# 8th Grade Math Worksheets

Geometry gets much more difficult at this level. Algebra begins to take part in the mix and is expected to be understood. Three step problems become commonplace and are required to complete the majority of the problem types that you will encounter. Functions become very routine and students need to have a full grasp of the difference between equations and expressions. We also have 8th grade math posters. Having access to our 8th grade math tests can be really helpful for students and teachers.

### The Number System

- Irrational Numbers and Decimal Expansion (8.NS.A.1) - When you cannot write a real number as a fraction, it is called irrational. We look at moving decimal values through base-10 operations.
- Approximations of Irrational Numbers (8.NS.A.2) - We spend some time with assessing imperfect square roots and placing them on a number line.

### Expressions and Equations

- Properties of Integer Exponents (8.EE.A.1) - We look at exponents when they undergo several different forms of operations.
- Evaluating Negative Exponents (8.EE.A.1) - Negative exponents result in a reciprocal being raised to a positive power.
- Products of Exponents (Product Rule) (8.EE.A.1) - When multiplying exponents that have the same base, we simply add the exponents.
- Products and Quotients to a Power (8.EE.A.1) - If you add exponents when multiplying powers to the same base, the opposite is true when dividing.
- Quotients of Exponents (8.EE.A.1) - This is a straight review for the above topic.
- Zero and Negative Exponents (8.EE.A.1) - Anything raised to a zero power will result in the value of one.
- Square and Cube Roots (8.EE.A.2) - We look at how to approach calculating the final values.
- Square Root Word Problems (8.EE.A.2) - These story problems all require a square root to be calculated.
- Powers of Ten and Scientific Notation (8.EE.A.3) - We look at how to write large and small values by using scientific notation.
- Scientific Notation Word Problems (8.EE.A.4) - Obviously most of these problems lend themselves to science based scenarios.
- Scientific Notation Addition and Subtraction (8.EE.A.4) - Students learn how to calculate sums and differences of values that are in scientific notation.
- Scientific Notation Multiplication and Division (8.EE.A.4) - We look at the other two major operations in this environment.
- Graphing Proportional Relationships (8.EE.B.5) - Learning to do this well will help you spot trends in data.
- Using Similar Triangles to Find Slope (8.EE.B.6) - When all the angles of two triangles are congruent, you can use this powerful method to learn missing parts of one of the triangles.
- Linear Equations in One Variable (8.EE.C.7a) - This helps students really master the concepts behind linear equations.
- Simultaneous Linear Equations (8.EE.C.7b) - This is where you start moving into more advanced forms of algebra.
- Finding Where Lines Intersect (8.EE.C.8) - These worksheets focus on finding a point that both lines share.

### Functions

- Functions as Inputs and Outputs (8.F.A.1) - You feed the function with inputs and it will produce an output for you.
- Solving Basic Function Tables (8.F.A.1) - Use the data tables to determine the function that is exhibited by the data.
- Comparing Properties of Two Functions (8.F.A.2) - We focus on the algebraic and graphically methods of comparison.
- Equation of a Straight Line (8.F.B.3) - We describe lines with equations that show us points on the line.
- Using Functions to Model a Linear Relationship (8.F.B.4) - These models can help us find the rate of change that a function displays.
- Point and Slope (8.F.B.4) - We compare the slope that exists between two given points.
- Understanding the y-Intercept (8.F.B.4) - The point at which a line touches the y-axis.
- Analyzing Functional Relationships by Graphing (8.F.B.5) - Understanding what the data in a graph indicates is a flagship portion of this section of the curriculum.

