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Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

• Xmas Tree Trim Use the lights provided to decorate each of the Christmas trees so that no two trees are the same.
• Ice-cream Combinations How many two-scoop 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.
• Design a badge How many different badges can you make using three different coloured squares put together to make a rectangle?
• How Many Triangles? A self marking step by step approach to calculating the number of triangles in a design.
• Football Scores If you know the final score of a football match, what might the half time score have been?
• Transum Club How many different colour schemes can you devise for the Transum Club Badge.
• Six Keys Use just six keys on your calculator to make a given total. How many different ways can it be done?
• 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?
• Listing Strategies Making a list in a logical order will help you avoid repetition and omission when finding combinations and permutations.
• 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?

Here are some exam-style questions on this statement:

• "Students in Year 10 at Riverdale High School can choose two different courses for their Friday afternoon elective lessons. Their two choices must be from two different school departments." ... more
• "A restaurant offers 6 starters, 14 main courses and 5 different desserts." ... more
• "Michael decides to order a starter and a main course from the restaurant menu." ... more
• "Patty O'Dores is reading the menu in a restaurant." ... more
• "There are four dials on a combination lock." ... more

See all these questions

Here are some Advanced Starters on this statement:

• Safest Safe
  What is the difference in the number of combinations available for the two safes? more
• Vowel Code
  How many ways can you create a code for the vowels by assigning to each vowel a different vowel? more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

• Combinations "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 In Primary school pupils should practise sorting and grouping items noting similarities and differences. They should develop strategies for finding all the ways a small number of items can be arranged so that missing or duplicates can be found quickly. By the end of Secondary school pupils will have learnt the formulas for combinations and permutations and apply them when solving probability problems.