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Broad Topics > Sequences, Functions and Graphs > Sequences

Lost Books

Stage: 2 Challenge Level:

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?

Sticky Triangles

Stage: 2 Challenge Level:

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

Polygonals

Stage: 2 Challenge Level:

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

Magazines

Stage: 2 Challenge Level:

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.

Beads

Stage: 2 Challenge Level:

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Pyramid Numbers

Stage: 2 Challenge Level:

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Play a Merry Tune

Stage: 2 Challenge Level:

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

Taking a Die for a Walk

Stage: 1 and 2 Challenge Level:

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.

A Shapely Network

Stage: 2 Challenge Level:

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.

Lawn Border

Stage: 1 and 2 Challenge Level:

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?

Calendar Patterns

Stage: 2 Challenge Level:

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?

Triangular Hexagons

Stage: 2 Challenge Level:

Investigate these hexagons drawn from different sized equilateral triangles.

Sets of Numbers

Stage: 2 Challenge Level:

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

Domino Sets

Stage: 2 Challenge Level:

How do you know if your set of dominoes is complete?

The Numbers Give the Design

Stage: 2 Challenge Level:

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

Next Number

Stage: 2 Short Challenge Level:

Find the next number in this pattern: 3, 7, 19, 55 ...

More Pebbles

Stage: 2 and 3 Challenge Level:

Have a go at this 3D extension to the Pebbles problem.

The Mathemagician's Seven Spells

Stage: 2 Challenge Level:

"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?

Function Machines

Stage: 2 Challenge Level:

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Holes

Stage: 1 and 2 Challenge Level:

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?

Street Sequences

Stage: 1 and 2 Challenge Level:

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

Cuisenaire Environment

Stage: 1 and 2 Challenge Level:

An environment which simulates working with Cuisenaire rods.

Times Tables Shifts

Stage: 2 Challenge Level:

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Number Tracks

Stage: 2 Challenge Level:

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Exploring Wild & Wonderful Number Patterns

Stage: 2 Challenge Level:

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Extending Great Squares

Stage: 2 and 3 Challenge Level:

Explore one of these five pictures.

Intersecting Circles

Stage: 3 Challenge Level:

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

Seven Squares

Stage: 3 Challenge Level:

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Sets of Four Numbers

Stage: 2 Challenge Level:

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Carrying Cards

Stage: 2 Challenge Level:

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?

Light Blue - Dark Blue

Stage: 2 Challenge Level:

Investigate the successive areas of light blue in these diagrams.

Paving Paths

Stage: 3 Challenge Level:

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

Maxagon

Stage: 3 Challenge Level:

What's the greatest number of sides a polygon on a dotty grid could have?

Mobile Numbers

Stage: 1 and 2 Challenge Level:

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Lower Bound

Stage: 3 Challenge Level:

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

Converging Means

Stage: 3 Challenge Level:

Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .

1 Step 2 Step

Stage: 3 Challenge Level:

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Seven Squares - Group-worthy Task

Stage: 3 Challenge Level:

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

Charlie's Delightful Machine

Stage: 3 and 4 Challenge Level:

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Logoland - Sequences

Stage: 3 Challenge Level:

Make some intricate patterns in LOGO

Differs

Stage: 3 Challenge Level:

Choose any 4 whole numbers and take the difference between consecutive numbers, ending with the difference between the first and the last numbers. What happens when you repeat this process over and. . . .

A Calendar Question

Stage: 2 Challenge Level:

July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When did July 1st fall on a Monday again?

Clock Squares

Stage: 3 Challenge Level:

Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.

Happy Numbers

Stage: 3 Challenge Level:

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

Pebbles

Stage: 2 and 3 Challenge Level:

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?

Remainder

Stage: 3 Challenge Level:

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

Millennium Man

Stage: 2 Challenge Level:

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?

Sissa's Reward

Stage: 3 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

Two Much

Stage: 3 Challenge Level:

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

Regular Hexagon Loops

Stage: 3 Challenge Level:

Make some loops out of regular hexagons. What rules can you discover?