# Coloured Sheep

## A Maths Starter of The Day

There are 16 sheep in a field as shown here:

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 ?

Topics: Starter | Probability

• Mr Heeley's Y7 lambs, Rawthorpe High School
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• 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
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• This is a great starter to begin the day with. The students thought that it was great.
• MSJ, 8x3
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• Keenan thought it was Baarilliant.
• Mrs Porter, Upholland High
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• 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
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• Great activity.
Has the word "not" been forgotten in the part d answer?
• Transum,
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• Thanks M Phillips for pointing out the error. It has now been corrected.
• Zoe Thompson, Channing Junior School, Highgate
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• 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
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• I think this an absolutely delightful question but surely the answer is 12, I don't get it.
• Transum,
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• 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
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• 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
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• 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.

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.

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This starter has scored a mean of 3.1 out of 5 based on 291 votes.

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.

 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=May19

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

Transum.org/go/?to=prob

## Striped Sheep

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

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...

## 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.

## 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?

Transum.org/go/?to=estimate

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.

Transum.org/go/?to=herding

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

Transum.org/Maths/Worksheet/?name=birthday_card

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

Transum.org/Maths/Exam/Question.asp?Q=289

For Students:

For All: