Snails

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
Student Activity

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? Specific Learning Outcomes
Measure using cm.
Solve problems using minutes as the unit.
Devise and use problem solving strategies to explore situations mathematically
Description of Mathematics

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.

Required Resource Materials

Copymaster of the problem (English)

Picture of a snail (for introduction)

Copymaster of the problem (Māori)

cm rulers

Activity

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

1. Have the students estimate 2 cm using their fingers. Ask:
What do you use to estimate 2 cm?
2. Introduce Sally the snail and the time it takes for her to travel 2 cm. Ask:
Do you think that 2 cm is reasonable?
3. Pose the problem for the students to work on with a partner.
4. 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?
5. 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.

Attachments
Snails.pdf271.16 KB