Quantity is a fundamental concept in mathematics that refers to the amount or number of something. It is used to describe and measure the size, amount, or extent of a particular object or phenomenon. In mathematics, quantity is typically represented using numbers and units of measurement.

There are two main types of quantities: discrete and continuous.

A discrete quantity refers to a countable number of individual items. For example, the number of students in a class, the number of apples in a basket, or the number of cars in a parking lot are all examples of discrete quantities.

A continuous quantity refers to a measurement that can take on any value within a certain range. Examples of continuous quantities include length, weight, time, and temperature.

Quantities are often measured using units. Units of measurement provide a standard way to express the amount or size of a quantity. For example, length can be measured in units such as meters, centimeters, or inches, while weight can be measured in units such as grams, kilograms, or pounds.

Here are some key concepts to understand when studying quantity:

- Understand the difference between discrete and continuous quantities.
- Learn how to represent quantities using numbers and units of measurement.
- Practice converting between different units of measurement for the same quantity.
- Explore real-world examples of quantities and how they are measured.
- Master the use of quantities in mathematical operations such as addition, subtraction, multiplication, and division.

By mastering the concept of quantity and its applications, you will be better equipped to solve mathematical problems and understand the world around you.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

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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.