## The stupid gardener

Concepts | Arithmetic, arithmetic shortcuts |
---|---|

KS3 curriculum | 3.1b |

KS4 curriculum | 3.1b |

### Resources

### Teaching notes

To find the solution, students can either add all the numbers from 1 to 100, and double this for the return journey, or add all of the even numbers from 2 to 200.

Rather than simply adding all 100 numbers together, a quicker way of working out the total is to pair the numbers up, ie 1 + 99, 2 + 98, 3 + 97, and so on up to 49 + 51. This gives 49 x 100 = 4900. Then add the 100 and the 50, and double the total to include the return journeys.

### Solution

The total is *10,100 m*, or 10.1 km.

### Extension

- Ask students to find the nth term for any number of plants planted.
- What if the gardener picks the strawberries two or three at a time?