High School Number and Quantity Worksheets

We really start to extend the level of understanding in exponents and integer classification at this level. For some reason, this is biggest underserved area of the Core Curriculum teacher resource wise. I had a huge problem trying to find any material to use as a reference when creating these worksheets. I believe that this is because this particular area was put together in very loosely associated fashion.

The Real Number System

• Properties of Exponents and Roots (HSN-RN.A.1) - Students learn how these two serve different, but related purposes in equation and expressions.
• Fractions with Exponents (HSN.RN.A.1) - We learn to apply the law of exponents and general rules to simple and complicated fractions.
• Rewriting Radical and Exponential Expressions (HSN-RN.A.2) - Learn how to navigate between the two and back again.
• Multiplying and Adding Rational and Irrational Numbers (HSN-RN.B.3) - This can be tricky when you first try it.
• Adding and Subtracting Rational Numbers (HSN-RN.B.3) - This is typically where most teachers start their curriculum with this topic.
• Rational and Irrational Numbers (HSN-RN.B.3) - We learn the differences and how perform operations with both types of numbers.

 

Numbers and Quantities

• Choosing Appropriate Units in Formulas (HSN-Q.A.1) - This is essential to have a correct answer, no matter how good your math is.
• Quantities and Descriptive Modeling (HSN-Q.A.2) - We start to make practical real-world applications with math.
• Accuracy and Precision (HSN-Q.A.3) - We look at how accurate or precise a problem requires you to be for the answer to be valid.
• Approximating Values (HSN-Q.A.3) - We look at many different values. We spend some time on irrational and complex numbers.
• Significant Figures (HSN-Q.A.3) - The learn how many digits are required to maintain a good degree of validity, as an answer.

 

The Complex Number System

• Simplifying Complex Numbers (HSN-CN.A.1) - How can we represent these values in a much more understandable manner?
• Adding and Subtracting Complex Numbers (HSN-CN.A.2) - A look at the most common operations you will perform with these values.
• Conjugates and Dividing Complex Numbers (HSN-CN.A.3) - This is a much more advanced operation which requires a different approach and requires a higher level of thought.
• Rectangular and Polar Forms of Complex Numbers -HSN-CN.B.4) - This helps us get a better understanding by bringing the values to life in an image.
• Graphing Complex Numbers (HSN-CN.B.4) - We start out very basic and towards the end kick it up a notch.
• Multiplication of Complex Numbers (HSN-CN.B.5) - We build you up to products by reminding you of sums and differences first.
• Calculating Distance in the Complex Plane (HSN-CN.B.6) - This is a precursor to working with vectors.
• Solving Quadratic Equations (HSN-CN.C.7) - We teach you a basic four step approach to achieving this.
• Polynomial Identities as Complex Numbers (HSN-CN.C.8) - We learn to find all the possible values of the variables that are involved.
• The Fundamental Theorem of Algebra (HSN-CN.C.9) - This is a key to understanding how to work with polynomial equations.

 

Vector & Matrix Quantities

• Drawing Vectors (HSN-VM.A.1) - We learn how to model objects that have some momentum in a certain direction.
• Finding the Components of a Vector (HSN-VM.A.2) - We learn how to determine a vectors magnitude and direction.
• Vector Based Word Problems (HSN-VM.A.3) - These types of problems lead us towards understanding the basic Laws of Motion. Thanks Newton!
• Adding Vectors End to End (HSN-VM.B.4b) - This can help compare two moving objects in a variety of ways.
• Vector Sums Magnitude and Direction (HSN-VM.B.4b) - We focus more on the math that is involved to better understand a relationship between the two.
• Vector Subtraction (HSN-VM.B.4c) - We teach you how to reverse a vector and then add the two vectors to find differences.
• Multiply a Vector by a Scalar (HSN-VM.B.5) - We need to have a full understanding of the vector components in order to be able to perform this.
• Magnitudes of Scalar Multiples (HSN-VM.B.5b) - Scalar is a big fancy word for any real number. These scalar can have an impact on a vector.
• Using Matrices to Represent Data (HSN-VM.C.6) - Computers are constantly crunching data in this form to save on memory.
• Multiply Matrices by Scalars to Produce New Matrices (HSN-VM.C.7) - Just take the regular number (scalar) and find the product on every matrix entry.
• Add, Subtract, and Multiply Matrices (HSN-VM.C.8) - We provide you a simple technique to perform all these operations.
• Unique Properties of Matrix Operations (HSN-VM.C.9) - This are for rare situations, but they help better apply the root theory.
• Null, Identity and Inverse Matrices (HSN-VM.C.10) - A look at the three unique trends that apply directly to computer science.
• Multiplying a Vector by a Matrix (HSN-VM.C.11) - We apply a technique we learned earlier to a new situation.
• Determinants and Inverses of 2 x 2 Matrices (HSN-VM.C.12) - I like to start this section by reminding students about the use of cross multiplication and then this sinks in really quick.

 

A Basic Approach to High School Math Problems

Can you measure the mental frustration and struggle a student goes through when faced with a difficult mathematical problem? When you open a mathematics book, there are all kinds of problems in the book. Figuring out their solution is not always as easy as it seems. While there are some problems, that are straightforward and immediately solvable, there are many that requiring jogging your mind. They require something more than math skills. Not being able to solve a mathematical problem without the help of a skilled teacher or instructor is very frustrating and demotivating. In such situations, individual guidance is the way to crack it. Being able to think through the problem and get your mind in the critical thinking process phase is the way to solving even the hardest problems. Let's learn the basic approaches to solving high school mathematical problems. Four Basic Approaches to Solving Math Problems - Here are four key basic approaches to solving high-school mathematical problems:
1. Analyzing the problem, giving it a good read and understanding what is this all about?
2. Developing the plan to identify what to find.
3. Identify the information and get the plan in action.
4. Workout the problem.

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