Underneath the Stars

Maths Unit
Looking up!

The aim of this unit is to help pupils understand the significance of the constellations of the night sky in terms of patterns, location and scale.

Key Questions:

  1. How can we find something in the night sky?
  2. Can we model our place in space?
  3. Can we travel through time?
  4. What is the farthest thing we can see?


Developing Pupils’ Thinking Skills and Personal Capabilities

Developing Pupils’ Knowledge, Understanding and Skills

Thinking, Problem-Solving, Decision-Making:

  • identifying and clarifying the problem
  • coming up with possible solutions
  • thinking through the implications of each solution
  • selecting and trying out the most appropriate solution

Managing Information:

  • develop a research plan
  • check reliability of sources


 Knowledge and understanding of number.

The creative use of technology to enhance mathematical understanding.


How can we find something in the night sky?

Learning Intentions
Pupils are learning…

Possible learning, teaching and assessment activities

…about different ways to describe a position.

Class considers the problem:
“How do we describe the position of an object in the sky at night, for example, the moon, a particular star, satellites, etc.?”

Class come up with a range of ideas and discuss these, identifying their relative merits.  
They also discuss possible difficulties, for example:

  • parts of the sky could obscured by clouds and mist;
  • objects move;
  • the sky changes from day to night and from season to season.

Using a celestial sphere/map
Introduce the idea that the sky can be viewed from Earth as a sphere which we appear to be inside- a complete circle 360 degrees that can be split into segments like an orange.
Explore how to divide the sky into segments, for example 45 degrees, 90 degrees. Can we see the entire night sky at one time. Why not?

Useful resource -  star-finder/planisphere.
The planisphere can be created as part of the maths exercise or during a science lesson.


…to recognise patterns of stars in the sky.







…to measure and record angles in different contexts.
…to communicate using precise directional language

Making sense of the sky
Discuss questions, for example, how did ancient civilisations make sense of the stars? How did they remember where a particular star was?
Prompt idea of breaking the sky up into bits and making patterns out of stars, creating constellations or star maps. Pupils reflect on and evaluate the usefulness of this solution for ancient navigation and other uses.

Ask pupils if they know the names of any constellation and if they can describe their shapes (for example, star signs).

Measuring and Using Angles
Pupils work in groups and choose a constellation. They locate it on the planisphere.

They print out/photocopy the classical figure(s) related to their constellation. They draw lines, if necessary, to complete the star pattern. (Links to activity in English).
They measure the angles making up the shapes and record their results.

Each person creates a new pattern from the constellation using a limited number of stars. They measure all the angles. They then go into pairs. Sitting back-to-back one person describes their unique pattern to a partner who can’t see the pattern but has to draw it.

After a few minutes they match the two versions and discuss what made it easy/difficult for the person trying to draw the unseen pattern, for example, the clarity of the description, the precision of the instructions, the use of directional language relating to distance, angles, size etc. They then swap roles and attempt the other constellation taking into account the need for precise directional language and description.

Opportunity to develop/assess Communication – talking & listening


… to develop a sense of perspective about the physical world.








…to give an individual response to a poem

Distance and Scale

Use prompts such as:

  • How far away are the stars?
  • Are all the stars the same distance away?
  • What is the greatest distance you can think of?
  • What is the smallest thing you can think of?
  • What words can you use to describe these sizes/distances? 
  • Do we have enough words to describe them?
  • How else can we convey a sense of size?
  • What units do we have to measure them?

Pupils discuss these questions in small groups and share their answers. The most interesting answers are agreed and recorded.

Pupils read the poem “0”   by John Agard in Einstein, The Girl Who Hated Maths   Hodder 0-7502-4288-4.

  • What is the poet saying about scale?
  • How does this help us understand scale?


…to use appropriate units of measurement






…to write numbers in standard form.



Measuring a journey – powers of ten (standard form)
Pupils measure or estimate the distance of a journey, for example, journey to school (for example, using Infomapper, OS maps).
They explore different ways of describing the journey, for example, in terms of distance or time. They decide the most appropriate units to measure the distance, for example, km, m, cm, mm. How long does it take?

They consider how this journey would/will differ:

  • 10 years ago,
  • 100 years ago,
  • 10 years in the future,
  • 100 years in the future, etc.

They give reasons to support their ideas. The may predict the likelihood of some of the interesting and unusual predictions given.

Pupils look back at the journey they have chosen and try to use the km, m, cm and mm scales to measure it. What happens to the numbers as the unit used changes?
Where appropriate, write the number using powers of ten (standard form) notation.








Getting smaller
Pupils consider how to measure something very small, for example, a human hair. They consider:

  1. How to measure its length and breadth?
  2. What units could be used to measure these in?

Linking with Science, use a microscope/digital eyepiece to observe and measure prepared slide or human hair using a graticule or other scale.

Discusses the importance of using powers of ten (standard form) to generate units and numbers that are easily manageable.

Can we model our place in space?

Learning Intentions
Pupils are learning…

Possible learning, teaching and assessment activities



…how to represent and sequence huge numbers.
…to clarify problems
…to think of possible solutions

…to think about the implications of each possible solution
…to select and try out the most appropriate solution
Thinking, Problem-Solving, Decision-Making





Getting bigger
The pupils are set the task of seeing if it possible to make a scale model of the Earth and Sun to show an Astronomical Unit (AU)
[1 AU = distance from earth to sun]

They consider the task and begin to identify the challenges of representing objects that have very different sizes and are a huge distance apart.
They can use the on-line calculator to scale the size and distances, at the link below:
Children's University of Manchester.

