Spider Sequences

2 Arrow 4 Arrow 6 Arrow 8 Arrow a
21 Arrow 43 Arrow 65 Arrow 87 Arrow b
25 Arrow -50 Arrow 100 Arrow -200 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.

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.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.1 out of 5 based on 491 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.

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.


Texas Instruments Nspire Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Click the images above to see all the details of these items and to buy them online.

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


©1997-2020 WWW.TRANSUM.ORG