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Level Three > Number and Algebra

On Beyond a Million: An Amazing Math Journey

Purpose: 

This is an activity based on the picture book On Beyond a Million: An Amazing Math Journey

Achievement Objectives:

Achievement Objective: NA3-4: Know how many tenths, tens, hundreds, and thousands are in whole numbers.
AO elaboration and other teaching resources

Specific Learning Outcomes: 
  1. Students will be able to create an “accordion” model of place value.
  2. Students will be able to accurately read large numbers and relate a place value house name to a power of 10.
Description of mathematics: 
  1. Place value can be expressed as a power of 10 (exponents).
  2. Multiplication is a powerful operation and can create very large numbers (exponential multiplication).
Required Resource Materials: 
On Beyond a Million: An Amazing Math Journey by David M. Schwartz
Place Value Houses – copymaster or commercially produced
Long strips of paper or card (1m+) same width as PV Houses
Scissors
Activity: 

Place Value Accordions
This activity is based on the picture book On Beyond a Million: An Amazing Math Journey

Author: David M. Schwartz
Illustrator: Paul Meisel
Publisher: Dragonfly Books (2001)
ISBN: 0-385-32217-8

Summary:
The problem is: how many pieces of popcorn is the out of control machine creating? Professor X and his dog, Y, demonstrate the exponential counting sequence with their Powers of 10. The numbers increase through the place value names reaching astronomical proportions with huge numbers like quindecillion and googol. Each 2-page spread has a “Did you Know?” section about facts related to the huge numbers, a blackboard section where the exponents are explained, and a central illustration where the professor is leading the group on a journey.

Lesson Sequence:

  1. Prior to reading, ask:
    What is the largest number you can read?
    Record a number with many places such as 1,234,567,890,123,456,789 or 1,000,000,000,000,000,000,000 and explore the understanding of the place value “houses” model with your students. Use the place value houses and insert digits in the places and practice reading the numbers, stressing to remember to name the house before you leave for the next one (example 42,509,670 read as 42 MILLION, 509 THOUSAND, 670)
  2. Share the book with your students on a first run through by sharing the story told in the middle sections of the 2-page spreads and focusing on the new vocabulary of the large numbers and the idea of infinity.
  3. Next, or in a second session, read through the book again this time focusing on the idea of exponents and the maths being explored by the professor’s dog on the sidebars. Have students record the numbers expressed as exponents and as ordinary notation.
  4. Revisit the Place Value houses and in each section of the house record the place as an expression of a power of ten.
     
  5. Explore this pattern with the rest of the standard place value houses (on the copymaster). Support students to discover the link between powers of 10 and the number of zeros in any large number which has a 1 in the highest place and zeros in the rest.
  6. In pairs or small groups challenge students to construct a giant place value accordion that will include the names and powers of ten for places given in the book. Students may first want to construct a class chart with the names in order. The accordion is made from paper or card folded into “houses” and the powers recorded in each section of the house. When complete the accordion can be folded up and pinned closed with a paper clip.
  7. Follow up activities could include:
    a. Reading “super large” numbers as team challenges for warm ups.
    b. Doing “super large” basic facts practice (24 quintillion x 2, or x 20, or 200).
    c. Exponent practice of recoding large numbers in scientific notation 30,000,000 as 3x107.
    d. Researching large numbers and the meaning of their names as an independent activity.