Wrong Way Round

Ron Gwairown always writes numbers down back to front. At school, he was once asked to do the following calculation:

Ron Gwairown

14 x 82

In his exercise book Ron wrote down:

41 x 28

1. What answer did he get?

2. What answer should he have got?

3. Investigate other pairs of calculations of this type? What can you discover?

A Mathematics Lesson Starter Of The Day

Topics: Starter | Arithmetic | Investigations | Place Value

  • LRH, MCS Brackley
  • I used this with a top set year 9. We collated our results after about 15 minutes and the students found an explanation using multiplication grids for a general rule linking all the pairs they found. A great success! More like this, please.
  • Y6, Tickhill St Mary's
  • Question 3 gives away the answer to question 2!
  • Mrs Rowe, Edenham High
  • I was warned that it was quite hard. Set for top year 8's lasted the majority of our first lesson of the year.
  • KS3 Form Teacher, West Midlands
  • This starter was very good for engaging a multi-ethnic y7-9 form group - to a certain extent, the older, more knowledgeable kiddies were able to address the queries of the little ones! Can be very suitable for a class whose English is perhaps not the best. A nice way of revising long multiplication for those who need it and an interesting quirk of mathematics for those who don't. Easy 20-ish minutes of class-wide engagement.
  • Jenna Turner, Coorara Primary School
  • This was a fun starter but I couldn’t figure out the answers. Are there any patterns to which ones work and which ones don’t?
  • Liz, Vietnam
  • Ok. But what was the pattern mentioned in question 3?

    [Transum: There is no pattern mentioned in question 3. Not all mathematical relationships can be described with a simple pattern, formula or rule. In this case the pupils are encouraged to make observations such as the basic "if the second number is the reverse of the first number the products will be the same" or "neither number can be a multiple of ten if the products are to be the same" or "if only one even digit is involved the products won't be the same". Pupils can also be encouraged to investigate the situation using technology, a spreadsheet perhaps or a programmable calculator.

    All of the possibilities along with an algebraic generalisation are available in the answer panel below for subscribers.]
  • John, Denmark
  • Have yu noticed that for small enough numbers you get a reversal for the digits in the results. Eg 31x12 = 372 and 13x21 = 273.

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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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 a related student activity.


Student Activity



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