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?


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

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 431 votes.

Previous Day | This starter is for 5 February | Next Day


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


Extension: What if there were 31 pennies and 5 envelopes?

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.


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.

Math with Bad Drawings

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone.

A Compendium Of 	Mathematical Methods

A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. 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 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

NSTAAF Podcast Transum Podcast Transum Podcast RSS

©1997-2020 WWW.TRANSUM.ORG