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Teaching Mathematics at Secondary Level
by Tony GardinerTeaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11-14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present. <p><p> This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.
CK-12 Advanced Probability and Statistics
by Ck-12 FoundationCK-12 Foundation's Advanced Probability and Statistics FlexBook covers the following chapters: An Introduction to Analyzing Statistical Data - Students learn definitions of statistical terminology, and review data, measures of center, and measures of spread. Visualizations of Data - histograms and frequency distributions, common graphs and data plots, and box-and-whisker plots. An Introduction to Probability - events, sample spaces, probability, compound events, the complement of an event, conditional probability, and basic counting rules. Discrete Probability Distribution - random variables, probability distribution for a discrete random variable, mean and standard deviation of discrete random variables and the Binomial Probability Distribution. Normal Distribution - standard normal probability distribution, the density curve of the normal distribution, and applications of the normal distribution. Planning and Conducting an Experiment or Study - surveys, sampling and experimental design. Sampling Distributions and Estimations - sampling distributions and the Central Limit Theorem. Hypothesis Testing - The P-value, testing a proportion hypothesis, testing a mean hypothesis, and testing a hypothesis for dependent and independent samples. Regression and Correlation - scatterplots and linear correlation, Least-Squares regression, inferences about regression, and an introduction to multiple regression. Chi-Square- the Goodness-of-Fit test, test of independence, and testing one variance. Analysis of Variance and the F-Distribution - the F-Distribution and testing two variances, the One-Way ANOVA test, and the Two-Way ANOVA test. Non Parametric Statistics - nonparametric statistics, the rank sum test and rank Correlation, and the Kruskal-Wallis test.
CK-12 Advanced Probability and Statistics Second Edition Volume 1
by Ck-12 FoundationAn open source textbook.
CK-12 Advanced Probability and Statistics Second Edition Volume 2
by Ck-12 FoundationAn open source textbook.
CK-12 Algebra 1 Second Edition Volume 1
by Ck-12 FoundationAn open source textbook: algebra 1, 2nd edition, volume 1.
CK-12 Algebra 1 Second Edition Volume 2
by Ck-12 FoundationAn open source textbook: algebra 1, 2nd edition, volume 2.
CK-12 Algebra I
by Ck-12 FoundationCK-12 Foundation's Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equations.
CK-12 Calculus
by Ck-12 FoundationCK-12 Foundation's Single Variable Calculus FlexBook covers the following chapters: Functions, Limits, and Continuity - A review of the basics of functions is given. Students use linear approximations to study the limit process, before a more formal treatment of limits is given. Differentiation - Students explore instantaneous rate of change, and the relationship between continuity and differentiability. The Chain Rule and implicit differentiation are reviewed. Applications of Derivatives - Students gain practice with using the derivatives in related rates problems. Additional topics include The First Derivative Test, The Second Derivative Test, limits at infinity, optimization, and approximation errors. Integration - This chapter includes indefinite integrals calculus, initial value problems, definite integrals, the Fundamental Theorem of Calculus, integration by substitution, and numerical integration. Applications of Integration - This chapter includes applications of the definite integral, such as calculating areas between two curves, volumes, length of curves, and other real-world applications in physics and statistics. Transcendental Functions - This chapter includes differentiation and integration of logarithmic and exponential functions, exponential growth and decay, derivatives and integrals involving inverse trigonometric functions, and L'Hospital's Rule. Integration Techniques - Students explore integration by substitution, integration by parts, integration by partial fractions, trigonometric integrals, trigonometric substitutions, and improper integrals. Infinite Series - This chapter introduces the study of sequences and infinite series. The properties presented describe the behavior of a sequence or series, including whether a sequence approaches a number or an infinite series adds to a number.
CK-12 Geometry
by Ck-12 FoundationCK-12 Foundation's Geometry FlexBook covers the following chapters: Basics of Geometry - undefined terms, defined terms, basic postulates of points, lines and planes; distances on a coordinate grid; complementary and supplementary angles; vertical angles; linear pairs and classification of polygons. Reasoning and Proof - inductive reasoning, deductive reasoning, conditional statements, properties of equality and two-column proofs. Parallel and Perpendicular Lines - the parallel line postulate, the perpendicular line postulate, and angles formed by two parallel lines and a non-perpendicular transversal. Congruent Triangles - the Triangle Sum theorem, triangle congruence, the SSS and ASA postulates, the AAS congruence theorem, two-column and flow proofs, the HL congruence theorem, AAA and SSA relationships, isosceles and equilateral triangles. Relationships Within Triangles - the midsegment theorem, the perpendicular bisector theorem, the angle bisector theorem, the concurrency of medians theorem, Napoleon's theorem, and the triangle inequality theorems. Quadrilaterals - interior angles of convex quadrilaterals, classifying quadrilaterals, properties of parallelograms, properties of rhombi, rectangles and squares, and properties of trapezoids. Similarity - ratio and proportion, properties of similar polygons, AAA and AA rules for similar triangles, using SSS and SAS to solve problems about similar triangles, identifying proportional segments in triangles and similarity transformations. Right Triangle Trigonometry - using the Pythagorean theorem when working with right triangles, classification of triangles, the converse of the Pythagorean theorem, using the geometric mean, properties of special right triangles, and trigonometric ratios. Circles - relationships between congruent and similar circles, the equation of a circle, tangent lines, arc measures, chords, inscribed angles, and angles formed by chords, secants and tangents. Perimeter and Area - finding the area of polygons, using scale drawings or models, finding the circumference of a circle, areas of circles and sectors, calculating the areas and perimeters of regular polygons and geometric probability. Transformations - transformations of figures in two-dimensional space including translations, reflections, rotations and dilations.
CK-12 Probability and Statistics - Basic (A Full Course)
by Ck-12 FoundationAn open source textbook.
CK-12 Trigonometry
by Ck-12 FoundationCK-12 Foundation's Trigonometry FlexBook covers the following chapters: Trigonometry and Right Angles - introduction to the trigonometric functions. Circular Functions - introduction to radian measure, circular functions and periodic functions. Trigonometric Identities - confirm, verify and derive various trigonometric identities. Inverse Functions and Trigonometric Equations - inverse functions to trigonometric functions, and will apply the domain, range and quadrants of the six inverse trigonometric functions to evaluate expressions. Triangles and Vectors - introduction to vectors and vector applications. Polar Equations and Complex Numbers - plot points in a polar coordinate system, graph and recognize limaçons and cardiods, and work with real-world applications involving polar coordinates and polar equations.
Collaborative Statistics
by Barbara Illowsky Susan DeanCollaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two- and four-year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it.
Elementary Algebra
by Denny Burzynski Wade EllisElementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.