Montana8th Grade Math
Montana 8th Grade Math Curriculum
Video lessons and practice for every 8th grade math topic. Aligned to Montana Math Content Standards so Montana students can keep up with class or get ahead.
Montana 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 in Montana
Montana 8th grade math covers a wide range of topics that bridge middle school concepts and high school algebra and geometry. Students work with irrational numbers, master integer exponents and scientific notation, solve linear equations and systems of equations, explore functions, apply geometric transformations, use the Pythagorean Theorem, and analyze bivariate data. All of these topics are part of the Montana Math Content Standards assessed through MontCAS in Grade 8.
Key Topics in Montana 8th Grade Math
- Number Systems: Rational vs. irrational numbers, decimal expansions, and rational approximations of irrational numbers
- Exponents and Scientific Notation: Properties of integer exponents, square and cube roots, and operations with numbers in scientific notation
- Linear Equations and Functions: Slope, proportional relationships, y = mx + b, solving one-variable equations, and systems of linear equations
- Functions: Definition of a function, comparing functions in different representations, linear vs. nonlinear functions, and modeling with functions
- Geometry: Rotations, reflections, translations, dilations, congruence, similarity, angle relationships, and triangle properties
- Pythagorean Theorem: Proof, application to real-world problems in 2D and 3D, and finding distances in a coordinate system
- Statistics and Data: Scatter plots, lines of best fit, linear models, and two-way tables for bivariate categorical data
How StudyPug Supports Montana 8th Graders
StudyPug provides video lessons and practice problems aligned to every Montana Math Content Standards topic for Grade 8. Students can look up any topic from the table above, watch a clear step-by-step video lesson, and then practice with problems that match what they are learning in class. This makes it easy to get homework help, review for the MontCAS, or get ahead before the next unit.
Each lesson is broken into short segments of 5 to 15 minutes so students can learn at their own pace without getting overwhelmed. StudyPug works on any device, meaning students can study at home, on the go, or anywhere they have a few minutes to spare.
Preparing for MontCAS Grade 8 Math
Montana tests math from grades 3 through 8 using the MontCAS assessment. The Grade 8 test covers key standards including linear functions, the Pythagorean Theorem, scientific notation, and data analysis. StudyPug's topic-by-topic structure makes it easy for students to review exactly what they need before test day.