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. "Compare and order real numbers and compare rational approximations to exact values."
   1. Line Up Cards - Number Relationships (IV.3.HS.1)
      After reading the page about what rational and irrational numbers are, a teacher could use the idea of Line Up Cards to get them to order the real numbers. This could be done with or without irrational numbers or a calculator so the students would have to remember the rational approximations of fractions.
   2. Math Magic Cycle 14 - Number Relationships (IV.3.HS.1,3,4&5)
      Using addition and subtraction signs the participant needs to find 6 more true equations without changing the order of the numbers.
   3. Rational and Irrational Numbers - Number Relationships (IV.3.HS.1)
      Students could read through this site to better understand rational and irrational numbers. It describes what they are, gives examples of each, and explains that they are both real numbers. It also gives them practice with the approximations of rational and irrational fractions. It would go well with the site named Line Up Cards from http://regentsprep.org/Regents/math/rational/Tcards.htm.
2. Benchmark 2. "Express numerical comparisons as ratios and rates."
   1. Lesson #22 - Rates and Proportions - Number Relationships (IV.3.HS.2)
      This site is a lesson plan. It is not a student activity. However, it is a good lesson plan for teaching ratios and proportions. It includes lesson plans for the teacher, homework worksheets for the students, and sheets for a team competition. Once the students have completed the homework worksheets, the intent is for them to work in teams for the "team competition". This is a great way for kids to practice working together.
   2. Ratios and Proprtions-Distance, Rate, and Time - Number Relationships (IV.3.HS.2)
      Outstanding - This is an excellent interactive site that defines ratios and rates and gives plenty of exercises on how to find rates and use proportions to solve problems. Examples of problems are car trips, similar triangles, and other polygons with similar sides. The site includes a true and false quiz at the end.
   3. Your Age on Other Worlds - Number Relationships (IV.3.HS.2&5)
      There is a converter that compares your age in days and years on earth to that of other planets. It contains many great links including another converter that compares your weight on earth to other planets and moons. It has a good summary of why these differences occur.
3. Benchmark 3. "Extend the relationships of primes, factors, multiples and divisibility in an algebraic setting."
   1. Elementary Properties of Numbers - Number Relationships (IV.3.HS.3)
      This is an 8 question multiple choice test on the properties of numbers like approximations of fractions, prime numbers, factors, absolute value, and operations with parentheses. The site will evalute each question as you go along if you like and give you a total score at the end. There is more than one correct answer to each question.
   2. Math Magic Cycle 14 - Number Relationships (IV.3.HS.1,3,4&5)
      Using addition and subtraction signs the participant needs to find 6 more true equations without changing the order of the numbers.
   3. Primo Math - Cycle 022 - Number Relationships (IV.3.HS.3,4&5)
      This site contains eleven review problems to solve. The problems vary in difficulty.
   4. Radical Expressions - Number Relationships (IV.3.HS.3)
      This is a 10 slide Power Point presentation on radical expressions.  Slides are well done.  Each slide has explanation and then problems to work.  Answers to problems are given on the next slide.  Teacher resource.
4. Benchmark 4. "Express number relationships using positive and negative rational exponents, logarithms and radicals."
   1. Diophantice Equations -Cycle 7- Number Relationships (IV.3.HS.4&5)
      This site contains problems that have integer solutions. It also contains problems dealing with nested square roots.
   2. Math Magic Cycle 14 - Number Relationships (IV.3.HS.3,4&5)
      Using addition and subtraction signs the participant needs to find 6 more true equations without changing the order of the numbers.
   3. Primo Math - Cycle 022 - Number Relationships (IV.3.HS.3,4&5)
      This site contains eleven review problems to solve. The problems vary in difficulty.
5. Benchmark 5. "Apply their understanding of number relationships in solving problems."
   1. Diophantice Equations- Cycle 7 - Number Relationships (IV.3.HS.4&5)
      This site contains problems that have integer solutions. It also contains problems dealing with nested square roots.
   2. Math Magic Cycle 14 - Number Relationships (IV.3.HS.1,3,4&5)
      Using addition and subtraction signs the participant needs to find 6 more true equations without changing the order of the numbers.
   3. Primo Math - Cycle 022 - Number Relationships (IV.3.HS.3,4&5)
      This site contains eleven review problems to solve. The problems vary in difficulty.
   4. Smokey the Bear Takes Algebra - Number Relationships (IV.3.HS.5)  
      This lesson introduces students to the many factors that play a role in creating a forest-fire danger rating index. To complete the activities related to these indexes, students should be comfortable with linear, quadratic and exponential functions.  Lesson plan with links and worksheets.
   5. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - Number Relationships (IV.3.HS.5)
      This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population.  Many links are included for students and teachers to utilize in the lesson.  Could be student interactive or a teacher resource depending on how the teacher chose to use it.
   6. Your Age on Other Worlds - Number Relationships (IV.3.HS.2&5)
      There is a converter that compares your age in days and years on earth to that of other planets. It contains many great links including another converter that compares your weight on earth to other planets and moons. It has a good summary of why these differences occur.