Spider Sequences

9 Arrow 18 Arrow 27 Arrow 36 Arrow a
31 Arrow 67 Arrow 103 Arrow 139 Arrow b
4 Arrow 16 Arrow 64 Arrow 256 Arrow c
26 Arrow -52 Arrow 104 Arrow -208 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.

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This starter has scored a mean of 3.1 out of 5 based on 569 votes.

Previous Day | This starter is for 31 March | Next Day



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?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.


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."

Extension 1 Answers


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