Here to There 1 2 3
Problem
Move from the START to the FINISH by moving across, down or up to the next square. You can only move into each square once.
Add the numbers as you go.
Find the path that gives the smallest total.
Find the path that gives the highest total.
Find a path that equals exactly 12.
How many paths make 12?
Getting Started
Try looking for the lowest numbers on the grid.
Will visiting the largest number of squares give us the greatest total? Can we visit all the squares?
Student Solutions
Olivia and Poppy from St Mary's School, and Yanqing from Lipson Community College all suggested that the smallest total they could find is 8 using the route: 1-2-1-1-1-1-1.
Eva who goes to Benenden School sent in the largest total and describes the route:
1 (right to) 2 (right to) 1 (right to) 2 (down to) 1 (left to) 3 (left to) 3 (left to) 2 (down to) 1 (down to) 2 (right to) 1 (up to) 1 (right to) 1 (down to) 3 (right to) 1 Total = 25
Eva also sent in a path that made 12:
1 (right to) 2 (down to) 3 (down to) 1 (right to) 1 (down to) 3 (right to) 1
Emma from Maryhill High School found a different route that also has a total of 12:
1-2-3-3-1-1-1
Children at New Earswick Primary School found some other solutions to make 12:
Alex found:
1 (down to) 2 (right to) 3 (right to) 3 (down to) 1 (right to) 1 (down to) 1.
1 (down to) 2 (right to) 3 (right to ) 3 (right to) 1 (down to) 1(down to) 1.
Perhaps one of the last two is the same as Emma's - but well descibed, Alex, Ben and Josh.
Teachers' Resources
Here to There 1 2 3
Move from the START to the FINISH by moving across, down or up to the next square. You can only move into each square once.
Add the numbers as you go.
Find the path that gives the smallest total.
Find the path that gives the highest total.
Find a path that equals exactly 12.
How many paths make 12?