Integers are whole numbers that can be positive, negative, or zero. They do not have any fractional or decimal parts. The set of integers is represented by the symbol "Z".

There are three types of integers:

- Positive Integers: These are numbers greater than zero, such as 1, 2, 3, and so on.
- Negative Integers: These are numbers less than zero, such as -1, -2, -3, and so on.
- Zero: The number 0 is neither positive nor negative.

When adding integers, use the following rules:

- If the numbers have the same sign (both positive or both negative), add their absolute values and keep the sign.
- If the numbers have different signs, subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.
- When adding a positive and a negative integer, subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.

When subtracting integers, add the opposite (additive inverse) of the second number to the first number and follow the rules for adding integers.

Multiplying and dividing integers follow different rules based on the signs of the numbers involved. When multiplying or dividing integers, the product or quotient will be positive if the two integers have the same sign and negative if the two integers have different signs.

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

Remember, practice is key to mastering the concepts of integers. Keep practicing and you'll become comfortable with working with integers in no time!

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.