1. Reasoning About Numbers, Systems and Quantitative Situations (L1)
Based on their knowledge of the properties of arithmetic, students understand and reason about numbers, number systems, and the relation ships between them. They represent quantitative relationships using mathematical symbols, and interpret relationships from those representations.
High School
- L1.1 Number Systems and Number Sense
- Buffon's Needle - Buffon's Needle is one of the oldest problems in the field of geometrical probability. It was first stated in 1777. It involves dropping a needle on a lined sheet of paper and determining the probability of the needle crossing one of the lines on the page. The remarkable result is that the probability is directly related to the value of pi.
- Calculating Pi - This is an activity where students understand the origin of Pi by measuring different sized cylinders in everyday life to find their area and circumference. Therefore seeing Pi's role in circle relationships..
- Cosmic Zoom - Outstanding - This site starts with a picture of a square meter and "zooms" you out by powers of ten to get a sense of what the base ten system represents.
- Dave's Short Course on Complex Numbers - A tutorial into the world of complex numbers.
- Introduction to Numbers - This site provides an overview of the entire number system- real, rational, irrational, transcendental, imaginary, integers, squares and sums.
- John and Betty's Journey Into Complex Numbers - An online story of complex numbers will keep kids engaged as they learn the concept of imaginary and real number parts.
- NOVA: Infinite Secrets: Approximating Pi - Students will explore the number pi by increasing the number of inscribed polygons using an interactive applet.
- Numbers Beyond Reason - Lesson plan used to develop an understanding of irrational numbers with student activities and handout included.
- Purple Math - Complex Numbers - A tutorial site for complex numbers including basic operations and graphing.
- Real Numbers - This is an interactive tutorial with real numbers.
- The Case of the Missing Negative - A lesson plan for introducing concepts of complex numbers. Students are asked to solve the mystery of the missing negative and are guided through internet activities to help them with their case! Links and details provided.
- Understanding Pi - A lesson plan that includes internet links for the students to investigate with respect to fostering their understanding of pi.
- L1.2 Representations and Relationships
- About e= 2.711828 - This site contains a definition of and methods to find E.
- Components of a Vector - Outstanding - This is an interactive student site where students can read about vectors then try to manipulate a vector. Students will see what happens as they change the length, direction, and position of the vector. Discussion questions follow.
- Edhelper - Provides teachers with a limited resource of worksheets involving matrix arithmetic.
- Exponential Fit - The M&M Activity - 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.
- Factoring Algabraic Expressions - Tutorial on factoring.
- Fermi Problems of Estimation - 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.
- Learning About Properties of Vectors and Vector Sums - 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.
- Million Dollar Giveaway - 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.
- Pi - This site contains a definition of and methods to find Pi. Pi = 3.14159
- QuickMath - Matrices: This section of QuickMath allows you to perform arithmetic operations on matrices. Currently you can add or subtract matrices, multiply two matrices, multiply a matrix by a scalar and raise a matrix to any power.
- Secret Worlds: The Universe Within - 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!
- SOSMath (Matrix Algebra) - Informational site consisting of the introduction and basic operations of matrices, matrix multiplication, algebraic properties, complex numbers as matrices, etc.
- Virtual Manipulatives - Function Machine - Students drag a number to the function machine and observe the output. After viewing four, students then need to determine the function and output of more problems. Student interactive.
- WebMathematica (Step by step matrix algebra) - Allows one to input matrices and choose a selected operation to compute. Deals with arithmetic of matrices, powers of a matrix, matrix products, transpose of a matrix, etc.
- Geometry help-free math help -NEW- If you need help with geometry you may be interested in viewing a geometry lesson and video lessons from our website. Browse our collection of geometry lessons as well as those from other websites.