# Snail Trail

### Task 82 ... Years 2 - 10

#### Summary

A 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

• wooden block of equally spaced holes (the well) and a dowel plug (the snail)

#### Content

• number patterns
• algebraic representation, generalisation and manipulation
• problem solving strategies

#### Iceberg

A 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:

• the height of the well
• the crawling up distance
• the sliding back distance
• the length of the time unit (eg: half hour units instead of one hour)
• whether the snail crawls up or down
Students can then set their own problem, explore it, find a number pattern and prepare a report (not necessarily written) to explain their investigation to someone else. The task then becomes a major investigation with an assessment purpose, so ensure students are aware of your assessment rubric before they begin their project.

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 Investigation

Tasks 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:

• If I tell you any number for each of these variables, can you tell me how to work out the time it takes the snail to get out of the well?

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 hands-on learning kits available from Years 3-10 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:

• MWA Pattern & Algebra Years 5 & 6
• MWA Pattern & Algebra Years 7 & 8

The Snail Trail lesson is an integral part of:

• MWA Pattern & Algebra Years 5 & 6
• MWA Pattern & Algebra Years 7 & 8
This task is also included in the Secondary Library Kit. Solutions for tasks in this kit can be found here.