# Resources tagged with: Describing patterns and sequences

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### There are 36 results

Broad Topics > Patterns, Sequences and Structure > Describing patterns and sequences

### Even Up

##### Age 11 to 14 ShortChallenge Level

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

### Summing Consecutive Numbers

##### Age 11 to 14Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

### 1 Step 2 Step

##### Age 11 to 14Challenge 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?

### Steps to the Podium

##### Age 7 to 14Challenge Level

It starts quite simple but great opportunities for number discoveries and patterns!

### Magic Letters

##### Age 11 to 14Challenge Level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

### Picturing Triangular Numbers

##### Age 11 to 14Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

### Elevenses

##### Age 11 to 14Challenge Level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

### Seven Squares - Group-worthy Task

##### Age 11 to 14Challenge 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?

### Tower of Hanoi

##### Age 11 to 14Challenge Level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

### Frogs

##### Age 11 to 14Challenge Level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

### Maxagon

##### Age 11 to 14Challenge Level

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

### Triangle Numbers

##### Age 11 to 14Challenge Level

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

### Partly Painted Cube

##### Age 14 to 16Challenge Level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

### Impossibilities

##### Age 11 to 14Challenge Level

Just because a problem is impossible doesn't mean it's difficult...

### Cuisenaire Environment

##### Age 5 to 16Challenge Level

An environment which simulates working with Cuisenaire rods.

### Odds, Evens and More Evens

##### Age 11 to 14Challenge Level

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

### Painted Cube

##### Age 14 to 16Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

### Seven Squares

##### Age 11 to 14Challenge Level

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

### Changing Places

##### Age 14 to 16Challenge Level

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

### Pattern Power

##### Age 5 to 14

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

### Days and Dates

##### Age 11 to 14Challenge Level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

### Fibonacci Surprises

##### Age 11 to 14Challenge Level

Play around with the Fibonacci sequence and discover some surprising results!

### Lastly - Well

##### Age 11 to 14Challenge Level

What are the last two digits of 2^(2^2003)?

### Paving Paths

##### Age 11 to 14Challenge 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?

### Growing Surprises

##### Age 11 to 14Challenge Level

Can you find the connections between linear and quadratic patterns?

### Magic Crosses

##### Age 7 to 14Challenge Level

Can you find examples of magic crosses? Can you find all the possibilities?

### Beach Huts

##### Age 11 to 14Challenge Level

Can you figure out how sequences of beach huts are generated?

### Picturing Square Numbers

##### Age 11 to 14Challenge Level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

### Digital Roots

##### Age 7 to 14

In this article for teachers, Bernard Bagnall describes how to find digital roots and suggests that they can be worth exploring when confronted by a sequence of numbers.

### Train Spotters' Paradise

##### Age 11 to 16

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.

### Shifting Times Tables

##### Age 11 to 14Challenge Level

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

### Quadratic Patterns

##### Age 11 to 14Challenge Level

Surprising numerical patterns can be explained using algebra and diagrams...

### Attractive Tablecloths

##### Age 14 to 16Challenge Level

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

### Pocket Money

##### Age 11 to 14Challenge Level

Which of these pocket money systems would you rather have?

### Sept 03

##### Age 11 to 14Challenge Level

What is the last digit of the number 1 / 5^903 ?

### Farey Sequences

##### Age 11 to 14Challenge Level

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