# Exemplification

Examples of what children should be able to do, to show a broad grasp of the content of this topic

## Example A

- Here is a list of seven numbers

From the list, write down

(i)a square number,

(ii)a number that is a multiple of 7,

(iii)two numbers that are factors of 40,

(iv)two numbers that are prime.
- Express the following numbers as products of their prime factors.

(i)56

(ii)84

(iii)Find the Highest Common Factor of 56 and 84.
- Tyrone says that “6 is a cube number because 23 = 6”.

Tyrone is wrong. Explain why.
- Paul writes down two sums.

**1 + 2 = 3**

**7 + 8 = 15**

Paul says “The sum of two whole consecutive numbers is never a square number”.

Give an example to show that Paul is wrong.

## Example B

- Write the number
**seventeen thousand, two hundred and two** in figures.
- Write the number 5262 correct to the nearest hundred.
- Write down the value of the 4 in the number 274 663
- Write 37 591 correct to 1 significant figure.
- Write 0.000 755 9 correct to 1 significant figure.

## Example C

- Write 15 as a percentage.
- Write 25 as a decimal.
- Write 0.3 as a fraction.
- Write 11% as a fraction.
- Write 0.25 as a percentage.
- Write 8% as a decimal.

## Example D

Write these numbers in order of size.

Start with the smallest number.

- –3,0,–7,–1,5
- 0.72,0.7,0.07,0.702,0.072
- 67%340.722335
- 3412162338

## Example E

- Some students each chose one PE activity.

15 of the students chose hockey.

38 of the students chose football.

All the rest of these students chose basketball.

What fraction of the students chose basketball?

- A school has 1200 pupils.

625 of these pupils are boys.

25 of the girls like sport.

35 of the boys like sport.

Work out the total number of pupils in the school who like sport.

## Example F

- Ron went to Spain.

He changed pounds (£) into Euros (€). The exchange rate was £1 = €1.22

The value of the pound has decreased from €1.22 to €1.13

Calculate the percentage decrease in the value of the pound.

- Hugh went on holiday to Italy.

While on holiday, he went shopping.

He bought a tee shirt and a belt.

The tee shirt cost 25 euros.

The belt cost 14 euros.

The exchange rate was £1 = 1.18 euros.

Work out the total cost of the tee shirt and the belt.

Give the total cost in pounds.

## Example G

- In a sale all the normal prices are reduced by 18%.

In the sale Manim pays £12.71 for a bag.

Calculate the normal price of the bag.

- Bill bought a box of 40 oranges for £2.

310 of the 40 oranges were damaged so he threw them away.

He sold the remaining oranges at *x* pence each.

He made a profit of 40%.

Calculate the value of *x*.

- A year ago, Donna weighed 51.5 kg.

Donna now weighs 8.5% less.

Work out how much Donna now weighs.

Give your answer to an appropriate degree of accuracy.

## Example H

Mr Holland uses 367 units of electricity in one month.

He pays 5.84p for each unit of electricity.

Mr Holland also pays a fixed charge of £6.14 for the month.

Work out the **total amount** he pays.

## Example I

Here is part of a railway timetable.

Aytoun | 11 30 | 11 55 | – | – | 12 30 | 12 55 |

Beeston | 11 34 | 11 59 | 12 04 | 12 29 | 12 34 | 12 59 |

Carton | 11 39 | 12 04 | 12 09 | 12 34 | 12 39 | 13 04 |

Dunton | 11 53 | – | 12 23 | – | 12 53 | – |

Eastleigh | 11 59 | – | 12 29 | – | 12 59 | – |

Farnton | 12 17 | 12 30 | 12 48 | 13 05 | 13 17 | 13 31 |

A train leaves Aytoun at 11 55

- At what time should this train arrive in Farnton?

Another train leaves Aytoun at 12 55

- Work out how many minutes it should take this train to get to Farnton.

James is going to Farnton.

He will catch the train in Dunton.

Jerry needs to arrive in Farnton **before** 13 00

- Write down the time of the latest train he can catch from Dunton.

## Example J

Mr White stayed some time at the South Pole.

The highest temperature there was –28 °C.

The lowest temperature there was –55 °C.

- Work out the difference between the highest temperature and the lowest temperature at the South Pole.
Mr White returned to his house in England.

The temperature outside his house was –1 °C.

The temperature inside his house was 15 °C higher.

- Work out the temperature inside his house.

## Example K

- Work out the value of 4 + 5 × (2 + 3)
- Add brackets ( ) to make each statement below correct.

You may use more than one pair of brackets in each statement.

(i) 2 + 3 × 4 + 5 = 29

(ii) 2 + 3 × 4 + 5 = 45

- Use your calculator to work out (2.7 + 1.9)
^{2} × 1.07

Write down all the figures on your calculator display.
- Put brackets in the expression below so that its value is 45.024

1.6+3.8×2.4×4.2

## Example L

One gigabyte is 1 073 741 824 bytes.

- Write the number 1 073 741 824 in standard form.

A hard disk can store 500 gigabytes of data.
- How many bytes is this? Write your answer in standard form.