Numbers are used to quantify and measure things. They can be classified into various types such as whole numbers, integers, rational numbers, and irrational numbers.

Whole numbers are the numbers 0, 1, 2, 3, 4, ... and so on. They do not include negative numbers or fractions.

Integers are the set of whole numbers and their negative counterparts, along with zero. They are represented as ..., -3, -2, -1, 0, 1, 2, 3, ...

Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. This includes fractions and terminating or repeating decimals.

Irrational numbers cannot be expressed as a simple fraction and their decimal representation goes on forever without repeating. Examples include the square root of 2 and pi.

Real numbers include all rational and irrational numbers. They can be represented on the number line.

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e., the square root of -1).

- What are whole numbers and give examples?
- Explain the concept of integers with examples.
- Differentiate between rational and irrational numbers.
- Draw and label a number line with different types of numbers.
- Simplify the expression (3 + 4i) - (2 - 5i).

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.