Math Extensions for Cosmic Education

There are a lot of educators and scientists talking about Deep Time these days. Maria and Mario Montessori worked on developing this big worldview into a curriculum for young children in the 1940’s …and probably for some time before. If you’d like some background info on the Montessori perspective, you can read all about it in Children of the Universe: Cosmic Education in the Montessori Elementary Curriculum by Michael and D’Neil Duffy.

Fossilicious got started as we worked on designing curriculum and materials to go with this study. We wanted to put meaningful activities into the hands of children at the precise time their interest in the magnitude of the earth and all its history, science, and culture are at its peak: throughout the ages of 6 through 12.

If you’re a Montessori elementary teacher, you can just skip the next few paragraphs of explanation and return at the subtitle; this is all familiar territory for you. If you’re not, you may want to read on…

The Montessori method of teaching involves telling a story and then providing materials to enhance independent study guided by the child’s interests. All of the learning materials found at have been developed for this purpose. We’ll use these learning materials as an opportunity to more deeply integrate the curriculum with math and language. This series of articles will explore a few ways that a teacher can use the materials to extend into these subject areas.

The first Great Lesson in Montessori is called The God with No Hands. There’s a pretty nice write-up of the story, along with photos of the impressionistic charts that illustrate parts of the story, a list of experiments, and some directions for giving the presentation at Montessori Commons (

This first story tells about the creation of the universe. It is designed to impress the child with the huge power of the natural forces that resulted in our magnificent solar system and our planetary home. The story fills the children’s imaginations with wonder, while the experiments are the start of exploration into some of the earth’s guiding principles. Shortly after this impressionistic story follows a lesson called the Clock of Eras. This lessons shares the passage of time since the Big Bang compared to a clock to give a visual representation and thee first experience with the geology time groups of Eras: Hadean, Archaean, Proterozoic, Paleozoic, Mesozoic, and Cenozoic. 

We call this the Clock of Eras and you can download a copy of the chart and some related activities here:

The booklets we’ve written to accompany the clock tell the story of each era in greater detail. This is where the extensions for math and language can really be put to use. Each booklet gives an idea of what was happening during that particular chunk of time on the clock. I’ll use just one of these booklets to share a few ideas for extending the information into mathematical realms.

Math and the Hadean

For the youngest students, the immense size of the numbers used to express time is a point of interest. This is a great time to investigate writing numbers: place value, hierarchies, and patterns. Here are some sample activity titles to develop for the six and seven year olds:

  • Units, Tens, Hundreds, Thousands
  • Millions, Billions, Trillions
  • Using Zeros and Commas to make HUGE numbers
  • How much is a billion?
  • The Hadean time started around 4.5 billion years ago. Write that numeral.
  • The Hadean time lasted until approximately 3.8 billion years ago. Write that numeral.

These can become increasingly complex as the students get older and more experienced.

  • How many stars are in the universe? Do some research to find out and then write that numeral. (Relates to the formation of our star, the sun.)
  • Volcanoes grow into tall mountains. Do some research to find the three tallest volcanic mountains. Write their names and heights into a chart. (Relates to the ideas of volcano eruptions that resulted in the formation of the earth’s crust.)
  • What is the boiling point of these three things: water, olive oil, iron. (Relates to the ideas of gases in the universe.)
  • At what temperature is iron a solid? A liquid? A gas?
  • What is a freezing point.

Once you feel you’ve exhausted all the ways to play with large numerals, you can use these same numerals to practice all the operations. (addition, subtraction, multiplication, and division) The level of difficulty will be modified by the age and ability of the student, but there are many ways to integrate these math problems into the science or history curriculum. Here are a few examples of problems you could make up.

  • The universe is constantly changing. New stars are born and old stars die out. Using the numeral you wrote for the number of star in the universe, take one away. How many are left? Write that numeral. Start again, add one, how many stars exist after one is added. Write that numeral.
  • Use two large (say 10-digit) numerals to practice simple addition or subtraction facts.
  • Use one large (say 9-digit) numeral to practice multiplication facts. (Children will need to be able to carry on this one.
  • What is the difference in height between the tallest volcanic mountain and the next tallest?
  • Compare the boiling points of different substances using subtraction.
  • How long was the Hadean time? Use subtraction to find out.

This simple series of relatable math activity is only limited by your imagination and creativity as a teacher. In reading through each booklet, you can easily create a group of math problems…or make them up on the spot, just to fit that particular student’s needs.

Coming next time: Language skills with the Era’s booklets.


1While these eras are constantly evolving, for the purpose of the young child, these distinctions align closely with the current time distinctions, although scientists now use a more refined and detailed system of time classification. You can find a chart of this classification at

Geologic Time

Geologic Time Line

Geologic Time Periods

Clock of Eras

Cenozoic Era

Mesozoic Era

Paleozoic Era

Proterozoic Era

Archaean Time

Hadean Time

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