Spider Sequences

8 Arrow 16 Arrow 24 Arrow 32 Arrow a
35 Arrow 55 Arrow 75 Arrow 95 Arrow b
29 Arrow -58 Arrow 116 Arrow -232 Arrow c
3 Arrow 9 Arrow 27 Arrow 81 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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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.

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.

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Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

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Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

Online Maths Shop

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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