In mathematics, a quantity is anything that can be measured or counted. It can be represented by a number or a unit of measurement. Quantities can be discrete, such as the number of students in a classroom, or continuous, such as the temperature of a room.

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

**Discrete Quantities:**These are countable and take on specific values. Examples include the number of apples in a basket, the number of students in a class, or the number of cars in a parking lot.**Continuous Quantities:**These are measurable and can take on any value within a given range. Examples include time, temperature, distance, or weight.

Quantities are often accompanied by units of measurement, which specify the standard for measuring the quantity. For example, distance can be measured in units such as meters, kilometers, or miles, while time can be measured in seconds, minutes, or hours.

Basic arithmetic operations can be performed with quantities. These include addition, subtraction, multiplication, and division. When working with quantities, it's important to pay attention to the units and ensure that they are consistent throughout the calculations.

Here are some key points to remember when studying quantities in mathematics:

- Understand the difference between discrete and continuous quantities.
- Be familiar with common units of measurement for different quantities (e.g., length, time, mass).
- Practice converting between different units of measurement (e.g., converting meters to kilometers).
- Pay attention to units when performing arithmetic operations with quantities.
- Work on word problems that involve quantities to apply your understanding in real-life situations.

By mastering the concept of quantities, you'll be better equipped to solve problems involving measurements and quantities in various mathematical contexts.

.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.