Math 6 – Outcome #1

N6.1 Demonstrate understanding of place value including:

  • greater than one million
  • less than one thousandth
  • solving situational questions using technology.

a. Explain, concretely, pictorially, or orally, how numbers larger than one million found in mass media and other contexts are related to one million by referencing place value and/or extending concrete or pictorial representations.
What are the students interested in? If they are interested in sports, have them research salaries or costs of race horses. If they are interested in health, they could research how many litres of pop are consumed each year in the world.
Use authentic sources such as Tobacco article or Energy_Revenue_Deficit and have children organize numbers found within in place-value charts.
Contrast the way the numbers in above article are written with the way the numbers in Tomato Article are written. Why?
Use visualizations such as Planet Distances to examine large values. Have students use authentic data like http://www.allsands.com/science/planetsdistanc_aju_gn.htm (convert to metric) to create scale representations.

b. Change the representation of numbers larger than one million given in decimal and word form to place value form (e.g., $1.8 billion would be changed to $1 800 000 000) and vice versa.
Have students create popular media using authentic, large-number data. For example, they could write a newspaper article using planet distances, internet hits, or whatever data they researched in step a.
c. Explain, concretely, pictorially, or orally, how numbers smaller than one thousandth found in mass media and other contexts are related to one thousandth by referencing place value and/or extending concrete or pictorial representations.
To bridge from large to small, use visualization like Cells Alive to see what the common rhinovirus looks like when magnified one million times.

If one rhinovirus is 1/1000 000 of the size of a pin head, how big is it in terms of a square mm?
d. Explain how the pattern of the place value system (e.g., the repetition of ones, tens, and hundreds), makes it possible to read and write numerals for numbers of any magnitude.
Use Place Value Tents (template example ) to help students break up numbers and represent them in expanded form.

e. Solve situational questions involving operations on quantities larger than one million or smaller than one thousandth (with the use of technology).
f. Estimate the solution to a situational question, without the use of technology, involving operations on quantities larger than one million or smaller than one thousandth and explain the strategies used to determine the estimate.

Web resources – http://www.emints.org/ethemes/resources/S00001120.shtml