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Although this problem 'just' involved some calculating, explaining the results was a little more tricky. Charlie, Tom, James and Jonathan from Avenue Junior School looked at the journeys that Tom and Ben made:Tom starts at B then goes right and gets $5$ more which takes him to $15$.
Jessica from Egerton Primary School described how her class found lots of different ways of going from B to E on the grid:We found that in all four of our journeys we got $28$. The whole of the class got $28$ at least two times. Aidan and I used red and blue crayon to mark which way we went. Aidan and I think that we got $28$ because when you go one way you always have to go back the same way.
Harry, who goes to St Anne's Primary School, had a go at the routes on all three grids. He wrote:grid 1) We have found out that they both ended up on $28$. It doesn't matter how long or short their trial is, it will end up on the same answer.
Harry also played around with the grids a bit, changing addition to multiplication and subtraction to division or vice versa. This changed the answer but the answer was still always the same, no matter what route you took.
Jack and Skye from Swavesey Primary had a go at the third grid. They said:No matter what way you go, you will always end up with the same anwser. We tried a few ways using our computer screen following the journey with our fingers, this was on the multiplication and divide square.
Above, Jessica began to explain why she thought she always got $28$ on the first two grids. The Maths Galaxy Explorers from North Walsham Junior School clearly thought very hard about this:We spent our week trying to solve the Journeys in Numberland mathematical challenge. Here is our solution:
Well done too to Barbara, Cong and Nazra from Arnhem Wharf Primary School who also realised that they would always get the same score for a particular grid.
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?