There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Combinations. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### 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?

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 foot-long 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?

#### Xmas Tree Trim

Use the lights provided to decorate each of the Christmas trees so that no two trees are the same.

Transum.org/go/?to=xmastrim

### Curriculum for Combinations:

#### Year 6

Pupils should be taught to enumerate possibilities of combinations of two variables. more...

#### Years 10 and 11

Pupils should be taught to apply systematic listing strategies, {including use of the product rule for counting} more...

#### Years 12 and 13

Pupils should be taught to understand and use the binomial expansion of (a + bx)n for positive integer n; the notations n! and nCr link to binomial probabilities. Extend to any rational n, including its use for approximation more...

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"I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson."

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 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!"

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"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks."

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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

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.

### Combinations Teacher Resources:

Ice-cream Combinations: How many two-scoop 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:

How Many Triangles?: A self marking step by step approach to calculating the number of triangles in a design.

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?

Scouts in Boats: Arrange a rota for the Scouts to travel in boats so that they are with different people each day.

Six Keys: Use just six keys on your calculator to make a given total. How many different ways can it be done?

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.

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?

Triplets: Find as many sets of three of the available numbers as possible which add up to the given total.

Xmas Tree Trim: Use the lights provided to decorate each of the Christmas trees so that no two trees are the same.

### Combinations Investigations:

Design a badge: How many different badges can you make using three different coloured squares put together to make a rectangle?

Egg Box Investigation: In how many different ways can two eggs be arranged in an egg box?

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?

Traffic Jams: How many ways can three cars be lined up in a traffic jam?

Transum Club: How many different colour schemes can you devise for the Transum Club Badge.

### Combinations Videos:

Combinations and Permutations: Learn how to tell the difference between permutations and combinations and use the formulae to answer questions.

Permutations: A video lesson on Permutations, calculating them using the counting principle and the nPr formula.

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.

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:

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#### How Many Triangles?

A self marking step by step approach to calculating the number of triangles in a design.

Transum.org/go/?to=howmany

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Saturday, September 18, 2021

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