Spider Sequences

11 Arrow 22 Arrow 33 Arrow 44 Arrow a
28 Arrow 67 Arrow 106 Arrow 145 Arrow b
3 Arrow 9 Arrow 27 Arrow 81 Arrow c
20 Arrow -40 Arrow 80 Arrow -160 Arrow d
10 Arrow 9 Arrow 60 Arrow 90 Arrow e

Hint: Scroll down this page to see the extension activity (Extension 2) for help with the fifth sequence above.

A Mathematics Lesson Starter Of The Day

Topics: Starter | Sequences

  • J Lunnon, Holgate School
  • You say e = 70. 'Seventy' being the largest number spelt with 7 letters. What about 'hundred'?
  • N Peters, Uplands Junior School
  • What about million or billion or zillion ??
  • Miss Reakes, West Island School, Hong Kong
  • My students enjoyed doing these and I got them to write the nth term for the first 4. They all needed a hint for the 5th one.
    Hundred cannot be an answer as you would need to say how many hundreds....
  • Ellis Mcleod, High School Of Dundee 2nd Year
  • This game was good today, however E was very hard.
  • Bargeddie Primary, Primary 7
  • We thought that 66 was the biggest number to be spelled with 8 letters.
  • MrW, England
  • Seventy is the largest number!
    Hundred is incorrect as correctly it should be one hundred.
  • Horrid Henry, Dovecote Primary School
  • We had lots of diferent answers which we prefer but we did have some good maths thinking!
  • Mr Phillips, Stone
  • My class found this so much fun that they wept tears of maths pleasure.
  • 4MR, CEJA
  • Our class loved this activity first thing in the morning. To work out "e" we needed a tiny hint but then we raced away with other options once we understood the rule.
  • Rushy & Co, Hindsford
  • We think the answer to c is 528. Anyone else agree?
  • Dorain, Lumberton
  • The answer to c is 544 (rule you multiply by -2).
  • Transum,
  • Thanks to everyone for their comments. It is really wonderful to see so many people contributing their thoughts and ideas. Please note that any specific answers mentioned above may not apply to the version of the Starter you are looking at thanks to the random number generating code that is built into this page.
  • Mr Hilton, Wellfield Junior School
  • For the 7 letter number in the sequence, would "Graham's" count as Graham's number is the largest number ever used in a mathematical proof? It would very comfortably be the largest option.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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Extension 1

Can you also find a general rule for predicting the nth term of the sequences?

nth term

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

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Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:


However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to sequences of patterns made with matchsticks.


Student Activity

More Sequences

Extension 2

There is an old tradition of using logic puzzles to test job candidates at interview. Here is the version of part (e) above that is said to be asked of Google job candidates:

Find the next number of this sequence:
10, 9, 60, 90, 70, 66...


Count the number of letters in the words of the numbers in the sequence.

The numbers are the largest numbers that can be spelled in a given number of letters.

Some say 96 but others have said 'one googol' or even 'ten googol'! More information about this question can be found in the excellent book 'Are you smart enough to work at Google?' by William Poundstone."

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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