# Big Numbers

Purpose

This is an activity based on the picture book Big Numbers

Achievement Objectives
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
Specific Learning Outcomes
1. Students will be able to create a model of the “whole” of a specific length of time and use a meaningful scale to illustrate fractions within that length of time.
2. Students will be able to demonstrate an understanding of the mathematical relationships between of units of time.
Description of Mathematics
1. The visualisation or conceptualisation of “the whole” is key to understanding what a fraction, decimal or percentage represents.
Required Resource Materials
Big Numbers by Mary and John Gribbin
Activity

This activity is based on the picture book: Big Numbers

Author: Mary and John Gribbin
Illustrator: Ralph Edney and Nicholas Halliday
Publisher: Wizard (2003)
ISBN: 1-84046-431-3

Summary:
This book is a series of 1-2 page illustrated articles about the very large and very small numbers related to different topics. The text is brief and supported by engaging illustrations that provide springboards for creative thinking about relativity and the mathematics around us.

Lesson Sequence:
Note: This book has dozens of short articles, any one of which can be used as a reading assignment, class opening session for discussion, or a springboard for investigation. Below is one suggested activity for the pages 126-131: The timescale of life.

1. Prior to reading, draw a line of the board and mark one end Earth is formed and the other end Present Day. Ask students to estimate how much time they believe the line represents. Put some of the estimations on the board to refer to later. Ask some volunteers to mark when they think the first cells appeared on earth, the dinosaurs appeared and died out and when humans appeared.
2. Share the article with your students. You may want to have multiple copies of the pages or scan them to share on laptops or data projector so they can follow along and engage with the illustrations. As you read, emphasise how the “whole” of time Earth has existed has been condensed to another unit such as a year (the calendar box) or a day (the clocks). Discuss the length of time (4.5 billion year) and the fractions related to this whole for the different events.
3. As you read ask volunteers to come to the board and adjust the estimations on the time line. Discuss what sort of model could represent the idea of the age of the dinosaurs being 3% of the age of the Earth and the age of humankind being 3% of the age of the dinosaurs.
4. Ask students to work together to create a model to represent the age of the Earth. They have seen it modeled as a day (the clocks), as a year (the calendar box), as a mountain (illustrations) and as a timeline (on the board). Their model must be able to represent the whole, 4.5 billion years, and illustrate the relative size or position on the scale of the key events. If students are stuck for ideas about new models they could create their own version of ones already presented.
Possible ideas include:
• a pie graph (a very big one to get some of the very small slices to show up, like one drawn in chalk on the netball court)
• a string 4.5 m long (so what will each metre, and millimeter represent?)
• a glass jar with 4,500 pieces of rice dyed different colours to represent the different eras
• a large map of pieces of grid paper taped together to represent an area of small squares, each one representing a certain length of time
• a tall graduated cylinder with liquids of different densities or jelly of different colours layered to represent the different eras