Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in equations and formulas. It involves solving for unknown variables and manipulating mathematical expressions to solve problems.

**Variables:**In algebra, letters such as x, y, and z are used to represent unknown numbers or quantities.**Expressions:**Algebraic expressions are combinations of numbers, variables, and operations (such as addition, subtraction, multiplication, and division).**Equations:**An equation is a mathematical statement that shows that two expressions are equal. It contains an equal sign (=).**Functions:**In algebra, a function is a rule that assigns to each input value exactly one output value.

**Addition and Subtraction:**In algebra, terms can be added or subtracted by combining like terms.**Multiplication and Division:**Algebraic expressions can be multiplied using the distributive property and divided to simplify the expressions.**Factoring:**Factoring involves expressing a number or algebraic expression as a product of its factors.**Solving Equations:**Equations can be solved by performing operations to isolate the variable on one side of the equation.

Linear equations and inequalities involve algebraic expressions of degree 1. They can be represented graphically on a coordinate plane.

Quadratic equations involve algebraic expressions of degree 2. They can be solved using methods such as factoring, completing the square, or using the quadratic formula.

Exponents and radicals are important algebraic concepts that involve raising numbers to powers and extracting roots.

Here are some practice problems to test your understanding of algebra:

- Solve the equation 2x + 5 = 11 for x.
- Factor the expression 4x^2 - 9.
- Graph the inequality y < 2x + 3 on a coordinate plane.

Remember, practice is key to mastering algebra. Keep practicing and seeking help when needed to improve your skills in this important branch of mathematics!

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.