Combinations Starters:Bus Stop: How many different ways can four people stand in line? How Many Squares? 2: How many squares can be found by joining four dots on the grid? How Many Triangles? 1: How many Triangles can you find in the diagram? How Many Triangles? 2: How many triangles are hidden in the pattern? What strategy might you use to count them all to ensure you don't miss any out? How Many Triangles? 3: Find a systematic way of counting the number of triangles in the given diagram. Ice Cream: How many different ice cream cones can be made by choosing two scoops from six flavours? Noughts and Crosses: In how many different ways can the first X and O by placed on the grid? Snowman and Woman: How many different ways can you spell out the word snowman by moving from snowflake to snowflake. Thai Baht: How many different ways can you make a given total with Thai coins? Tran's Hats: In how many different ways might Tran decide to wear his hats in one week?
Small images of these Starters :: Index of Starters Combinations Advanced Starters:Back To The Factory: Find all the numbers below 1000 which have exactly 20 factors Nine Digit Numbers: How many different nine digit numbers are their that contain each of the digits from one to nine? Restrained Flea: How many different places could the flea find itself after 8 footlong jumps either north, south, east or west? Vowel Code: How many ways can you create a code for the vowels by assigning to each vowel a different vowel?
Curriculum for Combinations:Year 6Pupils should be taught to enumerate possibilities of combinations of two variables. more... Years 10 and 11Pupils should be taught to apply systematic listing strategies, {including use of the product rule for counting} more... Years 12 and 13Pupils should be taught to understand and use the binomial expansion of (a + bx)^{n} for positive integer n; the notations n! and ^{n}C_{r} link to binomial probabilities. Extend to any rational n, including its use for approximation more... ExamStyle Questions:There are almost a thousand examstyle questions unique to the Transum website. Feedback:Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex: "This website was brilliant. My class and I really enjoy doing the activites." Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. 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I nearly wet my pants with joy. Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School: "This is a great memory aid which could be used for formulae or key facts etc  in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is  my pupils love it! Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon: "Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated." Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School: "What a brilliant website. We have just started to use the 'starteroftheday' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources online we have found. The kids and staff love it. 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Keep up the good work and thank you very much Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School: "Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work." Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS: "This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles." Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull: "Dear Transum, Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.: "A really useful set of resources  thanks. 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The only problem is that there is too much good stuff here!!" Comment recorded on the i asp?ID_Top 'Starter of the Day' page by Ros, Belize: "A really awesome website! Teachers and students are learning in such a fun way! Keep it up..." Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai: "It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages." Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." 
Notes:"A combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruit, say an apple, orange and pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange."  Wikipedia Combinations Teacher Resources:Icecream Combinations: How many twoscoop ice creams can you make from the given flavours? Snake Sort: Sort the coloured snakes in a logical order. This activity introduces systematic listing. Combinations Activities:Xmas Tree Trim: Use the lights provided to decorate each of the Christmas trees so that no two trees are the same. Icecream Combinations: How many twoscoop ice creams can you make from the given flavours? Misfits: A Misfit is a character with a head, body and legs. How many different Misfits can you create? Snake Sort: Sort the coloured snakes in a logical order. This activity introduces systematic listing. Striped Sweets: Learn how to be systematic by colouring the sweet wrappers so that no two are the same. How Many Triangles?: A self marking step by step approach to calculating the number of triangles in a design. Six Keys: Use just six keys on your calculator to make a given total. How many different ways can it be done? Triplets: Find as many sets of three of the available numbers as possible which add up to the given total. Systematic Listing: Apply systematic listing strategies to find the number of combinations and permutations of choices. Take Baht: How many different ways can you make a given total with Thai coins? Scouts in Boats: Arrange a rota for the Scouts to travel in boats so that they are with different people each day. Combinations Investigations:Egg Box Investigation: In how many different ways can two eggs be arranged in an egg box? Design a badge: How many different badges can you make using three different coloured squares put together to make a rectangle? Transum Club: How many different colour schemes can you devise for the Transum Club Badge. Traffic Jams: How many ways can three cars be lined up in a traffic jam? House Painting: The houses in Mathsland are all three storeys tall. Each storey is painted using one colour. How many ways can the houses be painted? Odd Dice: Take three dice. How many ways can they be turned so that they show only odd numbers on top? Combinations Videos:Listing Strategies: Making a list in a logical order will help you avoid repetition and omission when finding combinations and permutations. Permutations: A video lesson on Permutations, calculating them using the counting principle and the nPr formula. Combinations and Permutations: Learn how to tell the difference between permutations and combinations and use the formulae to answer questions. The Counting Principle: The Counting Principle, Permutations, and Combinations. A fast paced, clearly illustrated video. Combinations Worksheets/Printables:Snowman Worksheet: This printable may help pupils work out how many different ways there are to spell snowman on the snow flake grid. Combinations External Links:Links to other websites containing resources for Combinations are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below: SearchThe activity you are looking for may have been classified in a different way from the way you were expecting. You can search the whole of Transum Maths by using the box below.

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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 inparticular 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"