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How to learn Grade 8: Mathematics

Indiana academic standards: Mathematics, Grade 8

0 of 12 concepts ready to learn · Markdown, for your AI

1. Data Analysis, Statistics, and Probability · For events with a large number of outcomes, understand the use of the multiplication counting principle. Develop the multiplication counting principle, and

  1. Complementary events: Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))

2. Data Analysis, Statistics, and Probability · Represent sample spaces and find probabilities of compound events (independent and dependent) using organized lists, tables, and tree diagrams.(E)

  1. Tree diagrams: Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes

3. Data Analysis, Statistics, and Probability · Write and use equations that model linear relationships to make predictions, including interpolation and extrapolation, in real-world situations involving

  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

4. Data Analysis, Statistics, and Probability · Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantitative variables. Describe pa

  1. 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

5. Geometry and Measurement · Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and other mathematical problems in two dimensions. (E)

  1. 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

6. Geometry and Measurement · Solve real-world and other mathematical problems involving volume of cones, spheres, and pyramids and surface area of spheres. (E)

  1. Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

7. Geometry and Measurement · Explore dilations, translations, rotations, and reflections on two-dimensional figures in the coordinate plane. (E)

  1. 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

8. Algebra and Functions · Approximate the solution of a system of equations by graphing and interpreting the reasonableness of the approximation. (E)

  1. Simultaneous Equations: Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations
  2. 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

9. Algebra and Functions · Compare properties of two linear functions given in different forms, such as a table of values, equation, verbal description, and graph (e.g., compare a distance-time graph to

  1. 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

10. Algebra and Functions · Generate linear equations in one variable with one solution, infinitely many solutions, or no solutions. Justify the classification given.

  1. 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

11. Number Sense · Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions. (E)

  1. Number Sets & Infinity: Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers