Coloured Sheep

A Maths Starter of The Day

There are 12 sheep in a field as shown here:

Yellow Sheep Yellow Sheep Blue Sheep Green Sheep Green Sheep Green Sheep Green Sheep Red Sheep Red Sheep Red Sheep Red Sheep Red Sheep

1. How many sheep can say that there is at least one other sheep here of the same colour?

2. The farmer takes one sheep from the field at random. What is the probability it is
    a) Yellow   b) Blue   c) Green   d) Not red ?

[Give your answers as decimals to two decimal places]

Topics: Starter | Probability

  • Mr Heeley's Y7 lambs, Rawthorpe High School
  • We think your joke is a bit woolley! We think, however, that this is a fine starter, in fact it's baaarilliant!!
    God bless you x
  • Mrs. Grace, Hardwick School, South Australia
  • This is a great starter to begin the day with. The students thought that it was great.
  • MSJ, 8x3
  • Keenan thought it was Baarilliant.
  • Mrs Porter, Upholland High
  • Fantastic starter - have used it with all years of all abilities Level 4 to A* - just change the questions to get some very difficult conditional probability questions.
    Also planning to use it to introduce ratio - it has been the most useful starter so far.
  • M Phillips, Dorset
  • Great activity.
    Has the word "not" been forgotten in the part d answer?
  • Transum,
  • Thanks M Phillips for pointing out the error. It has now been corrected.
  • Zoe Thompson, Channing Junior School, Highgate
  • I found this GREAT!! I loved it and found it challenging but not so I didn't want to do it!
    It has made maths REALLY fun for the kids, and it is a GREAT way for the kids to start the day!
  • Mr Khaira, Marriotts School
  • I think this an absolutely delightful question but surely the answer is 12, I don't get it.
  • Transum,
  • A yellow sheep has two lambs. One of them is male. What is the probability that the other lamb is male? Some say one half but others say that there are four different options. The two lambs, in order of age, could be MM, MF, FM or FF. If we know one is a male that eliminates the FF option. That leaves three possibilities, MM, MF and FM. Two out of these three possibilities have one of the lambs being female so the probability that the other lamb is male is one third. So is the correct answer one half or one third?
  • Mr Smith & S1 Class., Renfrew High School
  • Transum, surely an array such as MM, MF, FM and FF is order specific and whilst you eliminate FF correctly, should FM not also be removed given that the 'first' lamb was not F. This would leave you with MM and MF as the only two remaining options and with MM being the only one producing a further M lamb then the probabilty returns to the original predicition of 1/2. Just our thoughts on a very thought provoking question. Thank you.
  • Mr Smith & S1 Class., Renfrew High School
  • We are humbled and have realised we misread the question, we made the assumption that it was the gender of the first lamb, but upon re-reading the question Ben pointed out that it simply said 'one lamb' not the 'first lamb'. Thoroughly enjoyable.
  • Transum,
  • Q. What do you need to calculate the distance around a circle of sheep?
    A. Shepherds’ Pi.

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 19 May | Next Day



Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

Online Maths Shop

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


Striped Sheep

The wool on each of these sheep is of two different colours.

Striped Sheep

What is the probability of two sheep being picked at random sharing a wool colour?



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... #ad

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 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... #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.

Another Craig Barton Book

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

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
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



Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


More Sheepish Activities

How accurately could you estimate the number of sheep in a field without counting them? If there were only five sheep in the field your estimate would probably be very accurate but if there were fifty how close do you think your estimate might be? In the first case your estimate would have probably been perfect while in the second case you are unlikely to get it absolutely correct. What is the cut off number, between five and fifty where your estimate starts to become less accurate?

There is a sheep counting activity here on the Transum website. Try your skills and work to improve them. What strategies could you use?

Student Activity

Have you ever tried herding sheep? Not easy is it? The online herding sheep activity is much easier than real life herding and has proved to be a great introduction to loci.

Student Activity

Here is a sheepish mathematical birthday card which can be downloaded and printed.

Student Activity

Finally, for the more advanced, there's a sheep-themed exam style question for you to try.

Student Activity


©1997-2023 WWW.TRANSUM.ORG