# Planets

### Task 126 ... Years 4 - 10

#### Summary

Students are provided with the materials and measurements to build a model of our solar system at a moment in time. The activity involves considerable proportional reasoning and when complete offers the bridge into an astounding realisation about the relative sizes and distances within this minute corner of the universe. Perhaps one of the remarkable outcomes occurs when the question is finally asked:
In all the universe on which planet can we be sure there is life?.

#### Materials

• 9 planet cards, one sun card and 10 clips
• at least 6 metres of string and sticky tac

#### Content

• estimating number
• estimating length
• ratio & proportion
• scale
• units of measure
• metric measurement
• arithmetic of large numbers
• visualisation

#### Iceberg

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

The solution is shown on the left but the discussion and re-evaluation involved in reaching it, as suggested by these photos, is very important. These Year 7 students from St. Francis Xavier College, Berwick, Victoria are working in the space outside their task centre room.

You can read more of the work at St. Francis Xavier College here.

The measurements on the card are taken at a moment in time and represent an average. The movement of the planets is more complex than suggested by the table; for example not all the planets orbit the earth in the same plane, but occasionally they are in an alignment that allows the image of the string to be valid. Some students with an interest in astronomy may wish to discuss such details.

One of the exciting things about this task is that although it deals with very large numbers, judicious application of estimation (rounding off) and multiplication go a long way towards uncovering the wonder of the creation that resides within our solar system. The string is about 6 metres long. The solar system is about 6,000 million kilometres from the Sun to Pluto. This sets a scale:

• 1 metre = 1,000 million kilometres (roughly)

Half of the length to Pluto is about 3000 million kilometres and remarkably Uranus is at about that position. Half of the distance between Uranus and Pluto is 4500 million kilometres, and again a planet, Neptune, is there. Continuing this proportional reasoning helps to find a position for each of the other planets, with the only break from the pattern occurring between Mars and Jupiter. It was, in fact, this break from the pattern which led astronomers to look more carefully in this region and eventually discover the asteroids, which by some judgements are the fragments of a destroyed planet.

At senior levels, there is an opportunity here to link with work students may be doing in science related to the formulas which govern the gravitational forces between planets. An important question to a mathematician is Can I check it another way?. In this case the placement of the planet cards along the string can be checked by application of the scale in a more precise manner, namely:

• 1 metre = 1,000 million kilometres (roughly)
• 1 centimetre = 10 million kilometres
• 1 millimetre = 1 million kilometres
So on this scale, Mercury would be 5.8 centimetres from the Sun, Venus would be 10.9cm and Earth would be 15cm, as shown above in the left column. That is a very small proportion of the total 6m distance, and yet Earth is the only place in the Universe where we are sure there is life.

An extension of the task develops from the realisation that the cards are all the same size and therefore don't truly represent the diameters of the planets. Research will reveal the diameters of the planets and the students can work out what these would become if the solar system was only as big as the string.

#### 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.

To convert this to a whole class investigation, go outside and mark out sixty metres on the oval starting at the goal line. Use larger cards for each planet (name cards will do), divide the class into nine groups and give each group a card and tell them its distance from the sun. Continue guided by the information above.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 100, Planets.

Note: In this investigation there is lots of room for broader discussion across subject boundaries. For example, the Planets do not all orbit in the same plane so the straight line image presented by the task is a rare event. Also, in 2006, amongst considerable controversy, Pluto was declared a non-planet. It has apparently regained some astronomical status since as it seems to now be referred to as a dwarf planet. (We trust Mickey Mouse's dog has not been offended by this status change.)

#### 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 Planets task is an integral part of:

• MWA Chance & Measurement Years 5 & 6
• MWA Chance & Measurement Years 9 & 10

The Planets lesson is an integral part of:

• MWA Chance & Measurement Years 5 & 6
• MWA Chance & Measurement Years 9 & 10
This task is also included in the Primary Library Kit. Solutions for tasks in the latter kit can be found here.