# Which Floor?

### Task 52 ... Years 2 - 7

#### Summary

A person enters an elevator and takes a three step journey of ups and downs. If you know the journey and the starting floor, what is the finishing floor? The problem involves being aware of the limits created by the building itself. It has a fixed number of floors and no basements. At the initial level it is a closed question and can be addressed by logical reasoning using the 'building' as a form of truncated number line. However, the What happens if... questions offer many more challenging possibilities.

#### Materials

• Representation of the building
• Block to represent the movement of the elevator

#### Content

• logical reasoning
• counting
• sequencing
• informal concept of an equation

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

It doesn't take long for students to work out that Bronwyn entered at the 8th floor. They might use guess and check, they might work backwards, or they might write an equation (where S = Start):

S - 5 + 6 - 7 = 2
S - 6 = 2
S = 8
Whichever strategy is used this first challenge is closed. However the second challenge not only has more than one answer, it encourages students to find all the answers. The journey remains the same, but the exit floor is changed. Now students have to take into account the limits of the building. Bronwyn cannot enter from, or at any stage go above, the 10th floor. Similarly she cannot enter from, or at any stage go below, the 0th (Ground) floor. Therefore she can enter only from the 9th, 8th, 7th or 6th floors and correspondingly exit at the 3rd, 2nd, 1st or Ground floors.

These extension thoughts begin with keeping the exit floor the same and changing the journey:

• Use the same building and create your own 3-step journey for Bronwyn that finishes on the 2nd floor.
• What other 3-step journeys can Bronwyn take from the 8th floor to the 2nd floor?
• What about 2-step (or 4-step) journeys from the 8th to the 2nd.
• What happens if you use a 2-step (or 4-step) journey for other exit floors?
• What happens if you change the size of the building?
• Bronwyn and David work in a building with twin elevators like the one on the card. They enter at different floors, but both come out on the 3rd floor. What 3-step journey might each of them have taken?
• Can you design a 'Bronwyn and David' game?

#### 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.

You might like to introduce the problem in a physically involving way, perhaps outside the classroom. Many schools have number lines marked on the school yard. If not, it is easy to use signs to mark out the floors of the building and choose 'Bronwyn' to step out the instructions. Back at the classroom tables the problem can be recreated with a printed sheet of the building and a block or other object to represent the lift. Poly Plug can also be used, if you happen to have that resource.

Visit Which Floor? on Poly Plug & Tasks.

At this stage, Which Floor? does not have a matching lesson on Maths300.

#### 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 Which Floor? task is an integral part of:

• MWA Number & Computation Years 3 & 4