They identify possible implications for displaying a model, 

  1. what objects could be used to represent sun and earth?
  2. where could the model could be displayed?

(Note; if the sun is represented by a beachball with a diameter of 500mm, the earth would be a tiny ball of blue-tac – covering a pinhead. They would be situated almost 60 metres apart.)

The pupils consider where they could put their scaled model (would it fit in classroom, playground, pitch etc?). They select the appropriate measuring equipment for the distance between them (ruler, tape-measure, trundle-wheel, etc.) and draw a diagram to scale or record the model using a digital camera.

…to demonstrate a sense of curiosity or wonder.


Pupils consider the question; can the moon be represented on this model as well? Why/why not? How?

They consider questions about this model such as;
what surprised you about it? How does it make you feel?

The pupils record this distance between earth and sun in km, m, cm and even mm!
Introduces the Astronomical Unit (AU) as a unit of measurement and explains that 1AU is the distance from the Earth to the Sun.
Pupils express AU in terms of km.

This activity could be further extended to model other planets in the solar system.





What is the distance to the next star?
Pupils find the distance to the next star.
They consider the question, is the AU a suitable unit of measurement for this distance?
Teacher discusses the importance of the term Light Year as a unit of measurement. Pupils express 1 light year in Aus and km.

[1 light year = distance traveled by light in one year.]

Can we travel through time?

Learning Intentions
Pupils are learning…

Possible learning, teaching and assessment activities



…to appreciate size and scale.







Working in groups, pupils present a table of their respective birthdays. On it they work out how far light has traveled since they were born in:

  1. Light years
  2. Astronomical Units
  3. Km

Pupils may go on to research the distances in light years to other bright stars, such as The North Star, Beteleguese and Deneb, Vega and Altair (the Summer Triangle).

When looking into space, it is like looking back into time.  Objects are seen as they were when light left them.
They find out what major events (personal, historical, sporting, etc.) locally or globally took place at the time when the light left the star.

What is the farthest thing we can see?

Learning Intentions
Pupils are learning…

Possible learning, teaching and assessment activities



…to use on-line research grade technology.





…to reflect on their findings and express a sense of spiritual awareness.

Nearly everything we can see with the naked eye belongs to our galaxy, The Milky Way. The most powerful telescopes allow us to look in greater depth at objects within our galaxies and other galaxies.

The Faulkes Telescope Project operates two 2-metre optical telescopes, located in Hawaii and Australia. These telescopes are used by school students in the UK and other areas of the EU. Faulkes Telescope users from across the world can take beautiful images of objects in the night sky, live from their classrooms, and participate in international research programmes with astronomers from around the world.

Pupils can take control of the largest educational telescopes in the world and view objects within our galaxy and beyond. 

The web site provides details on how to observe and classify galaxies, for example, taking images of galaxies and classifying them using the Hubble Tuning Fork
Pupils choose a galaxy, for example, The Whirlpool Galaxy and record its distance in light years.

Teacher leads debriefing with statement stems such as;

  • What amazed me most was…
  • What really made me think was…
  • This make me feel…
  • Scale is when you …
  • Infinity means…

Responses are shared and compared.

Development of Learning Outcomes

  • research and manage information effectively to investigate and solve mathematical problems, using ICT where appropriate;
  • show deeper mathematical understanding by thinking critically and flexibly, solving problems and making informed decisions, using ICT where appropriate;
  • demonstrate creativity and initiative when developing ideas and following them through;

Links with Key Elements

Spiritual Awareness
Be aware of the infinite nature of number and space and the prevalence of pattern in the natural world

Cultural Understanding
Explore elements of geometry using patterns from different cultures


Links to useful resources:

Armagh Planetarium

The official astronomy and space science centre in Northern Ireland is the Armagh Planetarium. The Planetarium has a wide range of resources and teaching materials to support teachers at all key stages including:

Digital theatre presentations
Themed exhibition areas
Inreach and outreach workshops.


Locating Objects in the Night Sky

Children's University of Manchester
The Planisphere is the most practical tool for observing the Night Sky at any time of year. Schools can order them at a special rate from Armagh planetarium or pupils can make their own following the link here. The Planisphere can also be made as part of the science module link.

A great resource for identifying all 88 constellations.

Excellent free Planetarium software with loads of options for  viewing the Night Sky at any time from anywhere on Earth.

Another fantastic free piece of software that allows the pupils to travel through the
Solar System, discover the planets and fly out to the nearby stars

Powers of Ten (standard form)

Micro Magnet
Japlet interactive beginners guide to powers of ten (standard form) notation.

Textual and pictorial representation of PoT notation. Possible cut and stick exercises using print out images.

Powers of Ten
Another interactive PoT exercise that allows pupils to discover scale in metres.

NASA tour of the Solar System providing useful information on distance and scale.

Children's University of Manchester
Excellent interactive resource from the University of Manchester for pupils to investigate scale and create a scaled down Solar System model.

Take control of the largest telescopes in the world deducated to education and create your own cosmic journey. With curriculum related materials and projects.