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 relationships between them. They represent quantitative relationships using mathematical symbols, and interpret relationships from those representations.
High School
- L1.1 Number Systems and Number Sense
- Beginning Algebra Tutorials - This is a beginning algebra web tutorial. It covers all areas of beginning algebra. Could be used for students to access on their own or as a teacher presentation. Student and Teacher Resource.
- 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.
- 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.
- Number Properties - This site describes and gives examples of the three basic properties of operations. Examples for each are given.
- 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.
- 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.
- Understanding Negative Exponents -NEW- Students will be able to practice using negative exponents.
- Kuta Math -NEW- This website has free worksheets (with answers) for Pre-Algebra, Algebra I, Geometry, and Algebra II.
- L1.2 Representations and Relationships
- About e= 2.711828 - This site contains a definition of and methods to find E.
- 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.
- 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
- The Yo-Yo Problem - This site has a couple activities for students that a teacher can print that involve representing quantities with symbols and expressing their relationship with equations. In the Yo-Y-o problem, they must write and solve an equation. In the Penny Pattern, they explore another linear model with the calculator.