# In The Bag

### Task 73 ... Years 2 - 10

#### Summary

The initial challenges in this task are spatial. In essence students are using jigsaw pieces, but by doing the puzzles 'blind' inside a 'black bag' the students are calling on visual imagery and kinaesthetic sense and developing spatial perception. Spatial perception is very important to mathematicians, who often see their solutions before proving them, and equally important in life in situations involving packing and stacking (or reverse parking). The iceberg of the task is a surprise to many. It also models algebraic substitution.

#### Materials

• Specific foam shapes as shown

#### Content

• 2D spatial perception
• algebraic substitution

#### Iceberg

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

There are no specific solutions to this task. However, students can exit this task after any question and feel successful, then re-enter it at another time and try a higher level of difficulty. The most difficult puzzle is hard to get into the frame even when the pieces can be seen. Any student who can do it in the bag has great command of their tactile skills and visual memory.

The task can be related to:

• some of the work done by astronauts in outer space
• operating 'robot arms' inside containers of radioactive material
• doctors instructing a robot to operate while viewing a monitor on the other side of the room.
The task is also a geometric model of algebraic substitution and those who want to lead into the symbolic expression of this representation can apply the approach used in Task 65, Shape Algebra, and Task 71, Algebra Through Geometry. These tasks also provide recording sheets that can be used with In The Bag.

#### 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.

The two ways to turn this task into a whole class investigation are:

1. Use it at a work station that students come to over time. At intervals discuss the cues students use to solve the puzzles. If appropriate, introduce the x and y descriptions from Tasks 65 & 71.
2. Purchase additional copies of the materials for this task so that all pairs of students can be trying the puzzles at the same time. Given there are several puzzles in the one task and the students can swap, you may only need a few sets.
Students might also like to try creating their own 'In The Bag' puzzles from cardboard.

At this stage, In The Bag 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 In The Bag task is an integral part of:

• MWA Space & Logic Years 3 & 4
• MWA Space & Logic Years 7 & 8