Coins in Envelopes

Fifteen pennies are placed in four envelopes and the envelopes are sealed. It is possible to pay someone any amount from 1p to 15p by giving them one or more envelopes. How were the pennies distributed between the envelopes?

1p 1p 1p 1p 1p 1p 1p 1p 1p 1p 1p 1p 1p 1p 1p

A Mathematics Lesson Starter Of The Day

Topics: Starter | Number

  • Richard Walter, Gordano School Portishead
  • Hi there, my name is Richard Walter and I am a secondary school maths teacher at Gordano School in Portishead, near Bristol. I have used your starters consistently over the past two years since I began my career in teaching. I think that they serve as an excellent resource at the start of a lesson in settling and engaging my pupils in their mathematics. What is more, they really enjoy them!

    The starters I find most successful in their ability to engage pupils are the number orientated problems such as the magic/un-magic square, neighbours, the once where you have the numbers 1 to 8 and a seating arrangement and the pupil has to come up with a seating plan where no consecutive number can sit next to or diagonally opposite another, the probability starters involving coins of which I can't quite remember.... etc etc. Basically the starters that give pupils a chance to have a go at them by trial and error but also allow a high degree of differentiation to engage those more able pupils who can start to identify the mathematical principles behind those problems.

    Not so engaging for me are the ones which start, "Think of as many mathematical words as possible that begin with the letter 'A'." I avoid using these ones.....

    I will continue to use "starter of the day" and continue to push it's use in my maths department. Keep up the excellent work! And thank you!

    Richard Walter
  • G Oliver, Parkside Community School
  • The instructions on 5th of February aren't clear enough for use. It looks good but I don't think there is enough information
  • Mark Richer, Churchill School
  • I am Mark Richer, Teacher of Mathematics at Churchill School.
    This is always a popular activity with my students.
    For this amd similar activities, when we conclude I always like to ask those who were successful "Did you work this out through pure skill, or pure luck - perhaps we will never know?".
    I find it particularly useful as a lesson starter to refer back to as a plenary after we have explored binary numbers.
    The solution for 5 envelopes is 16, 8, 4, 2, 1. This shows that any decimal number can be generated from combining various powers of 2, which of course is what the Binary system is all about.
  • Transum, Twitter
  • Transum,
  • For a related challenge see Aunt Sophie at the Post Office, a Starter inviting you to find the ways of making up various postage amounts using 3p and 8p stamps. The extension activity is a Frobenius problem asking what is the largest whole number amount that can't be made with 5p and 7p stamps.

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.

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Globe of Flags

This activity is suitable for students of mathematics all around the world. Use the button below to change the currency symbol used to make it more relevant to your students. You may wish to choose an unfamiliar currency to extend your students' experience.

Globe of Flags


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What if there were 31 pennies and 5 envelopes?

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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

Do you need a visual aid to help you explain the binary system? Click below.

Student Activity

Are the coin values used today the most efficient choices? Listen to this excerpt from the 'No Such Thing As A Fish' podcast and investigate the claims made about 1p, 3p, 11p, and 37p coins.

Optimal Coin Values - Podcast Excerpt

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