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?

EnvelopeEnvelope
EnvelopeEnvelope

A Mathematics Lesson Starter Of The Day


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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
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  • 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
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  • 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.
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This starter has scored a mean of 3.2 out of 5 based on 293 votes.


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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

Answers

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



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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.

Transum.org/go/?Start=February5

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=Sticking

Student Activity


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

Transum.org/go/?to=Binary

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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