### Geometry

- Properties of Rotations, Reflections, and Translations (8.G.A.1) - We help students explain and interpret various transformations in a coordinate system.
- Two-dimensional Congruent Figures (8.G.A.2) - We look at congruence and what it means between two shapes.
- Understanding Congruent Shapes (8.G.A.2) - What is the significance of congruence?
- Dilations, Translations, Rotations, and Reflections (8.G.A.3) - We have students predict the outcome of various movements of shapes and points.
- Understanding Similar Figures (8.G.A.4) - Learn to identify what can be learned from two figures that are similar.
- Angle Sums and Exterior Angles of Triangles (8.G.A.5) - Internal angles of a triangle should measure one-hundred and eighty degrees. Exterior angles need to be evaluated on a case by case basis.
- Pythagorean Theorem Proofs and its Converse (8.G.B.6) - We learn a great deal about right triangles and how to use them to learn more about a system.
- Unknown Side Lengths in Right Triangle (8.G.B.7) - An application of the Pythagorean theorem.
- Pythagorean Theorem On Coordinate Systems (8.G.B.8) - We draw new lines and infer the values of measures with this technique.
- Pythagorean Theorem (8.G.B.8) - We see if we can determine when we can apply this formula.
- Pythagorean Theorem Word Problems (8.G.B.8) - These problems lend themselves to all forms of physical construction.
- Volumes of Cones, Cylinders, and Spheres (8.G.C.9) - The applications of these simple calculations are far reaching.

### Statistics & Probability

- Scatter Plots for Bivariate Data (8.SP.A.1) - This helps use understand the data and identify trends.
- Using Straight Lines to Model Relationships (8.SP.A.2) - We can easily see how two lines are related using this method.
- Interpreting Slope and Intercept (8.SP.A.3) - This tells us much more about a line than you would first think could be possible.
- Patterns of Association (Using Data Tables) (8.SP.A.4) - This is a look at raw data and identifying themes or trends between variables.

### What Math Skills Should a Student Entering High School Have?

Are you entering high school and fretting over what mathematical skills should you have? Are you in 8th grade and getting ready to go to the Big House soon? Undoubtedly, entering high school calls for having strong mathematical and analytical skills. They are of vital importance in dealing with complex statistical and mathematical concepts. Beyond academia, mathematical knowledge increases the ability to exercise judgment and logic in your daily life. Regardless of how well you have performed in the previous classes, high school needs you to upgrade and enhance your mathematical skills.
The following are the mathematical skills you need to enter before you enter high school.
**Number Sense and Operations:** To be able to deal with all arithmetic facets, you need to be well-versed with the concept of absolute numbers, the order of operations, ratio and proportions, the concept of real, rational and complex numbers.
**Algebra, Functions, and Modeling:** The use of algebraic models is very common in the engineering and technological fields when devising budgets and exploring unknown quantities. This skill also requires being able to translate words into numbers.
**Geometry:** This skill involves requiring interpretation of basic geometrical concepts, understanding corresponding or congruent angels. Finding arc lengths, volumes, and area all two-dimensional shapes.
**Probability and Statistics:** when interpreting and organizing data to conclude quantitative data, having probability and statistical skills are essential for high school.

As students transition from the 8th grade to high school, we see an increased level of math anxiety in the student population as a whole. It may be related to the increased testing and generalized assessments. Social pressures also encourage students to conform to general statement that they do not like math or that it is too hard. It is easier to say that then to push through and give your best effort. You will see that students tend to avoid things that they fear or have had a negative experience with. As is true of people of all ages. You can help overcome this, as a teacher or parent, by creating a positive environment where math is seen as a fun challenge. It also helps to help students who are struggling in small groups or one on one. The most important thing to remember is to be there for your students answer questions and model a positive math environment at all times. When things are not viewed as impossible, students will have a better mindset to work with.

### The 8th Grade Math Curriculum

As with all levels of the math curriculum there is a great deal of spiral learning here. Which means that students are building off of their prior knowledge of topics in many areas. The curriculum is broken into five major areas but having taught it for over a decade I can assure that are great deal of emphasis is set in certain areas. I feel like the concentrations on the units that involve number system, statistics, and probability are very short and they are solely taking what the students already know and help them elevate just a bit more.

The greatest amount of time is spent on helping students to start thinking algebraically. It begins with transitioning order of operations skills to solving single step equations. Students leaning heavily on understanding the properties of operations such as the associative, communicative, and distributive properties. The goal is to make them comfortable with manipulating expressions and equations so that they can advance further. They then advance to working with linear equations and interpreting data sets to locate trends, patterns, and even outliers that may exist. The focus of all this is to help students understand how to identify quantitative relationships that can be found within data sets.

Geometry also has a strong presence at this level. Previously students focused on naming shapes and some properties that they may have. At the 8th grade level students now begin to not only measure sides, angles, and planes; they learn to calculate missing or unknown values based on geometric postulates and theorems. Working of the concepts of similarity and congruence students begin to write mathematical proofs.