Lemon

Strawberry

Vanilla

Peach

Chocolate

Mint

Undo
Click the buttons on the ice cream machine.

# Ice Cream Starter Of The Day

Topics: Starter | Combinations | Probability

• Mrs Simpson and 2D1, Torry Academy, Aberdeen
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• We spent the whole lesson investigating triangular numbers and constructing formulae from this lesson starter. Our class enjoyed it very much!
• Katherine Morelli-Batters,
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• I would like to say I got 28 solutions and it says there are only 21!
• Mrs Wallace, Blenheim High School
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• I had no trouble finding just 21 solutions. Make sure you read the question carefully. A cone is not different if turning it around makes it the same as another cone. A good starter.
• Mr Heeley's Y 7 stars, NLC, Huddersfield
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• Reece adopted a systematic method from the start and helped everybody to get started. We thought this was a cushtie starter; it made us hungry for more!
In fact, we thought this was so nICE we sCREAMed with delight!!
Lots of love to you all at Transum xxxx
• Christine Pardo and 5P, ISH
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• I am slightly concerend at the number of (presumably trained) teachers writing in saying they got the wrong answer!! What hope do the pupils have??!! My class and I thought this was a great starter; it's fun and enourgaes children to read questions carefully and record their answers systematically. Excellent!
• Tegan Googum, class, 5S1, Victory Ocean State Skewl
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• We could only find fifteen different combinations!
This is a mind bending activity.
• Mr Taylor, Gartree High School, Leics, UK
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• My classes enjoyed this starter, although I didn't notice the solution diagram at the bottom of the page untill after I'd taught two classes. My lower ability groups liked being able to make the combinations on the cones, but it was a bit laborious for the groups that got the hang of it quickly.
Perhaps there could be a link at the top of each page that takes you straight to the answer, rather than having to scroll down the page manually, past all the comments.
• D. Bracher, Bacton Community Middle School
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• A very good starter. Ethan says "why wasn't your answer in the shape of a cone?".
• ACD, Rainham
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• My high & low ability classes really enjoyed this starter. Maybe the answer could include a 6*6 sample space diagram showing all the possible combinations. This could be used to show how 15 of the combinations were duplicates because the order was unimportant.
Excellent starter.
• David Bracher, Bacton Community Middle School
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• My class thought this was a great starter. I am a little concerned, however, that Miss Pardo sholuld comment on trained teachers' failure to get the right answer when she failed to spell 'concerned' and 'encourages' correctly! To quote her, "what chance have the children if their teachers cannot spell?" We all make mistakes, so don't be so superior!
• K.Ward, Wolverhampton
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• There are definately 21 combinations. If you work systematically. My class got into quite a heated debate but came up with 21 eventually.
• Chynah Saxton , Aged 11, Chilton Trinity Bridgwater Somerset England Europe
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• But cant you have 1 on its own like strawberry or chocolate on its own.
• J Heeley, Whp Federation
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• If you work systematically of course you will find the correct solution; it's quite concerning to think that so many are missing the crucial point that, for example, strawberry and chocolate is the same as chocolate and strawberry. I did laugh when I read the reviewer expressing concern over teachers' mathematical ability who herself then made a spelling error in her review LOL!! I will use this with my year 8 this week as we have just completed a functional skills piece from Boland titled Ice creams (so it fits nicely).
• Hanxiao, China
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• (1+6)*6/2=21
(1+7)*7/2=28
(x+1)*x/2
=(x^2+x)/2.
• Mrs A O'hagan, Holyrood Sec School Glasgow
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• Second year class enjoyed this starter.
• Magen, Motherwell
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• I got 27 because if you swap the two scoops around it is tecnically a different combonation!
• Sarah, Age 11, Channing School, Highgate
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• This was really fun but quite tricky!
• Alan Brooke-Feather, Wolverley CE High School
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• I tried this with my top set year 7 after studying probability and combined events. They realised straight away that the way to tackle this was by using the sample space diagram then looking for similar outcomes eg sv=vs. My middle set year 8 took the longer path of listing outcomes without a space diagram, but enjoyed the challenge.
• D Robinson, Minnesota
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• There are 6 minus 1 possible combinations for unique flavors.
Since they are used in combination, then it would be 6 divided by 2.
So far we have (6-1) * 6/2 = 5 * 3 = 15
Lastly, we need to include the possibility for each flavor being its own combination or 6.
Therefore, (6-1) * 6/2 + 6
5 * 3 + 6
15 + 6
21.
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• My class did this all maths lesson!
• D Spence, Tameside
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• My class and I couldn't do this. I'm concerned at the number of combinations of ice creams we failed to find. What hope do the children have if neither they nor I can solve such a mind bending task?
• Dr Duxbury, Edwinstree Middle School
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• A rather ambiguous question! Does 'different' mean you cannot have the same flavour twice (e.g. two strawberry scoops whch I like) or that you count strawberry on the bottom and chocolate on top the same as chocolate on the bottom and strawberry on top (most ice-cream sellers rarely put the ice-cream side by side!). Do you have to have two scoops or can you have just one scoop?
Many assumptions made here which makes for a very good discussion with your class where they can find a variety of answers! At the end of the day as long as students can justify and explain their answers, this is all that matters.
• 4KJ, Hong Kong
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• It is easy and fun!!
• Primary, North West
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• Nice resource. Lots of odd comments. Would much prefer mint to lime then we could one letter to record flavours e.g. SL (strawberry and lemon).

[Transum: Great idea. Lime has now been changed to Mint. Thanks very much for the suggestion.]
• Primary, North West
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• I will be using it tomorrow so thank you for the quick update!
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• Kaiser Soazay, Yorkshire
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• Thank you. Brilliant. Found 21 ways.
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• Veera, UAE
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• Its two different scoops, so same flavor will not be there, so its 15 ways.
• Cosette, St Gregory School District
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• Loved this, I really enjoyed this and did it multiple times. I had my own tactic and did all the mints first then the chocolate and so on. This was fun :).
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• We liked this challenge. We missed one out but got it in the end. More of these please.
• Miss Lil, 3c
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• My class found it easy .Any challenging ones?

[Transum: Good to hear, Yes, scroll down the page for more challenges]
• Norri,
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• I think this was a very fun interactive task thanks.
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• I recently told my students I want the lesson title "Maths" to be changed to "Logic and Problem Solving".

In our recent Grade 9 Unit of Probability the students had to investigate different ways to list all the outcomes and then make connections and predictions. This looks an easy task but the difficult part for applying the communication skills to the problem solving.

I always notice that boys in-particular will write the first couple of outcomes in a jumbled order and then end up missing or repeating.

Thank you John Tranter for making Transum.org with these wonderful interactive tools to help with listing outcomes of events and logical ordering.

I think the favourite was the Ice Cream task!

All my students loved these resources and it was wonderful to see them ordering them in different ways but still showing a clear method and logic with their thinking. #notonerightanswer

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.

Previous Day | This starter is for 12 November | Next Day

What if there were 7 different flavours?

What if there were n different flavours?

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 GĂ¶del'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

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

## 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

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

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

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

Transum.org/go/?Num=457

## Curriculum Reference

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

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