Snail TrailTask 82 ... Years 2  10SummaryA snail climbs up the wall of a well for given time but while resting slips back down a given amount. The climb/slip pattern continues. How long will it take the snail to get out of the well. There is a movement pattern implied already, which is made more visual by the materials, so there will be a matching number pattern and the possibility of a generalisation. A classic problem with many directions to travel because of the what if questions that can be asked. 
Materials
Content

IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
The card indicates some of the depth of this task. A good iceberg question is to discuss what there is in the problem that could be changed, ie: identify the variables. They are:
Read one such report from Connor Gibbins, Year 7, St. Mary MacKillop College, Swan Hill. Also read this story of how the staff prepare their students to produce this level of work. 
Whole Class InvestigationTasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works. 
This investigation begins very well with physical involvement outside or in a multipurpose room. Teams of students stand up along a base line and step out 11 normal steps chalking marks on the ground as they go. The base line is numbered 0 and the other marks are numbered to 11. Tell the story of the snail and ask for guesses at the number of hours. Teams then check. Discuss the results and perhaps explore another example before returning to the classroom. Experience suggests that students involved physically in an investigation benefit further if they are asked to create a table top model to represent the outside activity. Ask them to do this to check the result of the outdoor investigation. You might provide graph paper and counters or even a duplicated sheet with a well drawing, but it can also be enlightening to simply say You can use anything in the room that you think will show the important things. If you have Poly Plug, students might choose to use 3 red boards for each group of 4, line them up end to end with the central column of plugs popped out and use a yellow/blue plug for the snail. Now the students have a model to work with, explore the variables of the problem as above and encourage a group decision about which example to explore. As students get the results, record their variables and outcome on the board. This data allows you to approach the 'big' question (if you wish) which is:
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 64, Snail Trail, which includes an Investigation Guide. Visit Snail Trail on Poly Plug & Tasks. 
Is it in Maths With Attitude?Maths With Attitude is a set of handson learning kits available from Years 310 which structure the use of tasks and whole class investigations into a week by week planner. 
The Snail Trail task is an integral part of:
The Snail Trail lesson is an integral part of:
