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#### Resources tagged with Sequences similar to Light Blue - Dark Blue:

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Broad Topics > Sequences, Functions and Graphs > Sequences

### Light Blue - Dark Blue

##### Stage: 2 Challenge Level:

Investigate the successive areas of light blue in these diagrams.

### 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?

### 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?

### Next Number

##### Stage: 2 Short Challenge Level:

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

### Function Machines

##### Stage: 2 Challenge Level:

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

### 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.

### 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.

### 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?

### 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.

### 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?

##### Stage: 3 Challenge Level:

What is the total area of the first two triangles as a fraction of the original A4 rectangle? What is the total area of the first three triangles as a fraction of the original A4 rectangle? If. . . .

### Cuisenaire Environment

##### Stage: 1 and 2 Challenge Level:

An environment which simulates working with Cuisenaire rods.

### Polygonals

##### Stage: 2 Challenge Level:

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

### 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?

### 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?

### 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?

### Street Sequences

##### Stage: 1 and 2 Challenge Level:

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

### Farey Sequences

##### Stage: 3 Challenge Level:

There are lots of ideas to explore in these sequences of ordered fractions.

### 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?

### 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?

### 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"?

### 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?

### Regular Hexagon Loops

##### Stage: 3 Challenge Level:

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

### Pyramid Numbers

##### Stage: 2 Challenge Level:

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

### More Pebbles

##### Stage: 2 and 3 Challenge Level:

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

### 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?

### 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 =

### Triangular Hexagons

##### Stage: 2 Challenge Level:

Investigate these hexagons drawn from different sized equilateral triangles.

### 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.

### 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.

### Shifting Times Tables

##### Stage: 3 Challenge Level:

Can you find a way to identify times tables after they have been shifted up?

### 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.

### What an Odd Fact(or)

##### Stage: 3 Challenge Level:

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

### 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?

### Maxagon

##### Stage: 3 Challenge Level:

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

### Triangular Triples

##### Stage: 3 Challenge Level:

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

### Domino Sets

##### Stage: 2 Challenge Level:

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

### 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.

### Odds, Evens and More Evens

##### Stage: 3 Challenge Level:

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

### Logoland - Sequences

##### Stage: 3 Challenge Level:

Make some intricate patterns in LOGO

##### Stage: 3 Challenge Level:

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

### 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?

### 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. . . .

### 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?

### 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?

### 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?

### Designing Table Mats

##### Stage: 3 and 4 Challenge Level:

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

### 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?

### On the Importance of Pedantry

##### Stage: 3, 4 and 5

A introduction to how patterns can be deceiving, and what is and is not a proof.

### Extending Great Squares

##### Stage: 2 and 3 Challenge Level:

Explore one of these five pictures.