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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?
How many possible symmetrical necklaces can you find? How do you know you've found them all?
Create a pattern on the small grid. How could you extend your pattern on the larger grid?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
This task requires learners to explain and help others, asking and answering questions.
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
What can you see? What do you notice? What questions can you ask?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
An environment which simulates working with Cuisenaire rods.
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
Investigate the successive areas of light blue in these diagrams.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
This number has 903 digits. What is the sum of all 903 digits?
How many different sets of numbers with at least four members can you find in the numbers in this box?
"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?
What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When did July 1st fall on a Monday again?
Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?
Can you go from A to Z right through the alphabet in the hexagonal maze?
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
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?
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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?
Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Here are some ideas to try in the classroom for using counters to investigate number patterns.