2. Calculation, Algorithms, and Estimation (L2)
Students calculate fluently, estimate proficiently, and describe and use algorithms in appropriate situations (e.g., approximating solutions to equations). They understand the basic ideas of iteration and algorithms.
High School
- L2.1 Calculation Using Real and Complex Numbers
- 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.
- 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.
- Diophantice Equations - Cycle 7 - This site contains problems that have integer solutions. It also contains problems dealing with nested square roots.
- Edhelper - Provides teachers with a limited resource of worksheets involving matrix arithmetic.
- Elementary Properties of Numbers - 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 evaluate 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.
- Equations - Tutorial on solving equations.
- Factoring Algebraic Expressions - Tutorial on factoring.
- Integer Exponents - This is an interactive tutorial with exponents.
- John and Betty's Journey - From i to De Moivre's Theorem, this fun book introduces complex numbers in a way that is intuitive and enjoyable for students.
- John and Betty's Journey into Complex Numbers - This is an online "picture book" for high school students. It introduces concepts like imaginary numbers, complex numbers, and De Moivre's Theorem. Interesting!
- Lesson #22 - Rates and Proportions - 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.
- Math Magic Cycle 14 - Using addition and subtraction signs the participant needs to find 6 more true equations without changing the order of the numbers.
- Number Properties - This site describes and gives examples of the three basic properties of operations. Examples for each are given.
- Primo Math - Cycle 022 - This site contains eleven review problems to solve. The problems vary in difficulty.
- 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.
- Radical Expressions - 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.
- Ratios and Proportions - Distance, Rate, and Time - 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.
- Smokey the Bear Takes Algebra - 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.
- SOSMath(Matrix Algebra) - Informational site consisting of the introduction and basic operations of matrices, matrix multiplication, algebraic properties, complex numbers as matrices, etc.
- S.O.S Math: Solving Equations - This site presents examples and detailed solutions to several types of equations including linear and absolute value equations.
- Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - 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.
- 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.
- Your Age on Other Worlds - 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.