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
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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.

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.

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
Satisfactory
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 3.2 out of 5 based on 240 votes.

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.

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

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.

Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

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...

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 it 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...

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 Christmas gift for anyone.

You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

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...

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

 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).

Transum.org/go/?Start=February5

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

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