There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Sequences. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Sequences Starters:

Add 'em: Add up a sequence of consecutive numbers. Can you find a quick way to do it?

House Numbers: The numbers on five houses next to each other add up to 70. What are those five numbers?

Missing Terms: Find the missing terms from these linear sequences.

One one: Continue the given number pattern with the help of a little lateral thinking.

Sea Shells: A question which can be best answered by using algebra.

Sequence Dancing: Find the next term of the number sequences.

Sign Sequences: Continue the sequences if you can work out the rule.

Spider Sequences: Find the next term of the given number sequences. Can you also find a general rule for predicting the nth term of the sequence?

To Be Continued: Work out the next term in the given sequences.

Windmill Sequence: Find the value of the missing term of the sequence. It is easier than you may think!

#### Snooker Angles

This must be the most enjoyable way to practise estimating angles and learn about bearings. Snooker Angles is an interactive game for one or two players.

### Curriculum for Sequences:

#### Year 6

Pupils should be taught to generate and describe linear number sequences more...

#### Years 7 to 9

Pupils should be taught to generate terms of a sequence from either a term-to-term or a position-to-term rule more...

Pupils should be taught to recognise arithmetic sequences and find the nth term more...

Pupils should be taught to recognise geometric sequences and appreciate other sequences that arise. more...

#### Years 10 and 11

Pupils should be taught to recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rn where n is an integer, and r is a positive rational number {or a surd}) {and other sequences} more...

Pupils should be taught to deduce expressions to calculate the nth term of linear {and quadratic} sequences. more...

### Feedback:

Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School:

"Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work."

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset:

"A set of real life savers!!
Keep it up and thank you!"

Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex:

"This website was brilliant. My class and I really enjoy doing the activites."

### Notes:

A pattern of numbers following a rule is called a sequence. There are many different types of sequence and this topic introduces pupils to some of them.

The most basic sequences of numbers is formed by adding a constant to a term to get the next term of the sequence. This rule can be expressed as a linear equation and the terms of the sequence when plotted as a series of coordinates forms a straight line. More complex sequences are investigated where the rule is not a linear function. Other well-known sequences includes the Fibonacci sequence where the rule for obtaining the next term depends on the previous two terms.

Sequences can be derived from shapes and patterns. A growing patterns of squares or triangles formed from toothpicks is often used to show linear sequences in a very practical way. Diagrams representing sequences provides interesting display material for the classroom.

Typically pupils are challenged to find the next term of a given sequence but a deeper understanding is needed to find intermediate terms, 100th term or the nth term of a sequence.

### Sequences Teacher Resources:

Counter: A dynamic visual aid that counts! Choose the first term, common difference and the speed

Mystic Rose: Investigate the properties of the Mystic Rose by using this interactive diagram.

Sequence Generator: An online app which produces number sequences as words.

### Sequences Activities:

Arithmetic Sequences: An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.

Fibonacci Quest: A number of self marking quizzes based on the fascinating Fibonacci Sequence.

Geometric Sequences: An exercise on geometric sequences including finding the nth term and the sum of any number of terms.

Interest: Practise using the formulas for simple interest and compound interest.

Iteration: Find approximate solutions to equations numerically using iteration.

Matchstick Patterns: Create a formula to describe the nth term of a sequence by examining the structure of the diagrams.

Missing Terms: Can you work out which numbers are missing from these number sequences?

Pascal's Triangle: Get to know this famous number pattern with some revealing learning activities

Quadratic Sequences: Deduce expressions to calculate the nth term of quadratic sequences.

Tower of Hanoi: Move the pieces of the tower from one place to another in the minimum number of moves.

Watsadoo: Rotate the cogs to catch the flying numbers in the correct sections.

Finally there is Topic Test, a set of 10 randomly chosen, multiple choice questions suggested by people from around the world.

Alternatively, for the more advanced student, there is an ever-growing collection of Exam-Style Questions with worked solutions on the topic of Sequences.

### Sequences Investigations:

Aunt Lucy's Legacy: Decide which of the four schemes Aunt Lucy proposes will provide the most money. This investigation involves the sum of sequences as well as considering life expectancy.

Four Ever: Generate a number sequence based on the number of letters needed to spell the previous number.

Mystic Rose: Investigate the properties of the Mystic Rose by using this interactive diagram.

Steps: Investigate this growing sequence of steps.

Tower of Hanoi: Move the pieces of the tower from one place to another in the minimum number of moves.

### Sequences Videos:

Nature By Numbers: Cristóbal Vila created this short animated film that deals with geometric formulas that appear in nature such as the Fibonacci Sequence.

The magic of Fibonacci numbers: Arthur Benjamin gives a TED talk on Fibonacci numbers.

### Sequences Worksheets/Printables:

How Many Squares? 1: A printable grid containing many copies of the design used in the shape counting Starter.

How Many Squares? 2: A printable grid containing many copies of the design used in the second shape counting Starter.

Mystic Roses: Eighteen mystic roses to print out to help with the investigation.

Pascal's Triangle Worksheet: Various forms of Pascal's Triangle ready for printing.

Links to other websites containing resources for Sequences are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

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#### Fractions by Wholes

An exercise on multiplying and dividing proper fractions and mixed numbers by whole numbers. So far this activity has been accessed 65 times and 5 people have earned a Transum Trophy for completing it.

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