Street Sequences

Age
5 to 11
Challenge level
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Investigate what happens when you add house numbers along a street in different ways.
Caterpillars
problem
Favourite

Caterpillars

Age
5 to 7
Challenge level
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These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Triangle Shapes
problem

Triangle Shapes

Age
5 to 11
Challenge level
filled star empty star empty star
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
tiling
problem

tiling

Age
7 to 11
Challenge level
filled star empty star empty star
An investigation that gives you the opportunity to make and justify predictions.
Consecutive Numbers
problem
Favourite

Consecutive Numbers

Age
7 to 14
Challenge level
filled star empty star empty star

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Sweets in a box
problem
Favourite

Sweets in a box

Age
7 to 11
Challenge level
filled star empty star empty star

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?

Follow the numbers
problem
Favourite

Follow the numbers

Age
7 to 11
Challenge level
filled star empty star empty star

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.