Product Placement

These numbers have been asked to make some multiplications.

What is the largest product they could make?






A Mathematics Lesson Starter Of The Day

Topics: Starter | Place Value | Problem Solving

  • David Pamment, St Mark's Academy, UK
  • We found 29495761 by squaring 5431! Beat that!
    Dejan in my year 7 class found this.
    St Mark's Academy, London
    PS Now Omar is going mad with powers, like 5421 cubed!

    [Transum: Well done Dejan for thinking outside the box. It is up to the teacher to decide which mathematical operations are allowed (other than multiplication) and this Starter can be used in many different ways with different classes.]
  • Transum,
  • If you rely on trial and error you may be working for a long time and you'll never know if you have finished. This starter requires a great deal of thought about place value and the concept of multiplication. It would be nice to hear the justification students come up with to prove they have found the largest product.
  • Amy C, Coorara Primary School
  • Is there a way to tell what the answer is? My highest is 22,403.

    [Transum: Sorry Amy, the answers are only available to those who are Transum subscribers. However I can say that you have not quite found the largest product yet. Keep trying.]
  • Mr. Rutherford, Smith School
  • 22,412 is the highest we calculated.
  • Lachlan, Golden Grove High School
  • I got 52^(3^41) and the calculator says infinity.

    [Transum: Good try Lachlan but the challenge is to find a product. Your answer contains a power. Keep trying!]

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 the student version of this activity.

Student Activity


Curriculum Reference

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


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