In mathematics, the sum is the result of adding two or more numbers or quantities together. It is a fundamental operation in arithmetic and is denoted by the plus sign (+).

If we have the numbers 3, 5, and 7, the sum of these numbers is found by adding them together: 3 + 5 + 7 = 15.

**Commutative Property:**The order in which numbers are added does not change the sum. In other words, a + b = b + a.**Associative Property:**The way in which numbers are grouped does not change the sum. In other words, (a + b) + c = a + (b + c).**Identity Property:**The sum of any number and zero is the number itself. In other words, a + 0 = a.

To calculate the sum of two or more numbers:

- Write down the numbers to be added, one below the other.
- Align the numbers by place value (ones with ones, tens with tens, etc.).
- Start adding from the rightmost column (the ones column) and carry over any excess to the next column if necessary.
- Continue adding the columns to obtain the final sum.

Remember to apply the properties of addition to simplify calculations and understand the relationship between numbers in a sum.

.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.