How to learn High school: Mathematics

West Virginia academic standards: Mathematics, High school

0 of 13 concepts ready to learn · Markdown, for your AI

1. Introduction to Mathematical Applications · Use two- and three-dimensional shapes and circles, their measures, and their properties to describe objects.

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
2. Compound Units: Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units

2. Statistics · Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

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

3. Mathematics – Quantitative Reasoning · Use ratio and rate reasoning to solve real-world and mathematical problems.

1. Proportional Reasoning Vocabulary: Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts

4. Transition Mathematics for Seniors · Graph linear, quadratic, and polynomial functions expressed symbolically and show key features of the graph.

1. Quadratic Graphs: Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions
2. 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

5. Transition Mathematics for Seniors · Solve quadratic equations in one variable by inspection (e.g., x² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appro

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

6. Algebra II – Mathematics III · Interpret expressions including rational and polynomial expressions that represent a quantity in terms of its context.

1. 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

7. Geometry · Verify experimentally the properties of dilations given by a center and a scale factor.

1. Coordinates (age 12+): Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids

8. Geometry · Make formal geometric constructions with a variety of tools and methods, such as a compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.:

1. Understanding angles (age 12+): Use ruler and compasses to perform standard constructions: perpendicular bisector of a line segment, perpendicular to a line from or at a given point, and bisecting an angle

9. Geometry · Construct and justify the validity of a logical argument.

1. Sets & Venn Diagrams: Enumerate sets and their unions and intersections systematically using tables, grids, and Venn diagrams to organise and count outcomes
2. 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

10. Algebra I · Analyze and solve pairs of simultaneous linear equations.

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