South Dakota State Standards for Mathematics: Grade 8

SD.8.A. Algebra: Students will use the language of algebra to explore, describe, represent, and analyze number expressions and relations that represent variable quantities.

8.A.1. Use procedures to transform algebraic expressions.

8.A.1.1. Application: Students are able to use properties to expand, combine, and simplify 1st degree algebraic expressions with the set of integers.

8.A.1.1.a. Properties include associative, commutative, distributive, and identity properties.

8.A.1.1.b. Use order of operations with exponents and nested parentheses.

8.A.1.1.c. Determine if two 1st degree algebraic expressions are equivalent.

8.A.2. Use a variety of algebraic concepts and methods to solve equations and inequalities.

8.A.2.1. Application: Students are able to write and solve two-step 1st degree equations, with one variable, and one-step inequalities, with one variable, using the set of integers. (Inverse operations, Addition property of equality., Multiplication property of equality.)

8.A.3. Interpret and develop mathematical models.

8.A.3.1. Comprehension: Students are able to describe and determine linear relationships.

8.A.3.1.a. Determine slope from a line or ordered pairs on a graph.

8.A.3.1.b. Identify x and y intercepts from a graph.

8.A.4. Describe and use properties and behaviors of relations, functions, and inverses.

8.A.4.1. Synthesis: Students are able to create rules to explain the relationship between numbers when a change in the first variable affects the second variable.

8.A.4.2. Analysis: Students are able to describe and represent relations using tables, graphs, and rules.

8.A.4.2.a. Represent situations with patterns and relations to find exact or approximate solutions to problems.

8.A.4.2.b. Make predictions relating two variables using a rule or a graph.

SD.8.G. Geometry: Students will use the language of geometry to discover, analyze, and communicate geometric concepts, properties, and relationships.

8.G.1. Use deductive and inductive reasoning to recognize and apply properties of geometric figures.

8.G.1.1. Application: Students are able to describe and classify prisms, pyramids, cylinders, and cone.

8.G.1.2. Application: Students, when given any two sides of an illustrated right triangle, are able to use the Pythagorean Theorem to find the third side.

8.G.2. Use properties of geometric figures to solve problems from a variety of perspectives.

8.G.2.1. Application: Students are able to write and solve proportions that express the relationships between corresponding parts of similar quadrilaterals and triangles.

SD.8.M. Measurement: Students will apply systems of measurement and use appropriate measurement tools to describe and analyze the world around them.

8.M.1. Apply measurement concepts in practical applications.

8.M.1.1. Application: Students are able to apply proportional reasoning to solve measurement problems with rational number measurements.

8.M.1.1.a. Conversion within measurement systems.

8.M.1.1.b. Use scale drawings to represent situations.

8.M.1.1.c. Indirect measurement.

8.M.1.2. Comprehension: Students are able to find area, volume, and surface area with whole number measurements.

8.M.1.2.a. Use appropriate unit of measure

8.M.1.2.b. Apply strategies and/or formulas.

8.M.1.2.c. Volume of rectangular prisms, rectangular pyramids, cylinders, and cones.

8.M.1.2.d. Surface area of rectangular prisms and cylinders.

8.M.1.2.e. Area of composite shapes.

SD.8.N. Number Sense: Students will develop and use number sense to investigate the characteristics of numbers in a variety of forms and modes of operation.

8.N.1. Analyze the structural characteristics of the real number system and its various subsystems. Analyze the concept of value, magnitude, and relative magnitude of real numbers.

8.N.1.1. Comprehension: Students are able to represent numbers in a variety of forms and identify the subsets of rational numbers.

8.N.1.1.a. Exponents

8.N.1.1.b. Scientific notation

8.N.1.1.c. Absolute value

8.N.1.1.d. Radicals (perfect squares)

8.N.1.1.e. Graph on a number line

8.N.2. Apply number operations with real numbers and other number systems.

8.N.2.1. Application: Students are able to read, write, and compute within any subset of rational numbers.

8.N.2.1.a. Solve problems involving discount, markup, commission, profit, and simple interest.

8.N.3. Develop conjectures, predictions, or estimations to solve problems and verify or justify the results.

8.N.3.1. Application: Students are able to use various strategies to solve multi-step problems involving rational numbers.

8.N.3.1.a. Explain strategies and justify answers.

8.N.3.1.b. Formulate rules to solve practical problems involving rational numbers.

8.N.3.1.c. Use estimation strategies to make predictions and test the reasonableness of the answer.

SD.8.S. Statistics & Probability: Students will apply statistical methods to analyze data and explore probability for making decisions and predictions.

8.S.1. Use statistical models to gather, analyze, and display data to draw conclusions.

8.S.1.1. Comprehension: Students are able to find the mean, median, mode, and range of a data set from a stem-and-leaf plot and a line plot.

8.S.1.2. Application: Students are able to use a variety of visual representations to display data to make comparisons and predictions.

8.S.1.2.a. Double bar graph

8.S.1.2.b. Double line graph

8.S.1.2.c. Scatterplot

8.S.2. Apply the concepts of probability to predict events/outcomes and solve problems.

8.S.2.1. Comprehension: Students are able to find the sample space and compute probability for two simultaneous independent events.

8.S.2.1.a. Express probability as a ratio, decimal, or percent.