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 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, : "We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. 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We all often use the starters as the pupils come in the door and get settled as we take the register." Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales: "Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!" Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk: "Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!" 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 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." 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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"