Use multiplication to solve addition and subtraction problems.

Number Framework Stage 7

The famous mathematician Carl Friedrich Gauss was asked as a five year old to work out 1 + 2 + 3 + ... + 99 + 100. He almost instantly replied the answer was 5050. How could he have got the answer so fast?

#### Using Materials

This is the method Gauss used to add up the numbers 1 to 10.

Place cards from 1 to 10 in order

Place 10 under 1, 2 under 9, and so on.

Discuss the total of each pair. *(Answer: it is 11.)*

Discuss why the total is 5 x 11 = 55. *(Answer: There are 5 pairs each adding to 11.)*

Repeat for 1 + 2 + 3 + 4 + ... + 8, 1 + 2 + 3 + 4 + ... + 12, 1 + 2 + 3 + 4 + ... + 14

#### Using Number Properties

Solve Gauss’ problem: 1 + 2 + 3 + 4 + ... + 98 + 99 + 100.*(Answer: 1 and 100 = 101, 2 and 99 = 101 ... So the series adds up to 50 *_ *101 = **5050.)*

Repeat for 1 + 2 + 3 + 4 + ... + 999 + 1000,

1 + 2 + 3 + 4 + ... + 46,

1 + 2 + 3 + 4 + ... + 88.

#### Understanding Number Properties:

Find a formula for 1 + 2 + 3 + 4 + ... + 2 n. *(Answer: n*(2*n *+ 1)*.)*