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How to learn High school: Mathematics

South Carolina academic standards: Mathematics, High school

0 of 32 concepts ready to learn · Markdown, for your AI

1. Patterns, Algebra, and Functional Reasoning · Determine the exact or approximate solutions of equations and inequalities using graphs on the coordinate plane.

  1. 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

2. Patterns, Algebra, and Functional Reasoning · Interpret the structure of expressions, equations, and inequalities to analyze and make predictions in different contexts.

  1. 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
  2. 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
  3. Angles in triangles (age 11+): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning

3. Patterns, Algebra, and Functional Reasoning · Analyze the structure of an equation or inequality to determine an efficient strategy to find a solution, if one exists, then justify the solution.

  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

4. Numerical Reasoning · Represent all points on the number line as irrational and rational numbers in the real number system.

  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

5. Measurement, Geometry, and Spatial Reasoning · Investigate and apply relationships among segments and angles in circles.

  1. 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

6. Measurement, Geometry, and Spatial Reasoning · Discover and apply relationships in similar right triangles.

  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
  2. Trigonometry basics: Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem

7. Measurement, Geometry, and Spatial Reasoning · Demonstrate whether a conjecture or theorem is true or false using a variety of algebraic and geometric explanations.

  1. Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

8. Measurement, Geometry, and Spatial Reasoning · Determine that two figures are similar by demonstrating a similarity transformation or a sequence of similarity transformations that maps one figure onto

  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

9. Measurement, Geometry, and Spatial Reasoning · Determine that two figures are congruent by demonstrating that a rigid motion or a sequence of rigid motions maps one figure onto the other.

  1. Angles in triangles (age 12+): Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent

10. Data, Probability, and Statistical Reasoning · Solve problems involving the probability of compound events in real-world situations.

  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. 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

11. Data, Probability, and Statistical Reasoning · Analyze and interpret models for two quantitative variables.

  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

12. Patterns, Algebra, and Functional Reasoning · Reason with parent functions in varying representations to find families of functions that all have similar distinguishing attributes common to the family

  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

13. Patterns, Algebra, and Functional Reasoning · Represent and interpret functions symbolically and graphically.

  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

14. Patterns, Algebra, and Functional Reasoning · Create, solve, and transform equations and inequalities in two or more variables to represent relationships between quantities and graph the equations on

  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. 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

15. Data, Probability, and Statistical Reasoning · Analyze and interpret models for two categorical and quantitative variables

  1. Pictograms and tally charts (age 11+): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type

16. Patterns, Algebra, and Functional Reasoning · Explore and analyze quadratic and polynomial functions and inequalities and use them to model real-world situations.

  1. 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

17. Data, Probability, and Statistical Reasoning · Understand independence and conditional probability and use them to interpret data.

  1. The Probability Scale: Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible

18. Patterns, Algebra, and Functional Reasoning · Represent data with matrices, perform mathematical operations, and solve systems of linear equations for mathematical problems.

  1. Plotting Linear Graphs: Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line

19. Patterns, Algebra, and Functional Reasoning · Manipulate, prove, and apply trigonometric identities and equations to solve contextual mathematical problems.

  1. Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable

20. Numerical Reasoning · Represent and manipulate data using matrices.

  1. Using inverse operations: Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations

21. Patterns, Algebra, and Functional Reasoning · Apply theorems and rules of differentiation to solve mathematical and realworld situations.

  1. 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

22. Patterns, Algebra, and Functional Reasoning · Understand the concept of the derivative of a function geometrically, numerically, analytically, and verbally.

  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

23. Measurement, Geometry, and Spatial Reasoning · Apply theorems and rules of integration to solve mathematical and real-world situations.

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

24. Data, Probability, and Statistical Reasoning · Analyze data of a statistical experiment.

  1. 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
  2. Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

25. Measurement, Geometry, and Spatial Reasoning · Apply two- and three-dimensional representations, geometric transformations, and scale models in planning, designing, and constructing solutions to real-

  1. Scale and similar shapes (age 11+): Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versa

26. Data, Probability, and Statistical Reasoning · Use appropriate graphical and numerical methods to analyze data.

  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