South DakotaSouth Dakota 8th Grade Math Curriculum
Video lessons and practice for every 8th grade math topic. Aligned to South Dakota Math Standards so students can keep up with class or get ahead.
South Dakota 8th Grade Math Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
8.NS.A.1 | Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. |
8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). |
8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. |
8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. |
8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. |
8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. |
8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. |
8.EE.C.7 | Solve linear equations in one variable. |
8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. |
8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. |
8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). |
8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. |
8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. |
8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. |
8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. |
8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. |
8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. |
8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. |
8.G.B.6 | Explain a proof of the Pythagorean Theorem and its converse. |
8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. |
8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. |
8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. |
8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. |
8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. |
8th Grade Math Topics in South Dakota
South Dakota 8th grade math follows the South Dakota Math Standards, which cover a wide range of concepts across number systems, algebra, functions, geometry, and statistics. StudyPug provides video lessons and practice problems for every one of these standards, so students are never left behind.
Number System and Exponents
Students in 8th grade learn to distinguish rational from irrational numbers and understand decimal expansions. They apply properties of integer exponents and work with square roots and cube roots. Scientific notation is introduced for expressing very large and very small quantities and performing operations with them.
Linear Relationships and Equations
A major focus of 8th grade math is linear relationships. Students graph proportional relationships, interpret slope, and use similar triangles to explain why slope is constant on a line. They derive and use the equations y = mx and y = mx + b, solve linear equations in one variable, and analyze systems of simultaneous linear equations.
Functions
8th graders are introduced to the concept of a function — a rule that assigns exactly one output to each input. They compare functions represented in different forms, interpret linear functions, construct functions to model real-world relationships, and describe qualitative features of graphs.
Geometry and Transformations
Students verify properties of rotations, reflections, and translations, and understand congruence and similarity through sequences of transformations. They describe transformations using coordinates, explore angle relationships in triangles and with parallel lines, and explain the Pythagorean Theorem and its converse.
- Apply the Pythagorean Theorem to find unknown side lengths
- Use the Pythagorean Theorem to find distances in a coordinate plane
- Solve real-world problems involving volumes of cones, cylinders, and spheres
Statistics and Data Analysis
8th grade statistics introduces scatter plots for bivariate data, patterns of association, informal line fitting, and interpretation of linear models. Students also work with two-way tables to explore associations between categorical variables.
StudyPug covers all of these topics with clear video lessons and targeted practice — making it easier for South Dakota students to keep up with class, review before a test, or get ahead.