China by the Numbers
In reference to China's burgeoning population, Returned Peace Corps Volunteer Matthew Scranton ponders the question, "Can you conceive of 1.3 billion anything? In this lesson, students will learn about place value, exponents and how there's a number amount for everything.
From 2006 to 2008, Matthew Scranton served as a Peace Corps Volunteer in Chongqing, the fourth largest city in China. The city has a population of approximately 15 million, which is more than the total population in the state of Illinois.
- To use place value correctly to distinguish between small and larger quantities
- To identify place value patterns
- To create a visual representation of 100 or 1,000
- To represent numbers using exponents
- To identify the following words and their mathematical representations:exponential number, googol and infinity
- To locate China on a map
- Tell students, "We know how much is ONE, how much is TEN and how to represent those quantities as a number." Write the numbers on board.
- Select student/s to write number representations for 100 and 1,000 on board, highlighting pattern (more zeroes after the digit "1").
- Show map of the world and asks students to locate China. Ask students to estimate the population of China
- Read story "Numbers" to the class. On the board written with right-margin adjusted in order to see visual pattern, teacher adds to list of numbers using ones mentioned in the story. At end of story, ask students to describe visual pattern numbers created (longer, more digits, grow from right to left). Write other numbers on board, fitting them into chart, then reading them aloud with students.
- Distribute "China by the Numbers" visualization handout highlighting examples already completed on handout. Individually or working with a partner, students complete and discuss patterns.
- Have students share pattern observations, then introduce and explain definition of:
- exponential number: a number represented by using an exponent ( a symbol that is written above and to the right of a number to show how many times the number is to be multiplied by itself )
- googol: the figure 1 followed by 100 zeros equal to 10 100
- infinity: unlimited extent of time, space, or quantity
- From handout, highlight how to represent base ten numbers using exponent (number of zeros after the digit "1" = the exponent, which shows how many times the number is to be multiplied by itself ). Have students complete individually or working with a partner.
- Using number/word cards , students organize cards from least to greatest (or vice-versa).
Frameworks & Standards
- There is a name for all quantities, even quantities that cannot be concretely measured
- Numbers and quantities are all around us
- How can something that is “un-countable” be “counted” (quantified)?
- How do numbers help us quantify?
Common Core State Standards: Mathematics
Number and Operations in Base Ten
- Understand the place value system
Operations and Algebraic Thinking
- Analyze patterns and relationships
National Geographic Standards
Essential Element 1: The World in Spatial Terms
- Use maps and other geographic representations to acquire, process, and report information
Math Extensions :
- Students create a graph representation (picture, line, bar) showing the populations of other countries in comparison with that of the United States.
- Students research (and/or “estimate”) to discover the other country with a population over 1 billion (India)
- In class or for homework, students create a poster collage representation of 100 or 1000 (ex. 100 toothpicks glued to poster, chain of 1000 paperclips)
- With a partner, students write the numerical representation of a googol .
Language Arts Extensions:
- Students write a report, draw a picture or create a presentation on “one” important person in her/his life
- Teacher or students read related math story books