In this spot, we must develop a list of key mathematical skills and concepts that the students must learn. These are not "whole game" skills--they are simply mathematics--arithmetic, algebra, geometry. These are basic ACT or SAT subject-test material. These are skills that are crucial to understanding and solving science problems. Let's try to put these in some kind of order from the start, from more basic to more complex.
Prerequisites: (should be mastered before starting this course) Four basic operations on integers, fractions, decimals, and negative numbers Translate basic operations from English to mathematics (and back) Order numerical expressions on a number line Solve linear expressions in one variable Evaluate different functions, given values for the independent variable Simplify fractional expressions and convert from mixed numbers to improper fractions Graph points in two dimensions and graphing lines Multiply and divide simple exponential expressions Find areas and volumes of common shapes and solids Understand and use basic properties of triangles [angles = 180, area= (half of base times height), triangle inequality]
Skills: (should be mastered by the end of this course) Understand and use negative exponents Simplify like terms Multiply and divide exponential expressions Solve systems of two equations with two unknowns Use the Pythagorean theorem to find missing values on a right triangle Solve equations with squares, cubes, square roots, cube roots, etc... Complete the square to solve quadratic equations Solve equations by factoring Graph unknown functions in two variables with and without technology Use trigonometric ratios to discover missing values in right triangles Read functional notation, evaluate functions, and determine the function's domain and range
Let's try to put these in some kind of order from the start, from more basic to more complex.
Prerequisites: (should be mastered before starting this course)
Four basic operations on integers, fractions, decimals, and negative numbers
Translate basic operations from English to mathematics (and back)
Order numerical expressions on a number line
Solve linear expressions in one variable
Evaluate different functions, given values for the independent variable
Simplify fractional expressions and convert from mixed numbers to improper fractions
Graph points in two dimensions and graphing lines
Multiply and divide simple exponential expressions
Find areas and volumes of common shapes and solids
Understand and use basic properties of triangles [angles = 180, area= (half of base times height), triangle inequality]
Skills: (should be mastered by the end of this course)
Understand and use negative exponents
Simplify like terms
Multiply and divide exponential expressions
Solve systems of two equations with two unknowns
Use the Pythagorean theorem to find missing values on a right triangle
Solve equations with squares, cubes, square roots, cube roots, etc...
Complete the square to solve quadratic equations
Solve equations by factoring
Graph unknown functions in two variables with and without technology
Use trigonometric ratios to discover missing values in right triangles
Read functional notation, evaluate functions, and determine the function's domain and range