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

1. Benchmark 1. "Develop an understanding of integers and rational numbers and represent rational numbers in both fraction and decimal form."
   1. A View from the Back of the Envelope - Concepts and Properties of Numbers (IV.1.MS.1)
      This site has a game for teachers to lead a class into understanding the magnitude of numbers. These numbers are based on the number of zeroes at the end.
   2. Guess The Number - Concepts and Properties of Numbers (IV.1.MS.1)
      This is a game where students are given clues about an integer to help them guess the number.  This includes the four basic operations using positive and negative integers and varying levels of difficulty.
   3. Math Goodies - Concepts and Properties of Numbers (IV.1.MS.1)
      Students are introduced to integers through the number line. For each section information is given, then an interactive tutorial follows. Other sections include: Comparing and Ordering Integers, Adding, Subtracting, and Multiplying Integers, Operations with Integers, and Integers and the Real World. This is a student activity.
   4. Mrs.Glosser's Math Goodies - Concepts and Properties of Numbers (IV.1.MS.1)
      This is a good site for introducing integers to students.  It describes positive, negatives and opposites.  It also has other links on comparing and ordering, absolute value, and rules for adding, subtracting, multiplying and dividing.  Good source of worksheets and puzzles with solutions also.
   5. Place Value Puzzler - Concepts and Properties of Numbers (IV.1.MS.1)
      This is a game which reviews the concept of place value.  The questions include up to 7 numbers before the decimal point and 7 after it.  Besides naming the place values, there is also a rounding game also using 7 numbers before and after the decimal point in which students must round to the nearest ten, thousandth, etc.
   6. Study Works! Online - Concepts and Properties of Numbers (IV.1.MS.1)
      This is a student interactive website that uses an alien character in an interactive video to teach methods for working with fractions, percents, and decimals.
   7. Visual Fractions - Concepts and Properties of Numbers (IV.1.MS.1)
      This is an on-line tutorial that gives instructional and practice problems on all types of fractions  There are several links to specific types of fractions and even a few games.
   8. Who Wants Pizza? A Fun Way to Learn About Fractions - Concepts and Properties of Numbers (IV.1.MS.1)
      Cynthia Lanius provides a great web resource for upper elementary through middle school students learning fractions. The site contains interactive student activities as well as teacher notes and worksheets.
2. Benchmark 2. "Extend their understanding of numeration systems to include decimal numeration, scientific numeration and non-decimal numeration systems."
   1. AAA Math: Comparing Standard Notation and Scientific Notation Numbers - Concepts and Properties of Numbers (IV.1.MS.2)
      At this site students can practice comparing numbers in both standard notation and scientific notation. A brief tutorial is followed by interactive quizzes which are timed.
   2. CERN'S Powers of Ten - Concepts and Properties of Numbers (IV.1.MS.2)
      Site begins with a picture of a flower that is 1 meter square. Using a ruler, students can zoom in or out by powers of ten. The picture zooms out to a picture of a galaxy that is 150 million light years across and in to protons and neutrons in the nucleus.
   3. Converting from Decimal Numbers to Scientific Notations - Concepts and Properties of Numbers (IV.1.MS.2)
      This site is an activity for the students to convert a decimal into a scientific notation. The process is explained, and problems are given for the students to answer. Their work is timed, and an assessment is given for the activity.
   4. Lost King of the Maya: Long Count Calendar System - Concepts and Properties of Numbers (IV.1.MS.2)
      Students will calculate the date of their birth in the Maya Long Count calendar system which uses a base 20 number system. The website is not interactive but includes teacher resources, worksheets and additional links.
   5. Scientific Notation - Concepts and Properties of Numbers (IV.1.MS.2)
      This program gives a very good defination for scientific notation.  It shows examples of how to convert from numbers to scientific notation and from scientific notation back to numbers.  Sample paper and pencil problems are available along with several sample problems requiring the use of calculators.
   6. Scientific Notation - Concepts and Properties of Numbers (IV.1.MS.2)
      With this program you can practice converting between scientific notation and normal numbers.
   7. What fun!  It's:  Practice with Scientific Notation - Concepts and Properties of Numbers (IV.1.MS.2)
      This site explains what scientific notation is and why we use it. It gives several examples and how to calculate the four operations using scientific notation.  There is also a worksheet link that the students can practice or the teacher my print up.
3. Benchmark 3. "Develop an understanding of the properties of the integer and rational number systems (e.g., order, density) and of the properties of special numbers including 0, 1 and ?, and the additive and multiplicative inverses."
   1. E-Lab : Two Step Equations - Concepts and Properties of Numbers  (IV.1.MS.3)
      Students will apply the additive inverse and multiplicative inverse properties  to solve two-step equations.
   2. Math Goodies: Intergers - Concepts and Properties of Numbers (IV.1.MS.3&4)
      Introduces students to integers, absolute value, comparing and ordering, and basic operations with intergers.  Practice questions are provided at the end of each lesson.
   3. Molecular Expressions, Science, Optics, and You - Concepts and Properties of Numbers (IV.1.MS.3)
      This site takes you through a step by step lesson to teach powers of 10 and has an interactive applet that allows you to view several things under a micrsoscope!
   4. The Derivation of Pi - Concepts and Properties of Numbers (IV.1.MS.3)
      This site contains lesson plans and resources for a student investigation of Pi. Directions are clear, directions for creating student tools for use on a computer are included as well as hyperlinks to other sites containing more information about the history of Pi. Very informativve site and useful site.
   5. The National Science Center - Concepts and Properties of Numbers (IV.1.MS.3)
      This site gives a lesson plan for an activity to discover the value of pi. Students will use measuring and averaging, and hopefully discover the value of pi.
4. Benchmark 4. "Apply their understanding of number systems to model and solve mathematical and applied problems."
   1. Figure This! Math Challenges for Families - Concepts and Properties of Numbers (IV.1.MS.4)
      Figure This! Mahtematics Challenges for Families provides interesting math challenges that middle-school students can do at home with their families. Each challenge features a description of the important math involved, a note on where the math is used in the real world, a hint to get started, complete solutions, a "Try This" section, additional related problems with answers, questions to think about, fun facts related to the math, and resources for further exploration. Math Challenges #17, 24, and 25 are examples of problems that would help teach this particular benchmark.
   2. Math Goodies: Intergers - Concepts and Properties of Numbers (IV.1.MS.3&4)
      Introduces students to integers, absolute value, comparing and ordering, and basic operations with intergers.  Practice questions are provided at the end of each lesson.