How to learn Grade 8: Mathematics

Florida academic standards: Mathematics, Grade 8

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1. Data Analysis and Probability

Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability
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
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

Proportion: Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations
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
Understanding angles (age 11+): Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems
Angle sums in triangles and polygons: Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons
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

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

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
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
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
Factorising Expressions: Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)

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
Numbers on a number line: Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations
Sign Rules for Multiplication: Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient
Percentages as Fractions: Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%