Chapter 8: Strategies and problem solving

## Combinations

You might need to find strategies for counting the total number of possible combinations

One way of finding combinations is to make a systematic list

Here are al the possible three-digit numbers that can be made from the number cards shown on the right

## Counting with calculation

Sometimes it’s impossible to write down every possible combination

You can count combinations by multiplying the numbers of choices for each opion

Here is a four-character password for a website

The total number of possible passwords is 26x20x26x2=27040

## Problem solving

Work out how many choices there are for each dial

Dial 1-letter = 26 choices

Dial 2-digit from 0 to 9=10 choices

Dial 3-digit from 0 to 9 = 10 choices

The numbers of choices for each fia; has changed sometimes so 26 choices would increase to 25 if a letter was used

## Factors and Primes

You have to use a whole number of building blocks in each row, so the length of each row has to be a multiple of the length of one block

The answer will be the lowest common multiple

Top tip

If you are not sure how to start draw a sketch and this might help you see that the lengths are multiples of the numbers

## Fractions

There are lots of steps in this question so makes sure you keep track of your working and write it down clearly

Top tip

Write words with each calculations to explain what you are doing

## Recurring decimals

Start by writing x = the amount if you work out 1000x and 10x you can keep all your working in whole numbers

Top tip

If a question says ‘show that’ or ‘prove that’ you have to show every step of your working clearly and neatly

If a question says ‘shows that’ or ‘prove that’ you have to show every step of your working clearly and neatly

# Chapter 8: Strategies and problem solving

## Combinations

You might need to find strategies for counting the total number of possible combinations

One way of finding combinations is to make a systematic list

Here are al the possible three-digit numbers that can be made from the number cards shown on the right

## Counting with calculation

Sometimes it’s impossible to write down every possible combination

You can count combinations by multiplying the numbers of choices for each opion

Here is a four-character password for a website

The total number of possible passwords is 26x20x26x2=27040

## Problem solving

Work out how many choices there are for each dial

Dial 1-letter = 26 choices

Dial 2-digit from 0 to 9=10 choices

Dial 3-digit from 0 to 9 = 10 choices

The numbers of choices for each fia; has changed sometimes so 26 choices would increase to 25 if a letter was used

## Factors and Primes

You have to use a whole number of building blocks in each row, so the length of each row has to be a multiple of the length of one block

The answer will be the lowest common multiple

Top tip

If you are not sure how to start draw a sketch and this might help you see that the lengths are multiples of the numbers

## Fractions

There are lots of steps in this question so makes sure you keep track of your working and write it down clearly

Top tip

Write words with each calculations to explain what you are doing

## Recurring decimals

Start by writing x = the amount if you work out 1000x and 10x you can keep all your working in whole numbers

Top tip

If a question says ‘show that’ or ‘prove that’ you have to show every step of your working clearly and neatly

If a question says ‘shows that’ or ‘prove that’ you have to show every step of your working clearly and neatly