Comparison is the process of determining the relationship between two quantities or numbers. In mathematics, comparison is often used to compare the size, value, or magnitude of numbers or objects. This can be done using various symbols and terms to indicate the relationship between the numbers.

There are several symbols used in math to compare numbers:

**Greater Than (>):**This symbol is used to compare two numbers and indicates that the number on the left is larger than the number on the right.**Less Than (<):**This symbol is used to compare two numbers and indicates that the number on the left is smaller than the number on the right.**Greater Than or Equal To (≥):**This symbol is used to compare two numbers and indicates that the number on the left is greater than or equal to the number on the right.**Less Than or Equal To (≤):**This symbol is used to compare two numbers and indicates that the number on the left is less than or equal to the number on the right.**Equal To (=):**This symbol is used to compare two numbers and indicates that the numbers on both sides are equal in value.

Here are some key points to remember when working with comparison in math:

- When comparing two numbers, use the appropriate comparison symbol to indicate the relationship between the numbers.
- When comparing quantities, consider the units of measurement and ensure they are the same before making a comparison.
- Remember that the equal to (=) symbol is used to show that two numbers are exactly the same in value.
- Practice comparing numbers using real-life examples and word problems to understand the practical application of comparison in everyday situations.

Understanding how to compare numbers and quantities is an important skill in mathematics and is used in various mathematical operations and problem-solving scenarios.

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.