This activity asks students to record possible paths and the associated sums and gives them a chance to practise mentally adding a series of numbers. It provides an opportunity for students to explore the mathematics of networks, a topic that is developed much later in the curriculum. (This connects to the geometry strand.)
Strategies for solving the problem and recording methods can be shared. Ask them to explain and justify how they know that all possible paths have been checked.
Students might like to try question 1 as a race. Working in pairs, one student could calculate mentally while the other checks with the calculator. This approach should reinforce the fact that mental strategies are often faster than using a calculator.
Students could use the information gathered to answer this additional question: “Which path should Rufus take if he wants to collect the least number of carrots?”
As an extension, suggest that students create a new map for Rufus and change the numbers to make the addition more challenging.

Answers to Activity

1. Rufus can get:
22 (4 + 7 + 6 + 5)
41 (4 + 7 + 6 + 4 + 8 + 3 + 9)
43 (4 + 7 + 6 + 4 + 8 + 3 + 2 + 9)
24 (4 + 5 + 4 + 6 + 5)
33 (4 + 5 + 4 + 8 + 3 + 9)
35 (4 + 5 + 4 + 8 + 3 + 2 + 9)
34 (8 + 3 + 8 + 4 + 6 + 5)
50 (8 + 3 + 8 + 4 + 5 + 4 + 7 + 6 + 5)
31 (8 + 3 + 8 + 3 + 9)
22 (8 + 3 + 2 + 9)
48 (8 + 3 + 2 + 9 + 3 + 8 + 4 + 6 + 5)
64 (8 + 3 + 2 + 9 + 3 + 8 + 4 + 5 + 4 + 7 + 6 + 5)
2. Rufus should follow the 8 + 3 + 2 + 9 + 3 + 8 + 4 + 5 + 4 + 7 + 6 + 5 path, which will give him 64 carrots.