- Course type: Self-paced
- Available Lessons: 35
- Average Lesson Length: 8 min
Eligible for Certificate: Yes
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Watch a preview:chapter 1 / lesson 1What Are the Five Main Exponent Properties?
Course SummaryThis informative course is designed to ensure your number and quantity math instruction closely aligns with Common Core State Standards. Short lessons work great as teaching supplements in the classroom, and mini quizzes and practice exams enable you to assess your students' math comprehension.
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- Comprehensive test covering all topics
- Detailed video explanations for wrong answers
About the Course
Common Core State Standards represent a collaborative effort among educators, parents and field experts to determine the knowledge level of students by grade. Math standards measure students' abilities to perform mathematical calculations as well as their understanding of the rules and concepts that govern the calculations. The chapters in this course cover the common core math topics in algebraic numbers and quantity equations according to high school standards in a way that makes them easy to follow and learn. Breaking down each component into smaller bite-sized points, the video lessons use examples, fun illustrations and stories to help students grasp the fundamentals of the following:
- The different types of numbers
- Zero and negative exponents
- Distributive properties of rational exponents
- Conversion of standard units of measure
- Properties of matrix multiplication
- Vector components
- Precision and rounding
- Complex numbers graphed on a complex plane
Math isn't the subject that everyone finds the most interesting, and our instructors realize this. But they also understand the importance of math, and present the lessons in an engaging way that helps students understand and retain the information. Along with each lesson, short quizzes test students' comprehension of the materials to ensure they're following along and can remember the terms, steps and math involved. The lessons taught in this course offer a helpful supplement to classroom lecture, and help prepare students for college and real life.
Rational Exponents: (CCSS.Math.Content.HSN-RN.A.1)
Standard: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)3 = 5 to the (1/3)3 to hold, so (5 to the 1/3 power)3 must equal 5.
These lessons explain the different types of numbers and the five main properties of exponents.
Rewriting Rational Exponents: (CCSS.Math.Content.HSN-RN.A.2)
Standard: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
This lesson teaches how to simplify expressions with exponents, rationalize the denominator and find the distributive property with rational exponents.
Sum or Products of Rational Numbers: (CCSS.Math.Content.HSN-RN.B.3)
Standard: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
This chapter covers computing the sums or products of rational and irrational numbers and explains how to define zero and negative exponents.
Defining & Interpreting Units: (CCSS.Math.Content.HSN-Q.A.1)
Standard: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
These lessons teach how to convert units using the metric system, how to read and interpret scales and meters, and how to solve problems with time.
Descriptive Modeling: (CCSS.Math.Content.HSN-Q.A.2)
Standard: Define appropriate quantities for the purpose of descriptive modeling.
This lesson defines a descriptive model, then teaches how to choose appropriate units, understand bar graphs and pie charts, create and interpret histograms, read line graphs, and recognize Venn Diagrams.
Mathematical Precision: (CCSS.Math.Content.HSN-Q.A.3)
Standard: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Help students learn the units of precision, precision in rounding, and how precision is used in mathematics.
Defining Complex Numbers: (CCSS.Math.Content.HSN-CN.A.1)
Standard: Know there is a complex number i such that i2 = -1, and every complex number has the form a + bi with a and b real.
Lessons provide clear and easy-to-follow definitions of imaginary and complex numbers.
Add, Subtract and Multiply Complex Numbers: (CCSS.Math.Content.HSN-CN.A.2)
Standard: Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
These lessons provide step-by-step instructions for adding, subtracting and multiplying complex numbers. They also show students how to solve quadratics with complex numbers as the solution.
Conjugates and Quotients of Complex Numbers: (CCSS.Math.Content.HSN-CN.A.3)
Standard: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Lessons cover the conjugate and modulus of a complex number and how to divide complex numbers.
Complex Numbers on a Complex Plane (CCSS.Math.Content.HSN-CN.B.4)
Standard: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
Show students how to graph a complex number on a complex plane. The lessons also explain polar to rectangular conversion and rectangular to polar conversion.
Arithmetic Functions of Complex Numbers on a Complex Plane: (CCSS.Math.Content.HSN-CN.B.5)
Standard: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + ?3 i)3 = 8 because (-1 + ?3 i) has modulus 2 and argument 120°.
These lessons describe addition, subtraction and multiplication of complex numbers on a complex plane.
Distances on the Complex Plane: (CCSS.Math.Content.HSN-CN.B.6)
Standard: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
Lessons show how to find distances on the complex plane and identify midpoints of segments on the complex plane.
Polynomial Identities of Complex Numbers: (CCSS.Math.Content.HSN-CN.C.8)
Standard: Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).
This chapter offers an explanation of how to apply identities to complex numbers.
The Fundamental Theorem of Algebra: (CCSS.Math.Content.HSN-CN.C.9)
Standard: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
Use these lessons to define and apply the Fundamental Theorem of Algebra and offers practice lessons using the theorem.
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