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!

Difference Cipher: Find the mathematical word from the cipher

Double or Half?: At ten percent change per day is doubling achieved faster than halving?

Grandmother: How far would grandma have travelled after a suitably large number of days given her walking regime?

Rice on a Chess Board: How many grains of rice are on a chess board if each square has twice the number of grains as the previous square.

Same Series Sum: Find an arithmetic series and a geometric series that have the same sum of the first five terms.

#### Missing Terms

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

Transum.org/go/?to=missing

### 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...

#### Years 12 and 13

Pupils should be taught to understand and use the binomial expansion of (a + bx)n for positive integer n; the notations n! and nCr link to binomial probabilities. Extend to any rational n, including its use for approximation more...

Pupils should be taught to work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form xn+1 = f(xn); increasing sequences; decreasing sequences; periodic sequences more...

Pupils should be taught to understand and use sigma notation for sums of series more...

Pupils should be taught to understand and work with arithmetic sequences and series, including the formulae for nth term and the sum to n terms more...

Pupils should be taught to understand and work with geometric sequences and series, including the formulae for the nth term and the sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of |r| < 1; modulus notation more...

Pupils should be taught to use sequences and series in modelling more...

### Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.

### Feedback:

Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales:

"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks."

Comment recorded on the i asp?ID_Top 'Starter of the Day' page by Ros, Belize:

"A really awesome website! Teachers and students are learning in such a fun way! Keep it up..."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

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 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 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 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

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."

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 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 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich:

"My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

"I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.
I rate this site as a 5!"

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School:

"This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register."

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 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London:

"I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable."

Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:

"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales:

"Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!"

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

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 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

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?"

### 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

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

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

### Sequences Activities:

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

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

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

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

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

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

Quick Add 'Em Quiz: Find the sum of a sequence of consecutive numbers using a quick, efficient, elegant method.

Iteration: Find approximate solutions to equations numerically using iteration.

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

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

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

Venn Diagram of Sequences: Find the formula for the nth term of sequences that belong in the given sets.

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

Sequences Table Challenge: Complete the table showing the terms of the sequences and the formulas for the nth terms.

Parts of Sequences: Find the formula that describes the part of the sequence that can be seen

Sigma: Practise using the sigma notation to find the sum of various number series.

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:

Steps: Investigate the numbers associated with this growing sequence of steps made from Multilink cubes.

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.

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.

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

### Sequences Videos:

Transum's Sequences Video

Arithmetic Sequences Video: A reminder of how to find the next term, the nth term and the sum of terms of an arithmetic or linear sequence.

4.3 Billion Dollars: Short Futurama clip: Fry's reaction to becoming a billionaire!

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

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

Log Tables: Logarithms and log tables - what Transum used before calculators! A Numberphile video.

### Sequences Worksheets/Printables:

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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#### Sigma

Practise using the sigma notation to find the sum of various number series.

Transum.org/go/?to=sigma

### Teaching Notes:

Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

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