The Earth is the third planet from the Sun and the only astronomical object known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets.

The Earth is composed of several layers:

**Crust:**The outermost layer, where we live, composed of solid rock.**Mantle:**The layer beneath the crust, composed of semi-solid rock.**Outer core:**The layer beneath the mantle, composed of liquid iron and nickel.**Inner core:**The innermost layer, composed of solid iron and nickel.

The Earth's atmosphere is a layer of gases that surrounds the planet and is held in place by gravity. It is composed of nitrogen, oxygen, carbon dioxide, and other trace gases. The atmosphere plays a crucial role in supporting life on Earth by providing the air we breathe and regulating the planet's temperature.

- What is the position of the Earth in the Solar System?
- Describe the layers of the Earth.
- What role does the Earth's atmosphere play in supporting life?
- How does the Earth's structure contribute to its ability to support life?
- What are some of the characteristics of the Earth that make it unique compared to other planets?

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.