How to learn Grade 8: Mathematics

North Dakota academic standards: Mathematics, Grade 8

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1. Eighth Grade

1. Scatter Graphs & Correlation: Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions
2. Scatter Graphs: Plot bivariate data on a scatter graph with correctly labelled axes and appropriate scales; describe the correlation (positive, negative, none) and draw an estimated line of best fit where appropriate
3. Types of angles (age 13+): Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts
4. Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles
5. Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original
6. Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients
7. Algebraic Transformations: Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations
8. Linear Function Graphs: Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context
9. Estimating answers (age 13+): Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts
10. Square and cube numbers: Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations
11. Mixed & Improper Fractions: Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
12. Powers of Ten Notation: Interpret and compare numbers in standard form A × 10ⁿ where 1 ≤ A < 10 and n is an integer; convert between ordinary numbers and standard form
13. Estimating by rounding: Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values