Coins in Envelopes

Starter of The Day Transum Mathematics Topics

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
Using small plastic bags and washers instead of envelopes and coins to do the "Coins in Envelopes" Maths Lesson Starter: https://t.co/KTLT95K9Gb The see-through feature makes all the difference. #mathschat #mathchat #mathsCPDchat #eLearning #edchat #Binary pic.twitter.com/NpDCiQcv55
— Transum (@Transum) February 20, 2018
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.

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

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.

Answers

Extension:

What if there were 31 pennies and 5 envelopes?

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Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

Go Genius Maths

Transform maths practice into an exciting adventure with Go Genius Maths! This award-winning board game is designed to make learning maths enjoyable and engaging for children aged 7 and above. Perfect for family game nights or classroom activities, Go Genius Maths helps players develop essential arithmetic skills while having heaps of fun.

Whether you’re looking for a gift to inspire young minds or a tool to supplement maths education, Go Genius Maths is the ultimate choice. Spark curiosity, nurture mathematical talent, and turn learning into an unforgettable journey!

How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more... #ad

Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life this is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more... #ad

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... #ad

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Craig Barton's Tips for Teachers

Teaching is complex. But there are simple ideas we can enact to help our teaching be more effective. This book contains over 400 such ideas." more... #ad

"The ideas come from two sources. First, from the wonderful guests on his Tips for Teachers podcast - education heavyweights such as Dylan Wiliam, Daisy Christodoulou and Tom Sherrington, as well as talented teachers who are not household names but have so much wisdom to share. Then there's what he has learned from working with amazing teachers and students in hundreds of schools around the world.

The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more... #ad

Christmas Maths

This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.

All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

A great source of ideas and another reasonably priced stocking filler. more... #ad

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... #ad

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. more... #ad

Click the images above to see all the details of these gift ideas and to buy them online.

Maths T-Shirts

Maths T-Shirts on Amazon

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 link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

Educational Technology on Amazon

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:

Transum.org/go/?Start=February5

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.

Transum.org/go/?to=Sticking

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

Transum.org/go/?to=Binary

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.