Sally the Snail crawls 2cm each minute.

She needs to rest at each dot for 5 minutes.

She wants to take the shortest time to reach a plant.

Which path should she take?

This problem explores time in minutes and distance in centimetres.

The calculations involve single digit addition and multiplication, and afford opportunities for students to apply a range of strategies.

Picture of a snail (for introduction)

Copymaster of the problem (Māori)

cm rulers

### Problem

Sally the Snail crawls 2cm each minute. She needs to rest at each dot for 5 minutes. She wants to take the shortest time to reach a plant. Which path should she take?

(see Copymaster for the picture of the paths)

### Teaching sequence

- Have the students estimate 2 cm using their fingers. Ask:
*What do you use to estimate 2 cm?* - Introduce Sally the snail and the time it takes for her to travel 2 cm. Ask:
*Do you think that 2 cm is reasonable?* - Pose the problem for the students to work on with a partner.
- As the students work, ask questions that focus them on communicating the steps they take to solve the problem.
*What was the first thing you did when solving the problem?*

Could you solve it another way?*How do you know that you are correct?* - Share solutions.

#### Extension to the problem

Get the students to create their own snail problem for others to solve. The may decide to vary the speed that Sally moves.

#### Solution

Path 1: The snail has to travel 2 + 4 + 6 + 2 = 14 cm which takes 7 minutes. She has 3 rest stops which take 15 minutes. So the total time for the trip is 22 minutes.

Path 2: The snail has to travel 2 + 2 + 2 + 2 + 2 + 2 = 12 cm which takes 6 minutes. She has 5 rest stops which take 25 minutes. So the total time for the trip is 31 minutes.

Path 3: The snail has to travel 4 + 6 + 2 + 4 = 16 cm which takes 8 minutes. She has 3 rest stops which take 15 minutes. So the total time for the trip is 23 minutes.

Path 4: The snail has to travel 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18 cm which takes 9 minutes. She has 8 rest stops which take 40 minutes. So the total time for the trip is 49 minutes.

Some students may add another 5 minutes for the final dot on each path but at that point Sally is already at the plant.

Th epath that takes the shortest time is path 1.