IV. Number Sense and Numeration

1. Concepts and Properties of Numbers
2. Representation and Uses of Numbers
3. Number Relationship

Additional Links to General Mathematics Sites

• Mathematics Games and Student Activities
• Mathematics Lessons Plans
• Interactive Learning and Problem Solving Activities
• Word Searches and Puzzles in Mathematics
• Miscellaneous Sites

High School

1. Benchmark 1. "Give decimal representations of rational and irrational numbers and coordinate and vector representations of complex numbers."
   1. Buffon's Needle - Representation and Uses of Numbers (IV.2.HS.1)
      This site is a Java Applet which uses a simple Monte Carlo method, called Buffon's Needle, for the estimation of the value of pi, 3.14159265... This activity is very brief, but very simple to do. Would require a bit of teacher direction for the students to understand why or how it works. This is a student activity.
   2. Learning About Properties of Vectors and Vector Sums - Representation and Uses of Numbers (IV.2.HS.1)
      Outstanding - This is a student interactive game using either a car or airplane with vectors to control its direction and speed. Students are able to see vectors have two components, magnitude and direction.
   3. What are we listening to? - Representation and Uses of Numbers  (IV.2.HS.1)
      Students gather data from a web site on the number of music albums sold by genre for the last two years. They convert these figures to fractions, decimals, and percents. They then display the results in bar graphs (using the raw data) and pie charts (using percents and degrees). Finally, they answer questions about their graphs.  Includes Teacher Lesson Plan with links.
2. Benchmark 2. "Develop an understanding of more complex representations of numbers, including exponential and logarithmic expressions, and select an appropriate representation to facilitate problem solving."
   1. Pi - Representation and Uses of Numbers (IV.2.HS.2&3)
      This site contains a definition of and methods to find Pi. Pi = 3.14159
   2. About e= 2.711828 - Representation and Uses of Numbers (IV.2.HS.2&3)
      This site contains a definition of and methods to find E.
   3. Guru Math- Exponentials - Representation and Uses of Numbers (IV.2.HS.2)
      A tutorial focused on exponential and logarithmic expressions with student interaction.
   4. Math Magic Cycle 18 - Representation and Uses of Numbers (IV.2.HS.2,4&5)
      Using addition, subtraction, multiplication, division, exponents, factors, square roots, and parentheses, the participants develop a 31 day calendar using the numbers 1 9 9 2 in a locked position within their equation. This file is a download.
   5. Secret Worlds: The Universe Within - Representation and Uses of Numbers (IV.2.HS.2)
      Outstanding! A Java applet demonstrates poweres of 10 from the Milky Way to subatomic particles. An awesome video that students and teachers will find amazing!
3. Benchmark 3. "Determine when to use rational approximations and the exact values of numbers such as e, ? and the irrational."
   1. Pi - Representation and Uses of Numbers (IV.2.HS.2&3)
      This site contains a definition of and methods to find Pi. Pi = 3.14159
   2. About e= 2.711828 - Representation and Uses of Numbers (IV.2.HS.2&3)
      This site contains a definition of and methods to find E.
4. Benchmark 4. "Apply estimation in increasingly complex situations."
   1. Fermi Problems of Estimation - Representation and Uses of Numbers (IV.2.HS.4)
      This site is a good resource of 5 interesting problems involving estimation of complex situations. The page also includes some facts for fun like the velocity of hair growth and the mass of delivered junk mail in the U.S. It is labeled AP Physics, so if it is used in a mathematics class, the teacher may have to provide some background information.
   2. Math Magic Cycle 18 - Representation and Uses of Numbers (IV.2.HS.2,4&5)
      Using addition, subtraction, multiplication, division, exponents, factors, square roots, and parentheses, the participants develop a 31 day calendar using the numbers 1 9 9 2 in a locked position within their equation. This file is a download.
   3. Million Dollar Giveaway -  Representation and Uses of Numbers (IV.2.HS.4)
      This site is a good resource of a worksheet activity that kids can do to work on their estimation skills. They must estimate how many one dollar bills can fit in a certain suitcase, how many suitcases it would take to hold $1,000,000 worth of one dollar bills, and how much a certain number of one dollar bills would weigh. This is a PDF download.
5. Benchmark 5. "Select appropriate representations for numbers, including representations of rational and irrational numbers and coordinate and vector representations of complex numbers, in order to simplify and solve problems."
   1. I Want a Credit Card--Or Do I? - Representation and Uses of Numbers (IV.2.HS.5)
      Students can research interest rates on various credit cards. They calculate the interest based on how much they pay and how long it takes to pay off the credit card. They can also make graphs to show how much they paid in interest compared to the principle. Hopefully they will learn some credit management techniques.
   2. Math Magic Cycle 18 - Representation and Uses of Numbers (IV.2.HS.2,4&5)
      Using addition, subtraction, multiplication, division, exponents, factors, square roots, and parentheses, the participants develop a 31 day calendar using the numbers 1 9 9 2 in a locked position within their equation. This file is a download.
   3. Exponential Fit - The M&M Activity - Representation and Uses of Numbers (IV.2.HS.5)
      This is a lesson plan for using M&M's or Skittles to give data for making a graph. The graph should form an exponential curve. The site includes a spreadsheet that students can download and use to record data. They can make graphs and find logs with the spreadsheet also.