It was interesting to read the solutions that came in. While doing this I found that the question had been interpreted in two ways. It was all about whether each new step meant a new start at zero or not. I think that it is right to accept both interpretations. This sometimes happens in the classroom with challenges or investigations.

Firstly, here's a solution from Badger Class at Fawkham C of E School:

First Leah made a jump of three along her number line and then a jump of four.

She landed on seven. We worked it out by adding four and three.

Next Leah made a secret jump along her number line.

Then she made a jump of five and landed on nine. We worked out by counting back three from seven and then add on five.

Then Leah made a jump of six and another secret and she landed on ten. So the secret number is four. We worked it out by the sum 6 + 4 = 10

TOM

First Tom made a jump of three up his number line and then a jump of two. So the number is five. We worked it out by adding three and two so that makes five.

Next Tom made a secret jump up his number line. Then he made a jump of six and landed on eight. He went back three jumps and forward six jumps.

Then Tom made a jump of four and another secret jump. He landed on seven. His second secret jump was three.

Thank you to Daniel from Englefield Green Infant School and Daina and Emma from Kelso State School for their solutions to the Number Lines problem. Daniel said:

Leah's first jump landed at 7, 3+4=7

Leah's first secret jump was 4, 4+5=9

Leah's second secret jump was 4, 6+4=10

Tom's first jump landed at 5, 3+2=5

Tom's first secret jump was 2, 2+6=8

Tom's second secret jump was 3, 4+3=7

Lastly, this was sent in by Alexander who goes to Freemantle Primary School in Australia:

Leah's first secret jump was 4, and her second secret jump was 4.

Tom's first secret jump was 2, and his second secret jump was 3.

If you come to this challenge after November 2013 please send in any further solutions and ways in which you worked them out.