# Martian Maths

### Task 98 ... Years 4 - 8

#### Summary

Students are presented with 'hieroglyphics' based on simple shapes and are challenged to work out the number system being used. Then they apply their system to represent new numbers.
• Can the students extend this system further?
• Can they operate with this system?
• Can they devise their own similar system?

#### Materials

• 4 squares, 6 circles & 5 triangles
• 6 squares, 4 circles & 5 triangles

#### Content

• basic arithmetic skills, particularly times tables and addition
• value based number system with a hint of place value
• history of mathematics, particularly the development of number systems
• problem solving #### 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 two versions of this task simply to make best use of the way the pieces are supplied from the manufacturer. Check the number in the bottom right hand corner of the card to determine which solution below is appropriate in your case.

98a = 25, = 5, = 1

86 =      39 =       98b = 25, = 5, = 1

86 =      39 =       Note: Answers given are the most efficient in that they use the least number of pieces. However other solutions are possible and not wrong because we have not been informed of the martian rules for using the symbols. However, this is certainly an opportunity to discuss why efficient use of the symbols might be useful.
How many ways could the Martians find to make 39? Record as many as you can.
Extensions
• If you are using the shapes in the most efficient way:
Which number uses the largest number of shapes?
What is the highest number you can make? Show how to make it.
Invent a new shape so you can keep on counting?
• Imagine the Martian number system was arranged in columns like ours is. Then they would only have to draw each shape once at the head of each column. What digits would they need to use? Write some Martian numbers and explain how you 'translate' them into our numbers.
• Draw a circle and put any number of red dots in it. To the left of the circle write the number of dots in our number system. To the right of the circle write the number of dots in the Martian system.
• Add any number of blue dots to the circle. To the left of the circle write an addition sum in our system that shows what has happened. To the right of the circle write an addition sum in the Martian system that shows what has happened.
• Create a page for a Martian maths text book ... and provide the answers.
• The Martian system is based on 5 and ours is based on 10. Create a number system of your own based on different number.
• Research the history of number systems.

#### 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.

Shapes such as those used in the task are fairly easy to find. You only need enough of three different types and it doesn't really matter what they are. Check the art room. There are always interesting things that the art teacher has sourced from many and various places. Make up bags of shapes for each pair and use the card and the information above to direct the investigation. There is a rich unit on number systems that could develop from this starting point.

At this stage, Martian Maths does not have a matching lesson on Maths300. However, lessons related to number systems are:

• Lesson 176, Counting Machines
• Lesson 169, Human Computer
• Lesson 35, Nine & Over

For more ideas and discussion about these investigation, open a new browser tab (or page) and visit 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 Martian Maths task is an integral part of:

• MWA Number & Computation Years 5 & 6 