8th Grade Math (Montana Content Standards)

The Number System (NS)

• MT.8.NS.1 Know real numbers include rational and irrational numbers, every number has a decimal expansion and repeating decimals are rational.
• MT.8.NS.2 Use rational approximations to compare and place irrational numbers and estimate expressions.

Expressions and Equations (EE)

• MT.8.EE.1 Use properties of integer exponents to make equivalent numerical expressions.
• MT.8.EE.2 Use square and cube root symbols to solve x² = p and x³ = p and evaluate small perfect squares and cubes.
• MT.8.EE.3 Write very large or very small quantities in scientific notation.
• MT.8.EE.4 Calculate with numbers in scientific notation.
• MT.8.EE.5 Graph proportional relationships, read the unit rate as slope and compare relationships.
• MT.8.EE.6 Use similar triangles to show slope is constant and derive y = mx and y = mx + b.
• MT.8.EE.7 Solve one-variable linear equations, including rational coefficients and the distributive property, and classify the number of solutions.
• MT.8.EE.8 Solve systems of two linear equations graphically and algebraically, including problems in context.

Functions (F)

• MT.8.F.1 Understand a function as a rule giving each input exactly one output, with its graph as the set of input-output pairs.
• MT.8.F.2 Compare two functions' properties through tables, graphs and equations.
• MT.8.F.3 Read y = mx + b as a linear function whose graph is a line with slope m through (0, b).
• MT.8.F.4 Build a linear function from data on two quantities and interpret its rate of change and starting value in context.
• MT.8.F.5 Describe in words how quantities relate from a graph, and sketch a graph from a verbal description.

Geometry (G)

• MT.8.G.1 Check by experiment that rotations, reflections and translations keep lines, lengths, angles and parallels, including Montana Indigenous and local contexts.
• MT.8.G.2 Understand congruence as reachable by rigid transformations and describe a sequence linking two congruent figures.
• MT.8.G.3 Use coordinates to describe how dilations, translations, rotations and reflections change 2D figures, including Montana Indigenous and local contexts.
• MT.8.G.4 Understand similarity as reachable by rigid motions plus dilations and describe a sequence linking two similar figures.
• MT.8.G.5 Give informal arguments about triangle angle sums, exterior angles, angles from a transversal and the AA similarity test.
• MT.8.G.6 Explain why the Pythagorean Theorem and its converse are true.
• MT.8.G.7 Use the Pythagorean Theorem for unknown sides in 2D and 3D problems, including Montana Indigenous and local contexts.
• MT.8.G.8 Find how far apart two points on a coordinate grid are with the Pythagorean Theorem.
• MT.8.G.9 Know and use volume formulas for cones, cylinders and spheres, including in context.

Statistics and Probability (SP)

• MT.8.SP.1 Make and read scatter plots of paired data and describe clusters, outliers and positive, negative, linear or nonlinear association.
• MT.8.SP.2 Know lines often model two-variable data, fit a line informally to linear scatter plots and judge the fit by closeness of points.
• MT.8.SP.3 Use a linear model's equation to solve problems with paired data and interpret slope and intercept.
• MT.8.SP.4 Build and read two-way tables of frequencies and relative frequencies to find patterns, including Montana Indigenous and local contexts.